Investigation of Structural, Electronic and Magnetic...

Investigation of Structural, Electronic and Magnetic

Properties of the Half-Metallic Ferromagnetic

Materials

By

MUHAMMAD ATIF SATTAR

A DISSERTATION

Submitted in the fulfillment of the requirements

for the degree

DOCTOR OF PHILOSOPHY

IN

PHYSICS

Department of Physics

The Islamia University of Bahawalpur Pakistan

2018

In the name of ALLAH, most gracious most merciful!

The Prayer of the believers!

Praise be to ALLAH,

The Cherished and sustainer of the worlds;

Most Gracious, most Merciful;

Thee do we worship,

And think and we seek,

Show us the straight way,

The way of those one whom

Thou haste bestowed the grace,

Those whose (portion)

Is not wrath,

And who go not astray.

(Surah Fatiha)

A dissertation entitled Investigation of Structural,

Electronic and Magnetic Properties of the Half-

Metallic Ferromagnetic Materials

In partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

IN

PHYSICS

By


Submitted to


The Islamia University of Bahawalpur Pakistan

2018

i

Preface

By An initial look at the title of this dissertation “Investigation of Structural,

Electronic and Magnetic Properties of the Half-Metallic Ferromagnetic Materials” may

possibly emerge two thoughts in our minds. The very first phrase is about the physical

properties like structural arrangement of the atoms, different states of electrons in the unit

cell of the compound and origin of magnetism. The second term deals with the half-metallic

(HM) ferromagnetic (FM) materials or half-metallic ferromagnets (HMFs). What are the

HMFs and what makes them so special and important in terms of research and applications.

In this study, we explore the issue like this one by one to learn how to discover brand new

HM materials as well as how we can really utilize these types of HM materials into the

spintronic applications.

More recently scientist making spintronic devices with brand new Ferro-magnetic

(FM) materials. These types of materials are referred as half-metals or HM materials. They

display multiple properties of metals and semiconductors and can be viewed as hybrids in

between metals and semiconductors. HMFs are the materials which have one spin channel

conductive, showing the metallic behavior and the other spin channel is showing a semi

conducting gap at the Fermi level (EF) or showing insulating behavior.

This unique feature encourages materials scientists to produce ideal devices for

spintronic. For the better spintronic device characteristic, the spin of the material should be

100% aligned. In HM materials, the spin of the each consisting element is totally lined up.

For instance, when the spin of the FM electrode is injected into a semiconductor (SCs), the

more alignment of the spin results in a greater injection of the spins.

HMFs are very important prospective materials regarding spintronic. These HM

materials may also be defined through their integer value associated with magnetic

moments according to the Slater–Pauling rule (SPR) which µ𝑡𝑜𝑡 = 𝑁𝑣𝑎𝑙 − 24 for the Full-

Heusler (FH) and µ𝑡𝑜𝑡 = 𝑁𝑣𝑎𝑙 − 18 for the Half-Heusler (HH) materials respectively where

µ𝑡𝑜𝑡 stands out as the total magnetization and 𝑁𝑣𝑎𝑙 is the total number of valance electrons.

It is very essential to produce HMFs, like HM with different elements which are called

hetero structures.

ii

In general, HMFs are formed by combining three elements which make the crystal

structure more complex as compared to the FM iron which contains only one element.

Therefore, In HMFs, there is benefit of 100% spin polarization (SP) but the drawback of

the very complex crystal structure.

It is a problem to determine how to prepare top quality materials with HM features

to ensure that these types of HMFs may be used to create practical spintronic applications.

In this project, not only the new HMFs will be find out but also step by step the basic

physical properties of these HMFs understood and physics behind these properties will be

thoroughly discussed and how to utilize these half-metals into practical spintronic

applications.

iii

CERTIFICATE

It is certified that the research work in this dissertation entitled

“Investigation of Structural, Electronic and Magnetic Properties of the Half-Metallic

Ferromagnetic Materials”

completed by Muhammad Atif Sattar to fulfill the partial requirements for the degree of

Doctor of Philosophy (Ph.D.) in Physics has been conducted under my supervision in the

department of Physics, The Islamia University of Bahawalpur.

Supervisor: Prof. Dr. Sheikh Aftab Ahmad


The Islamia University of Bahawalpur

Chairman: Dr. Saeed Ahmad Buzdar

(Associate Professor)


The Islamia University of Bahawalpur

iv

DECELRTAION

I, Muhammad Atif Sattar student of Ph.D. in the subject of physics, hereby declare and

certify that material printed in this dissertation “Investigation of Structural, Electronic

and Magnetic Properties of the Half-Metallic Ferromagnetic Materials” is my individual

research and that it has not been submitted concurrently to any other university or any

research institution for any degree or diploma in Pakistan or abroad.


v

FORWARDING CERTIFICATE

The research entitled “Investigation of Structural, Electronic and Magnetic Properties of

the Half-Metallic Ferromagnetic Materials” is carried out under my supervision and the

dissertation is submitted to The Islamia University of Bahawalpur, Pakistan in fulfillment

of the requirement for the degree of DOCTOR OF PHILOSOPHY (Ph.D.) in physics with

my permission.

Prof. Dr. S. A. Ahmad

vi

RIGHT OF DISSERETATION

All Rights of the dissertation are reserved to the author (researcher). No part of this

research may be reproduced or transmitted in any form or by any means, electronic or

mechanical, including photocopy, recording or any information storage and retrieval

system, without permission in writing from the researcher.


vii

ACKNOWLEDGEMENTS

All praises and thanks to Almighty Allah, the Beneficent and the Merciful, the

Creator of the universe, Who enabled me to complete my research work successfully. I

would like to offer my humblest thanks to His prophet Hazrat Muhammad (peace be upon

him), who is a source of guidance and knowledge for humanity.

I am especially thankful to my kind supervisor Prof. Dr. Sheikh Aftab Ahmad,

department of physics, The Islamia University of Bahawalpur, who provided me all

possible facilities in the laboratory and encouraged me to complete my research work. He

has always been very kind, friendly, easy to reach and helpful.

I am grateful to my mentor, Dr. Altaf Hussain, department of physics, The Islamia

University of Bahawalpur and my foreign supervisor Dr. Claudio Cazorla, School of

Material Science, University of New South Wales (UNSW), Australia, for their valuable,

sincere suggestions, guidance and providing me all the lab facilities to complete my thesis.

I appreciate my beloved brothers and close collaborators, Dr. Fayyaz Hussain, Dr.

Muhammad Rashid, Dr. Imran, Dr. Zafar, Dr. Shabir, Dr. Shakil, whose guidance and

co-operation really helped me in learning and solving different simulation problems

related to DFT investigation.

I have the honor to express my deep sense of indebtedness to ever affectionate my

dear friends, Muhammad Ali Abbas and PhD Scholars, Muhammad Nasir Rasul,

Muhammad Raza Hashmi, Salman Mehmood for their encouragement during my

research period and lastly to my all lab mates because they were always kind to me in every

matter of my research during PhD.

I am thankful to my friends Dr. Tariq , Dr. M. Ali and Dr. Jawad Ahmad for their

valuable guidance, keen interest and encouragement, kind and understanding spirit during

my research work at the UNSW, Australia. I express my special gratitude to all of them for

their endless support and make my stay comfortable.

Finally, I wish to express my nice feelings toward my mother for her affection and

to all family members who remembered me in their prayers and heartened me to continue

higher studies.


viii

DEDICATION

TO

My great parents whose prayers are always with me,

who are the sources of my success in every field of

life and whose substitutes are impossible,

innocent sister

and

Loving brothers.

ix

Abstract

Spintronics or magneto-electronics develop the focus on the fascinating class of

intermetallic Heusler alloys (HA) which is the active field of scientific research because

numerous HA appeared to be half-metallic ferromagnets (HMFs). It is very interesting by

counting the valence electrons of the HA, one can predict their half-metallic (HM)

properties. Half-Heusler (HH) alloys with 1:1:1 composition tend to be appealing prospects

pertaining to spintronic applications due to their structural resemblance towards the binary

semiconductors (SC), spin-polarization is offered 100% at the Fermi level (EF) and possess

higher values of Curie Temperature (TC). Prospective fields of applications and brand-new

properties arise continuously because one can easily control their atomic disorder and

structure interface. Devices depending on multifunctional properties i.e. the combined

magnetic and remarkable transport properties can revolutionize technological applications

as HH materials possess higher importance for the advancement of the spintronic devices.

To make use of the substantial prospective of HH materials, in this dissertation, a

detailed Density Functional Theory (DFT) investigation on the understanding of the basic

structural, electronic and magnetic properties of the HH XYZ family are explored.

Numerous newly HM HH materials like CrTiZ (Z= Si, Ge, Sn, Pb), FeVZ (Z= Si, Ge, Sn),

YMnZ (X= Si, Ge, Sn) along with YCrSb & YMnSb followed by the series of 90 HH XYZ

materials where (X = Li, Na, K, Rb, Cs & Y= V, Nb, Ta & Z = Si, Ge, Sn, S, Se, Te) are

studied by the First-principles calculations. The detailed results for the different series of

the HM HH XYZ materials are described below:

HM properties of new HMFs CrTiZ (where Z = Si, Ge, Sn, Pb) are studied by means

of the first-principles band structure calculations within the framework of DFT. From the

spin-polarized calculations using full-potential linearized augmented plane-wave (FP-

LAPW) method, we found that all these compounds are stable in the FM MgAgAs-type

crystal structure. The lattice parameters of CrTiZ compounds increase with increasing

atomic radius of X atom and ranges from 5.76 Å to 6.38 Å. The calculated electronic

structure of these compounds in MgAgAs-type structure shows that they are HM materials

with an integer magnetic moment of 4 µ𝐵. Densities of states, electronic band structure,

and origin of ferromagnetism have been discussed, and robust HM nature of these

compounds is analyzed which makes them fascinating compounds for spintronic devices.

x

DFT-based ab-initio calculations are utilized to investigate the electronic and

magnetic properties of new series of HH FeVZ (where Z=Si, Ge, Sn) compounds. The C1b-

type structure is considered for these materials in three different atomic configurations,

termed as α, β, and γ phases, to find the most stable geometric structure. The structural

properties of all three phases have been determined and the effect of spin-polarization has

been studied. Our calculated electronic properties suggest that the studied materials under

study are HMFs and stable in the α-phase. The Trans-Blaha modified Becke-Johnson (TB-

mBJ) local spin density approximation functional is employed for a better description of

the HM response of HH FeVZ materials. We have also shown that the HM nature of FeVZ

compounds is robust for a wide range of lattice constant, making these materials suitable

for spintronic applications.

Structural, electronic, and magnetic properties of newly predicted half-Heusler

YCrSb and YMnSb compounds within the ordered MgAgAs C1b-type structure are

investigated by employing first- principal calculations based on DFT. Through the

calculated total energies of three possible atomic placements, we find the most stable

structures regarding YCrSb and YMnSb materials, where Y, Cr (Mn), and Sb atoms occupy

the (0.5, 0.5, 0.5), (0.25, 0.25, 0.25), and (0, 0, 0) positions, respectively. Furthermore,

structural properties are explored for the non-magnetic (NM), FM and anti-ferromagnetic

(AFM) states and it is found that both materials prefer FM states. The electronic band

structure shows that HM HH YCrSb has a direct band gap of 0.78 eV while YMnSb has an

indirect band gap of 0.40 eV in the majority spin channel. Our findings show that YCrSb

and YMnSb materials exhibit HM characteristics at their optimized lattice constants of 6.67

Å and 6.56 Å, respectively. The half-metallicities associated with YCrSb and YMnSb are

found to be robust under large in-plane strains which make them potential contenders for

spintronic applications.

The basic structural stability, electronic, magnetic and thermoelectric properties of the

newly predicted HM YMnZ (Z=Si, Ge, Sn) alloys in HH phase are contemplated with

optimized lattice constants by ab-initio FP-LAPW method using DFT. The MgAgAs (C1b-

type) structure of these HH YMnZ materials in three different atomic arrangements (X-

type1, X- type2, X-type3) have been explored and X-type1 structure is found to be

energetically more favorable for YMnSi and YMnGe whereas YMnSn prefers the X-type2

structure. Moreover, NM, FM and AFM states computed for YMnZ HH materials favor

FM states. The presence of the energy gap in the majority spin bands and density of the

xi

states within the HH YMnZ are indications of potential HMFs. For the lattice constant

range of 6.2 Å to 7.4 Å, the total magnetic moment (µ𝑡𝑜𝑡) remains an integral value of 4.0

µ𝐵 per formula unit and obeys the modified Slater-Pauling rule (SPR). The calculations

reveal that YMnZ displays HM ferromagnetism having the µ𝑡𝑜𝑡 of 4.00 µ𝐵 which primarily

arises from the spin-polarization of d-electrons of Mn atom and partial involvement of p-

electrons of Z-atom. The half-metallicity of HH YMnZ materials might show that they are

ideal for applications in spin polarizers and spin injectors of magnetic nano devices due to

their larger EBG, which mean that they are steady at ambient conditions. The robustness

associated with half-metallicity contrary to the lattice constant is additionally ascertained

for desirable spintronics applications. Thermoelectric properties of the YMnZ materials are

additionally computed over an extensive variety of temperature and it is discovered that

YMnSi demonstrates a higher figure of merit than YMnGe and YMnSn.

Finally, in this dissertation, DFT-based systematically investigation on structural,

electronic, magnetism and vibrational stability of the unexplored 90 half-Heusler (HH)

XYZ materials where (X= Li, Na, K, Rb, Cz; Y= V, Nb, Ta & Z= Si, Ge, Sn, S, Se, Te) in

the C1b structure is carried out by using First-principles calculations. The energetically

most stable structure is determined among the three different atomic arrangement types

(T1, T2, T3) inside the C1b unit cell. The magnetic ground state; FM and AFM are also

checked for these HH XYZ materials. The electronic and magnetic properties are calculated

by using the TB-mBJ functional as it is proven to give the accurate values for the energy

band gaps. Among 90 HH XYZ materials, 28 HH XYZ materials show HM properties at

their respective stable phase (T1 or T3) with FM arrangement and obey the modified SPR.

The 5 NM SC, 2 FM SC, and 21 AFM HH XYZ materials are discovered in our findings.

Furthermore, the Curie temperature (TC) and mixing energy of the vibrational stable 28

HM HH XYZ materials are also calculated. The larger values of the energy band gap (EBG)

and HM gap (EHM) along with magnetic moments (up to 4 µ𝐵) show that these compounds

can be excellent spin-injectors for the spintronic applications.

xii

List of Publications

This dessertation is based on the following publications:

1. Sattar, M. A.; Rashid, M.; Rasool, M. N.; Mahmood, A.; Hashmi, M. R.; Ahmad,

S.; Imran, M.; Hussain, F., Half-metallic ferromagnetism in new half-Heusler

compounds: an ab initio study of CrTiX (X= Si, Ge, Sn, Pb). Journal of

Superconductivity and Novel Magnetism 2016,29 (4), 931-938.

2. Sattar, M. A.; Rashid, M.; Hashmi, M. R.; Rasool, M. N.; Mahmood, A.; Ahmad,

S., Spin-polarized calculations of structural, electronic and magnetic properties of

Half Heusler alloys FeVX (X= Si, Ge, Sn) using Ab-initio method. Materials

Science in Semiconductor Processing 2016,51, 48-54.

3. Sattar, M. A.; Rashid, M.; Hashmi, M. R.; Ahmad, S.; Imran, M.; Hussain, F.,

Theoretical investigations of half-metallic ferromagnetism in new Half–Heusler

YCrSb and YMnSb alloys using first-principle calculations. Chinese Physics B

2016,25 (10), 107402.

4. Sattar, M. A.; Rashid, M.; Hussain, F.; Imran, M.; Hashmi, M. R.; Laref, A.;

Ahmad, S., Physical properties of half-Heusler YMnZ (Z= Si, Ge, Sn) compounds

via ab-initio study. Solid State Communications 2018,278, 10-19.

5. Sattar, M. A.; Ahmad, S.A; Hussain, F.; Claudio, C.; First-principles prediction of

magnetically ordered half-metals above room temperature, Available online 11

April 2019, Journal of Materiomics.

Other Publications

6. Rasool, M. N.; Mehmood, S.; Sattar, M. A.; Khan, M. A.; Hussain, A.,

Investigation of structural, electronic and magnetic properties of 1: 1: 1: 1

stoichiometric quaternary Heusler alloys YCoCrZ (Z= Si, Ge, Ga, Al): An ab-initio

study. Journal of Magnetism and Magnetic Materials 2015,395, 97-108.

7. ur rehman Hashmi, M. R.; Zafar, M.; Shakil, M.; Sattar, A.; Ahmed, S.; Ahmad,

S., First-principles calculation of the structural, electronic, and magnetic properties

of cubic perovskite RbXF3 (X= Mn, V, Co, Fe). Chinese Physics B 2016, 25 (11),

117401.

xiii

8. Imran, M.; Hussain, F.; Rashid, M.; Ullah, H.; Sattar, A.; Iqbal, F.; Ahmad, E.,

Comparison of Electronic and Optical Properties of GaN Monolayer and Bulk

Structure: a First Principle Study. Surface Review and Letters 2016,23 (04),

1650026.

9. Behram, R. B.; Iqbal, M.; Rashid, M.; Sattar, M. A.; Mahmood, A.; Ramay, S. M.,

Ab-initio investigation of AGeO3 (A= Ca, Sr) compounds via Tran–Blaha-

modified Becke–Johnson exchange potential. Chinese Physics B 2017,26 (11),

116103.

10. Hussain, F.; Imran, M.; Sattar, M. A.; Tailoring magnetic characteristics of

phosphorene by the doping of Ce and Ti: A DFT study. Physica E: Low-

dimensional Systems and Nanostructures 2018.

11. Hussain, F.; Imran, M.; Rana, A. M.; Khalil, R. A.; Khera, E. A.; Kiran, S.; Javid,

M. A.; Sattar, M. A.; Ismail, M., An insight into the dopant selection for CeO 2-

based resistive-switching memory system: a DFT and experimental study. Applied

Nanoscience 2018, 1-13.

12. Hussain, F.; Imran, M.; Siddiqa, A.; Khalil, R. M. A.; Rana, A. M.; Sattar, M. A.;

NIAZ, N. A.; ULLAH, H.; AHMAD, N., Ab initio STUDY OF POINT DEFECTS

IN 2D GRAPHENE LAYER. Surface Review and Letters 2018, 1850142.

13. Maryam, A.; Abbas, G.; Rashid, M.; Sattar, A., Directional mechanical and

thermal properties of single-layer black phosphorus by classical molecular

dynamics. Chinese Physics B 2018,27 (1), 017401.

14. Rasul, Nasir; Anum, Asifa; Sattar, Atif; Manzoor, Alina; Hussain, Altaf., DFT

based structural, electronic and optical properties of B(1-x)InxP(x=

0.0,0.25,0.5,0.75,1.0) compounds: PBE-GGA vs mBJ-approaches. Chinese Journal

of Physics 2018, 56 2659.

15. Imran, M.; Hussain, F.; Sattar, M. A., A study of surface diffusion of ternary (Cu-

AgZr) adatoms clusters for applications in thin film formation, Surface and

Interface Analysis, Published online on 15 January 2019

16. Hussain, F.; Imran, M.; Khalil, R. A.; Rana, A. M.; Rasheed, U.; Khera, E. A.;

Mumtaz, F.; Sattar, M. A.; Javid, M. A., Effect of Cu and Al doping in ZrO2 for

RRAM device applications using GGA and GGA+U approach, submitted.

17. Hussain, F.; Imran, M.; Sattar, M. A.; Khalil, R. A.; Rana, A. M., An insight of

Mg doping in ZnO thin films: a comparative experimental and first-principle

investigations, submitted.

xiv

Table of Contents

Title Page No.

Preface………………………………………………………………………………….i

Certificate……………………………………………………………………………..iii

Declaration……………………………………………………………………………iv

Forwarding Certificate………………………………………………………………...v

Rights of Dissertation....………………………………………………………………vi

Acknowledgments……………………………………………………………………vii

Dedications………………………………………………………………………….viii

Abstract……….……………………………………………………………………....ix

List of Publications………………………………………………………………….xii

Table of Contents…………………………………………………………………….xiv

List of Tables…………………………………………………………………………xix

List of Figures……………………………………………………………………….xxii

List of Abbreviations……………………………………………………………….xxix

Chapter 1: Fundamentals……………………………………………………………1

1.1 Heusler Alloys (HA)………………………………………………………1

1.2 Types of Heusler Alloys (HA)…………………………………………….2

1.2.1 Full Heusler (FH) Alloys……………………………………...2

1.2.2 Half Heusler (HH) Alloys……………………………………..4

1.2.3 Quaternary Heusler (QH) Alloys……………………………...4

1.3 Crystal Framework of Heusler Alloys (HA)………………………………4

1.4 Structural Arrangement……………………………………………………8

1.4.1 Order-Disorder Phenomena in Half-Heusler (HH)

Materials……………………………………………………....8

1.5 Heusler Alloys (HA) and Magnetism……………………………………..9

1.5.1 Half-Metallic Ferromagnets (HMFs)…………………..........12

xv

1.5.2 The Slater-Pauling Rule (SPR)………………………………12

1.6 Applications of Heusler Alloys (HA) for Spintronic Devices…………...14

1.6.1 The Effect of Giant Magnetoresistance (GMR)

and Tunneling Magnetoresistance (TMR)…………..............16

1.6.2 Spin Polarization……………………………………..............18

1.6.3 Current-perpendicular-to-plane (cpp)

Giant-magnetoresistance (GMR)…………………………….19

1.6.4 Perpendicular Magnetic Anisotropy………………….………20

1.6.5 Spin Injection………………………………………………....22

1.6.6 Shape-Memory Compounds………………………………….22

1.6.7 Superconductors……………………………………………...23

1.6.8 Thermoelectric Compounds………………………………….24

1.6.9 Topological Insulators………………………………………..25

1.7 Heusler Moves Nano……………………………………………………..26

1.8 Dissertation Scheme……………………………………………………...26

Chapter 2: Literature Review……………………………………………………...29

2.1 Motivation for the work………………………………………………….32

Chapter 3: Basics of Density Functional Theory (DFT)………………………….34

3.1 Computational Material Science…………………………………………34

3.2 Many Particle Problem in Solids…………………………………...…….35

3.3 The Born Oppenheimer Approximation………………………………….35

3.4 Why Density Functional Theory (DFT) Needed?......................................37

3.5 Density Functional Theory (DFT)………………………………………..37

3.6 Hohenberg and Kohn (at the heart of DFT)……………………………...38

3.6.1 Theorem I…………………………………………………….38

3.6.2 Theorem II……………………………………………………38

3.7 The Kohn-Sham Scheme…………………………………………………39

3.8 Self-Consistency Scheme………………………………………………...39

xvi

3.9 Crystalline Solids and Plane-wave Density Functional Theory (DFT)….40

3.9.1 Cutoff Energy…………………………………………………..41

3.9.2 K-points………………………………………………………...42

3.10 Pseudo-Potentials……………………………………………………….42

3.11 WIEN2K………………………………………………………………...43

Chapter 4: Half-Metallic Ferromagnetism in New Half-Heusler Compounds:

an Ab-Initio Study of CrTiZ (Z = Si, Ge, Sn, Pb)……………………45

4.1 Introduction………………………………………………………………45

4.2 Crystal Structure and Computational Details…………………………….46

4.3 Results and Discussion…………………………………………………...49

4.3.1 Ground State Properties………………………………………...49

4.3.2 Electronic and Magnetic Properties……………………………52

Chapter 5: Spin-polarized Calculations of Structural, Electronic and Magnetic

Properties of Half-Heusler Alloys FeVZ (Z= Si, Ge, Sn)

Using Ab-Initio Method……………………………………………..61

5.1 Introduction………………………………………………………………61

5.2 Computational Details……………………………………………………63

5..3 Results and Discussions…………………………………………………63

5.3.1 Crystal Structure Stability……………………………………...63

5.3.2 Electronic Properties…………………………………………...65

5.3.3 Magnetic Properties…………………………………………….71

5.3.4 Half-Metallic (HM) Robustness.…….…………………………75

xvii

Chapter 6: Theoretical Investigations of Half-Metallic Ferromagnetism in

New Half-Heusler YCrSb and YMnSb Alloys Using First-Principle

Calculations…………………….……………………………………...79

6.1 Introduction………………………………………………………………79

6.2 Computational Details……………………………………………………80

6.3 Results and Discussion…………………...………………………………81

6.3.1 Structural Arrangements and Stability………..………………..81

6.3.2. Electronic Properties…………………………………………..87

6.3.3 Magnetic properties…………………………….………………93

6.3.4. Location Associated with Half-Metallicity……………………94

Chapter 7: Physical Properties of Half-Heusler (HH) YMnZ (Z = Si, Ge, Sn)

Compounds via Ab-Initio Study………………………………………96

7.1 Introduction………………………………………………………………96

7.2 Computational Insights…………………………………………………..98

7.3 Results and Discussions………………………………………………….99

7.3.1 Structural Properties……………………………………………99

7.3.2 Electronic Properties………………………………………….105

7.3.3 Magnetic Properties…………………………………………...109

7.3.4 Thermoelectric Properties…………………………………….114

Chapter 8: Structural Chemistry and Physical Properties of the Newly

Designed Half-Heusler XYZ Materials with Large Spin-Gap…….119

8.1 Introduction…………………………………………………….……….119

8.2 Computational Methods………………………………………………...121

8.3 Results and Discussion………………………………………………….122

8.3.1 Ground State Properties….…………………………………....122

8.3.2 Electronic Properties……………….…………………………128

8.3.3 Mixing Energy (Emix)………………………………………....130

xviii

8.3.4 Curie Temperature (TC)……………………………………….132

8.3.5 Band Structure and Density of States ……………...................134

8.3.6 Vibrational Properties ………………………………………...141

8.3.7 Magnetic Properties…………………………………………...143

Chapter 9 Overview of the Results……………………………………………….144

9.1 Future Directions………………………………………………………..147

References………………………………………………………………...………..148

Appendix-I……………………………...………………………………………….174

xix

List of Tables

Table No. Page No.

Table 1.1 Different atomic placement inside the C1b-type

framework. The ZnS-type sublattice is formed by the

4a and 4c Wyckoff positions whereas octahedral

holes are filled by the 4b position……………………………...7

Table 1.2 Various inequivalent Wyckoff positions and the

general formula with space group notations for the

different HA ………..………………………………………….11

Table 4.1 Different configurations of atomic arrangements in

HH structure…………………………………………………...48

Table 4.2 a (Å): lattice parameter, B (GPa): bulk modulus; ΔE

(Ry): Energy difference between FM and NM states

and EFor (eV): Formation Energy……………………………....55

Table 4.3 Total and individual magnetic moments of CrTiZ……………55

Table 5.1 Atomic arrangement of atoms X, Y and Z in α, β and

γ phases. The 4d position is empty…………………………….64

Table 5.2 Atomic optimization of the HH FeVZ alloys at the α,

β and γ phases, a(Å) is the lattice constant. Etot and

µ𝑡𝑜𝑡 are the total energy and magnetic moment per

formula unit respectively………………………………………67

Table 5.3 Total and partial magnetic moments (µB) of the HH

FeVZ (Si, Ge, Sn) compounds in the α-phase at the

equilibrium lattice constant……………………………………67

Table 5.4 Different physical properties of HH FVX (Si, Ge, Sn)

at the equilibrium lattice constant in the α-phase. VXC

is the exchange correlation potential, VBM is the

maximum value of the valance band, and CBM is the

minimum value of the conduction band, EBG is the

energy band gap, EHM is half-metallic gap. Transition

between the bands and nature of compound is also

given…………………………………………………………...70

xx

Table 6.1 The Site preferences of X, Y and Z atoms in three

atomic arrangements XI, XII and XIII in the C1b HH

structure. The 4d site is empty…………………………………82

Table 6.2 Values of optimized lattice constant aopt (Å), the bulk

modulus B (GPa), the pressure derivative of the bulk

modulus B, the total energy (Ry) of the YCrSb and

YMnSb materials………………………………………………85

Table 6.3 Calculated values of formation energy Efor (in eV) per

formula unit, spin-up band gap Eg (eV), half-metallic

gap EHM (eV), and the energy difference between FM

and NM states ΔEFM-NM (eV)

for HH YCrSb and YMnSb materials…………………………85

Table 6.4 Calculated values of total and local magnetic moment

(µB) of the individual atom and interstitial site for HH

YCrSb and YMnSb materials…………………………...…….85

Table 7.1 Inequivalent atomic arrangement inside the C1b-type

framework in which atoms placed on Wyckoff

positions 4a and 4b make a ZnS-type sublattice

whereas the octahedral holes occupied by the atoms

on 4b…………………………………………………………101

Table 7.2 Computed total energy (Ry/f.u.) at three unique

structural phases (X-type1, X-type2, X-type3) with

NM, magnetic (FM and AFM) states of the HH YMnZ

(Z=Si, Ge, Sn) materials. Also, predicted lattice

parameter a (Å), bulk modulus B (GPa) and the

formation energy Efor (Ry) of these studied materials

are given in the preferred FM state………………………....101

Table 7.3 The computed total µtot (µ/f.u.) and local magnetic

moments (µatomic/f.u.) of the half-Heusler YMnZ

(Z=Si, Ge, Sn) materials with X-type1 phase at the

two exchange-correlation potential (VXC) is given.

Band gap energy: Eg (eV) and half-metallic gap: EHM

(eV) is also described at the Electronic conductivity

xxi

(metallic, HM, or semiconducting)……………..………..…..112

Table 8.1 Equilibrium lattice parameter: a (Å), electronic

conductivity (SC and HM) represent the

semiconductor and half-metallic characteristics, µB is

equivalent to total magnetic moment, EBG& EHM are

the energy band gaps and HM gap, FM & AFM along

with EFM& EAFM shows the magnetic ground state and

energy of the FM and AFM respectively, TC & Emix

shows the Curie Temperature and mixing energy of

the each 30 interesting HH XYZ materials at their

preferred ground state (T1 or T3) with vibrationally

stability check at the γ-point………………………………….135

xxii

List of Figures

Figure No. Page No.

Fig. (1.1) Periodic table showing the large numbers associated with

HA could be created through mixture of the various

components based on the color plan…………………………………..3

Fig. (1.2) Crystal structures of (a) NaCl-type (Rock salt), (b) Zinc-

blende (c) HH & (d) FH……………………………………………….5

Fig. (1.3) Atomic placement inside the unit cell of the HH, FH, QH

and inverse Heusler alloys. In the lattice, there are four

interpenetrating f.c.c lattices for all the cases. It can also be

noted that the lattice will be b.c.c if all the atoms are same…………..7

Fig. (1.4) HA based on Mn2 with respect to the position of Y element

for each type, the inverse Heusler and the normal Heusler

framework…........................................................................................10

Fig. (1.5) Unit cell of (a) inverse Heusler framework CuHg2Ti as

well as quaternary edition LiMgPdSn……………………………….10

Fig. (1.6) (a) XYZ HH materials and TMs occupy only the octahedral

site and display magnetic moment (b) X2YZ FH materials.

The HH and FH have the one and two magnetic sublattice

respectively which means FH can be coupled in both FM

and AFM phases while the HH has only FM

and AFM phases while the HH has only FM phase…………………11

Fig. (1.7) Schematic outline for the DOS (a) metal (b) spin projected

metal (c) a ferro-magnet (d) a HM ferromagnet

(e) HM ferrimagnet…………………………………………………..13

Fig. (1.8) Various distinctive important physical properties of the

outstanding class of HA……………………………………………...15

Fig. (1.9) Outline of the fundamental spintronic gadgets………………………17

xxiii

Fig. (1.10) When conducting electrons move towards magnet, their

own spin preferentially line up within the magnet’s path.

Since the electrons experience the nanomagnet, sandwiched

in between levels associated with NM materials near to the

set alignment magnetic, the actual path associated with their

own spin is repolarized to complement from the

nanomagnet. Consequently, nanomagnet has the magnetic

moment starts to precess,

turns just like a spinning-top on its pivot……………..………………21

Fig. (1.11) Selected elements from the periodic table for the studied HH

XYZ materials in this dissertation based on the color

plan……………………………………………………………………28

Fig. (4.1) Crystal structure of HH XYZ compound with

(MgAgAs) C1b for Type 1……………………………………………48

Fig. (4.2) Volume optimization at various atomic positions (Type 1,

Type 2, Type 3) for (a) CrTiSi (b) CrTiGe (c) CrTiSn

and (d) CrTiPb…..……………………………………………………50

Fig. (4.3) Volume optimization for (a) CrTiSi (b) CrTiGe (c) CrTiSn

(d) CrTiPb for magnetic FM & NM state.……………………………51

Fig. (4.4) Electronic band structures of HH (a) CrTiSi, (b) CrTiGe, (c)

CrTiSn & (d) CrTiPb compounds for spin-up (↑)

and spin-down (↓)……………………………………………………..53

Fig. (4.5) Total and partial DOS of (a) CrTiSi, (b) CrTiGe,

(c) CrTiSn & (d) CrTiPb for spin- up (↑) and spin-down (↓)…………56

Fig. (4.6) Total and orbital resolved partial DOS of the HH (a) CrTiSi

(b) CrTiGe, (c) CrTiSn & (d) CrTiPb compounds……………………57

Fig. (4.7) Origin of semiconducting gap in the majority spin channel

in the α-phase for the CrTiGe as a prototype…………………………59

Fig. (4.8) Total Magnetic moment (µ𝑡𝑜𝑡) of the HM HH

CrTiZ (Z= Si, Ge, Sn, Pb) as a function of lattice constant…………..60

Fig. (5.1) Unit cell of cubic C1b-type structure for the HH FeVGe in

α-phase………………………………………………………………...64

xxiv

Fig. (5.2) Total energy as a function of volume for FeVGe in

different phases (α, β, γ) of atomic positions…………………………66

Fig. (5.3) Total energy as a function of volume for the HH FeVGe in

α-phase for the magnetic and NM states………...……………………66

Fig. (5.4) Spin-dependent total and partial DOS of HM FM materials

(a) FeVSi (b) FeVGe (c) FeVSn at equilibrium lattice

constant at the α-phase. Fermi level is set at zero. The top

portion (spin-up) displays the majority-spin channel and the

lower portion (spin-dn) is for the minority spin channel.

Solid and dotted lines show the DOS’s of GGA & mBJ-

GGA potential respectively ………………………………………….69

Fig. (5.5) Spin polarized band structure of the FeVSi for the α-phase

at equilibrium lattice constant. Solid and dashed lines

denote for the GGA and mBJ-GGA potential respectively…………...72

Fig. (5.6) Spin polarized band structure of the FeVGe for the α-phase



Fig. (5.7) Spin polarized band structure of the FeVGe for the α-phase



Fig. (5.8) Band structure of the HH FeVGe compound with mBJ

potential of α-phase at equilibrium lattice constant…………………..76

Fig. (5.9) Magnetic moment as a function of lattice constant of the

HH (a) FeVSi, (b) FeVGe & (c) FeVSn materials……………………77

Fig. (6.1) Conventional unit cells of YCrSb HH alloy in the MgAgAs

(C1b) structure for the three distinct XI, XII and

XIII atomic arrangements……………………………………………...82

xxv

Fig. (6.2) Variations of computed FM total energy with volume per

unit cell for the three feasible atomic arrangements XI, XII

and XIII of both HH (a) YCrSb (b) YMnSb with MgAgAs

(C1b) structure……………………………...………………………...84

Fig. (6.3) Variations of calculated total energy with volume of HH (a)

YCrSb (b) YMnSb materials in stable XI phase for NM,

FM and AFM states…………………………………………………..86

Fig. (6.4) Spin-resolved band structures of HH YCrSb (a) spin up

(b) Spin down. Fermi level is set to be zero…………………………..88

Fig. (6.5) Spin-resolved band structures of the HHYMnSb

(a) spin up (b) Spin down. Fermi level is set to zero………………….89

Fig. (6.6) Spin-polarized densities of state for the total and individual

atoms at the equilibrium lattice constant for the XI phase of

the HH (a) YCrSb (b) YMnSb materials……………………………...91

Fig. (6.7) Schematic representations of origin of semiconducting gap

in the majority spin state in the stable XI structure for the

HH YCrSb material…………………………………………………...92

Fig. (6.8) Lattice parameter dependences of the total magnetic

moment, and the spin moments of Y, Cr/Mn and Sb atoms

for the HH (a)YCrSb and (b) YMnSb, respectively…………………..95

Fig. (7.1) Conventional cubic unit cell of the HH YMnSi at the diverse

atomic arrangement X-type1, Xtype2, and X-type3……….………...100

Fig. (7.2) Total energy to be functionality connected with volume inside

three unique atomic positions X-type1, X-type2 and X-type3 for

the HH (a) YMnSi (b)YMnGe and YMnSn alloys. These curves

represent the FM state………………………………………………..103

Fig. (7.3) Total energy to be functionality connected with volume

inside ternary magnetic states (NM, FM, and AFM) for the

HH (a) YMnSi (b) YMnGe and (c) YMnSn alloys………....……….104

xxvi

Fig. (7.4) Spin-projected band structure with the HH YMnSi alloy.

Black solid lines show the GGA and red dotted lines are

for the GGA+mBJ…………………………………………………..106

Fig. (7.5) Spin-projected band structure with the HH YMnGe

compound. Black solid lines show the GGA and red dotted

lines are for the GGA+mBJ………………………………………...107

Fig. (7.6) Spin-projected band structure with the HH YMnSn

compound. Black solid lines show the GGA and red dotted

lines are for the GGA+mBJ………………………………………...108

Fig. (7.7) Total and partial DOS of the HH (a) YMnSi,

(b) YMnGe and (c) YMnSn compounds using GGA+mBJ……......110

Fig. (7.8) The computed total magnetic moment (µ𝐵) for the HH (a)

YMnSi, (b) YMnGe and YMnSn materials corresponding to

variation of lattice constant. The dashed vertical line

shows the optimized equilibrium lattice constant………………….115

Fig. (7.9) (a) Electrical conductivity, (b) thermal conductivity

(c) See beck coefficient and (d) Figure of merit as a function

of temperature …………………………………………………......117

Fig. (8.1) Conventual unit cell of the HH XYZ materials in three

different atomic arrangement types T1 [4c (1

4,

1

4,

1

4), 4d

(3

4,

3

4,

3

4), 4a(0, 0, 0)], T2 [4a(0, 0, 0), 4d (

3

4,

3

4,

3

4),

4c (1

4,

1

4,

1

4)] and T3 [4b (

1

2,

1

2,

1

2), 4d (

3

4,

3

4,

3

4), 4a(0, 0, 0)]…………..123

Fig. (8.2) Volume optimization of the HH HM NaVTe material at the

(a) three different atomic arrangement types (T1, T2 & T3)

(b) FM and AFM ground state…………………………………….125

Fig. (8.3) Summary of the 90 HH XYZ materials, at their preferred

stable ground state among three different types T1, T2 & T3

phases and magnetic ground state (NM, FM, AFM).

Illustration of the electronic properties of the each HH

materials is also presented at their preferred stable type and

magnetic ground state……………………………………………..127

xxvii

Fig. (8.4) Colors shows the width of the (a) Energy band gap (EBG) (b)

HM gap (EHM) of 90 HH XYZ materials. The species X, Y

and Z which represent the HH XYZ materials are signifying

on the three coordinates. Blue and yellow colors represent

the successively increasing values of these

energy band gaps…………………………………………...............129

Fig. (8.5) Mixing energy (eV/atom) of the 28 HM HH XYZ materials

at their respective stable state with FM configurations which

are also vibrationally stable at the gamma point. Blue shades

show the mixing energy less than 0.2 (eV/atom). Each

coordinate of the 3D plot symbolizes the X, Y, Z species of

the associated HM HH

XYZ materials………………………………………………..…….131

Fig. (8.6) The Curie temperature of the 28 HM HH XYZ materials at

their respective stable state with FM configurations which

are also vibrationally stable at the gamma point. The color

bar shows the values of the calculated TC (K) with +/- 25 K

tolerance. Each coordinate of the 3D plot symbolizes the X,

Y, Z species of the associated HM HH XYZ material

XYZ material……………………………………………………….133

Fig. (8.7) Phonon full spectrum curve for the (a) HM HH NaVSi &

(b) FM SC LiVGe ……………………………………………….....138

Fig. (8.8) Band structure of the HH FM SC LiVGe material in the

spin up and spin down channel. The horizontal dashed line

represents the Fermi level (EF) which is fixed at zero eV………….139

Fig. (8.9) Band structure of the HM HH CsVSe material in the spin up

and spin down channel. The horizontal dashed line

represents the Fermi level (EF) which is fixed at zero eV………….140

Fig. (8.10) Fig. (8.10) Spin projected total and partial density of state

(DOS) of HM HH RbVTe material at the equilibrium lattice

constant. The vertical dashed line in the middle

shows the Fermi level (EF = 0 eV)………………………………….142

xxviii

List of Abbreviations

HMFs = Half-metallic Ferromagnets

HM = Half-metallic

HA = Heusler Alloys

HH = Half-Heusler

FH = Full-Heusler

QH = Quaternary Heusler

TC = Curie temperature

TMs = Transition metals

VBM = Valance Band Maxima

VCM = Conduction Band Minima

𝑁𝑣𝑎𝑙 = Number of valance electrons

ZA = Atomic number

NM = Non-magnetic

FM = Ferromagnetic

AFM = Anti-ferromagnetic

SPR = Slater-Pauling Rule

µtot = Total magnetic moment

SP = Spin polarization

mBJ = modified Becke-Johnson approximation

TB-mBJ = Tran-Blaha modified Becke-Johnson

DOS = Density of States

EBG = Energy band gap

EHM = Half-metallic gap

xxix

EF = Fermi Energy

𝐸𝑓𝑜𝑟

= Formation Energy

𝐸𝑚𝑖𝑥 = Mixing Energy

SCs = Semiconductors

BZ = Brillouin Zone

TMR = Tunneling Magnetoresistance

GMR = Giant Magnetoresistance

1

CHAPTER 1

Fundamentals

Prior to presenting physical facets of this thesis, the introduction of half-metallic

ferromagnets (HMFs) must be presented. Up to now, half-metallic (HM) properties are already

noticed in several alloys, for instance, Heusler alloys (HA) ferromagnetic (FM) materials

(Bayar et al., 2011; Özdog and Galanakis, 2009; Sharma et al., 2010b), dilute magnetic

semiconductors (SCs) and zincblende transition metals (TMs) oxides (Soeya et al., 2002; Song

et al., 2009a; Szotek et al., 2004), pnictides and chalcogenides (Xie et al., 2003). Among

several HMFs are pointed out above, HA considered as the most inspiring possibility for

practical utilizations of spintronic materials because of high Curie temperatures (TC), high

magnetic moments, and their crystal structures equivalent with the traditional SCs. HMFs are

considered this kind of novel compounds. Consequently, it is much more useful to review the

Heusler framework along with brief history of the HA before the HMFs term must be cleared

up.

1.1 Heusler Alloys (HA)

Heusler alloys (HA) are recognized, more than a century. These are referred to after

Friedrich Heusler, a German engineer as well as a chemist, who found out in 1903 that

Cu2MnAl acts as FM, although, combination (Cu2MnAl) is made of non-FM or non-magnetic

(NM) constituents (Cu, Mn, Al). This exceptional material and its family members that right

now exist consist of huge selection more than 1000 alloys and are referred as HA.

The simultaneous advancement of computational materials modelling, and growth

methods at the nanoscale develop scientific interest on the research of many magnetic materials

such as HA. Interest in the HA has enhanced as the fact is established that their physical

properties may effectively adjusted by replacement of elements. Heusler materials undoubtedly

are a huge class of intermetallic materials representing different kinds associated with

electronic and magnet attributes (Webster and Ziebeck, 1988a). Many one of these HA are

HMFs, ferrimagnets, and antiferromagnets.

2

These materials have distinct attention because of the quite high TC range which often

surpasses 1000 k producing all of them well suited for spintronic applications (Hirohata and

Takanashi, 2014).

1.2 Types of Heusler Alloys (HA)

HA are type associated with intermetallic compounds which can be divided into four

main families: (a) the typical Full-Heusler (FH) alloys such as Co2MnSi with the chemical

composition is X2YZ in which valence associated with the X is larger than the valence

associated with the Y and Z atoms are similar, (b) the semi-Heusler also referred as HH alloys

like NiMnSb possess the chemical composition XYZ with X and Y represents the TMs,

whereas (c) the Quaternary Heusler (QH) alloys such as CoFeMnSi which have comparable

attributes like the FH alloys and lastly (d) the inverse-HA such as Cr2CoGa that also have the

chemical composition of X2YZ however right now valence associated with Z atom scale down

compared to Y and so result of modification of atomic placement in the crystal, the two Z

atoms are no longer similar (Webster and Ziebeck, 1988a).

1.2.1 Full Heusler (FH) Alloys

In earlier times, HA had been frequently recognized as an intermetallic material, even

though the framework as a possible intermetallic material is certainly more appropriate because

of their feature atomic order. Ternary FH alloys hold the basic general chemical formula X2YZ

in which X & Y = TMs whereas Z represents main group of the periodic table. An illustration

of FH alloys is presented in Fig. (1.1). Though, in certain cases, Y atom is exchanged with

alkaline earth metal or rare earth constituent. Usually, metals, that are available two times, is

set in the beginning with the formula, whilst the Z atom is put at the last, for example, Co2MnSi,

Fe2VAl (Nishino et al., 1997; Ritchie et al., 2003). These FH alloys have a stoichiometry of

2:1:1 and crystalizes in the cubic L21 structures.

Half-metallicity in the FH alloys may be blended both with all the physical appearance

regarding ferrimagnetism if the Z atoms inside the X2YZ could be the Mn and together with

ferromagnetism when Z atom will be Co. In each instance, the FH alloys have the total

magnetic spin moment in µB and follow the SPR of 𝑍𝑣𝑎𝑙 – 24 (Galanakis, 2002a).

3

Fig. (1.1) Periodic table showing the large numbers associated with HA could be created

through a mixture of the various components based on the color plan.

4

1.2.2 Half Heusler (HH) Alloys

The materials which have a stoichiometry of 1:1:1 tend to be a ternary SC or metallic

compounds additionally identified as half-Heusler (HH) alloys. Generally, HH alloys have

general formula XYZ can end up being recognized as materials comprising the covalent as

well as an ionic component. The X and Y possess unique cations identity although Z represents

the anionic version.

In literary works, there is a wide range of variations in the nomenclature of these

compounds. Three possible arrangements are found as they sorted out as alphabetically,

randomly or depending upon on electronegativity. The most-well recognized semi-Heusler

material is NiMnSb.

1.2.3 Quaternary Heusler (QH) Alloys

Apart from the most common and inverse FH materials, one more FH relative will be

the LiMgPdSn-type kinds, also referred to as LiMgPdSb-type Heusler material. These types of

materials tend to be QH materials using the chemical composition of XX′YZ exactly, in which

X, X′, as well as Y tend to be metallic atoms and Z is equivalent to sp-element. The valence

electrons involving X′ is lesser as opposed to valence involving X element, plus valence of Y

is simply lesser as opposed to valence involving the two X along with X′. The arrangement

from the atoms across the fcc cube’s diagonal is actually X-Y-X′-Z and vigorously probably

uttermost dynamic stable phase (Alijani et al., 2011). A couple of LiMgPdSn-sort of HM

materials have been analyzed (Gökoğlu, 2012; Izadi and Nourbakhsh, 2011) and some reviews

demonstrated that one can likewise discover spin gapless SCs among them (Xu et al., 2013).

1.3 Crystal Framework of Heusler Alloys (HA)

HA mainly divided into two unique families in which one has the composition 2:1:1

and the other has 1:1:1 stoichiometry. The very first family of HA analyzed were crystallizing

within the L21 structure that includes four fcc sublattices. Later, is found that if one of the fcc

sublattice is withdrawn from the L21 framework leads to the C1b framework. HH crystal is a

variant of the ternary ordered CaF2 structure. When the ZnS-type framework is filled by the

octahedral positions then it leads to the HH structure Fig. (1.2) (Graf et al., 2011).

5

Fig. (1.2) Crystal structures of (a) NaCl-type (Rock salt), (b) Zinc-blende (c) HH & (d) FH

6

Prominent aspect of the HH structural framework (C1b type) is that it contains three

filled and one vacant fcc sublattice which are hosted by X, Y and Z elements (Webster and

Ziebeck, 1988b). The HH structure crystallizes into a cubic non-centrosymmetric lattice with

F-43m space group (No. 216). The materials with C1b structural framework tend to be referred

as half- or feasibly semi-Heusler materials or just Heusler, although L21 materials are usually

called FH materials. The atomic arrangement filled by 4a (0, 0, 0), 4b (1

2,

1

2,

1

2) along with 4c

(1

4,

1

4,

1

4 ) Wyckoff positions for the HH materials. In theory, three inequivalent atomic

placements tend to be feasible in this structural framework which is described inside Table 1.1.

Usually, the HH structure can be considered as the ZnS sublattice in which Wyckoff position

was taken by 4a and 4c whereas the octahedral site generally filled by 4b.

This depiction underlines the covalent bonding among the two contained components

that perform a significant part to illustrate the electronic properties. An attention is drawn to

consider the appropriate atomic placements in the crystal which is very important to

comprehend structural properties for HA, as well as unique treatment, needs to be used

whenever carrying out theoretical research to acquire proper outcomes.

The FH X2YZ materials crystallizes into a cubic (L21-type) structural framework and

have space group (No. 225) Fm-3m using Cu2MnAl as a model (Bradley and Rodgers, 1934;

Heusler, 1934). The Wyckoff position for the X is 8c (1

4,

1

4,

1

4 ), whilst the Y & Z situated at 4a

(0, 0, 0) & 4b (1

2,

1

2,

1

2) individually .

Like HH materials, this framework comprises of 4 interpenetrating fcc sublattices, 2

associated with that are similarly involved by X atom, whereas the Y and Z comprise of

slightest and most electropositive elements form the rock salt-type lattice. The elements in FH

are usually synchronized octahedrally due to their ionic interaction persona. Alternatively, all

tetrahedral gaps are usually positioned by the X atom. Family of HA is highlighted within Fig.

(1.3). Besides the unit cell of HH and FH materials which are explained in the previous pages,

an inverse Heusler construction can be made when X and Y TMs selected from the same period

of periodic table and arranged in a unique manner that the atomic number (ZA) of Y, is greater

than the ZA of X. If TMs are taken from other periods, the Inverse Heusler framework also

exists in the HA (Puselj and Ban, 1969).

7

Table 1.1 Different atomic placement inside the C1b-type framework. The ZnS-sort sublattice

shaped by the 4a & 4c Wyckoff positions whereas octahedral holes are filled by the 4b position.

Structural phase 4a 4b 4c

Type I X Y Z

Type II Z X Y

Type III Y Z X

Fig. (1.3) Atomic placement inside the unit cell of the HH, FH, QH and inverse HA. In the

lattice, there are four interpenetrating f.c.c lattices for all the cases. It can also be noted that the

lattice will be b.c.c if all the atoms are same.

8

For every situation, X will be a lot more electropositive as compared to the Y. As a

result, X & Z shape NaCl-type crystal and X takes an octahedral coordination. By using 4-fold

symmetry, rest of the X & Y packed to tetrahedral gaps. Still, there are 4 interpenetrating fcc

sublattices inside the unit cell of the Inverse HA, however, a basic cubic unit cell is not shaped

by X anymore.

Rather the X occupy the Wyckoff placements 4a (0, 0, 0) and 4d (3

4,

3

4,

3

4 ), even though

the Y, as well as the Z, are situated with 4b (1

2,

1

2,

1

2) and 4c (

1

4,

1

4,

1

4 ), respectively. This

framework has the prototype of CuHg2Ti along with space group F-43m (No. 216).

Additionally, it is also feasible to distinguish the ordinary HA by indicating the chemical

composition as (XY)X′Z (Graf et al., 2011). The compounds based on Mn2 are often

considered as Inverse HA in which ZA(Y) > ZA (Mn) as outlined in the Fig. (1.4).

In Fig.(1.4), a properly researched illustration is shown for the inverse Heusler

materials i.e. Mn2CoSn or (MnCo)MnSn. Regarding QH materials, there are not one, but two

distinct elements X and X′. The Wyckoff positions 4a (0, 0, 0) & 4d (3

4,

3

4,

3

4 ) are taken by the

X & X′, whereas Y and Z are placed at 4b (1

2,

1

2,

1

2) and 4c (

1

4,

1

4,

1

4 ) respectively. LiMgPdSn is

the prototype of the QH alloys. An excellent example for the inverse Heusler framework and

of the QH alloys are provided within Fig. (1.5).

1.4 Structural Arrangement

1.4.1 Order-Disorder Phenomena in Half-Heusler (HH) Materials

The order and placement of the atoms inside the crystal, are very important and greatly

influence the electronic structure, and as a result effect the physical properties of HA. On that

basis, a detailed investigation on the structural framework is important to comprehend, along

with the prediction of the physical properties, for the different compounds. Sometime, a

halfway intermixture can adjust the electronic structure. HH materials tend to be tetrahedrally

stuffed structures that strongly linked to the binary SCs. Covalent bonding interactions perform

a substantial part, as well as their own crystalline arrangement, is maintained up to the

composed temperature (Skovsen et al., 2010).

9

Therefore, the structural disorder results in an occupancy from the empty lattice site

which happens seldom within HH materials, while the FH materials (X2YZ) structural

arrangements frequently show huge extents with atomic disorder. Different types of disorder

are possible within HH structural arrangement which is described in Table 1.2.

1.5 Heusler Alloys (HA) and Magnetism

HA initially pulled enthusiasm among the scientist in 1903, when F. Heusler

discovered, how the alloy Cu2MnAl gets to be distinctly FM, although none of its constituent

components is FM on its own. Even so, the idea needed about three ages prior to the amazingly

structural composition ended up being identified which has a deal with structure fcc lattice

(Bradley and Rodgers, 1934; Heusler, 1934). However, they pale virtually throughout oblivion

in the next ages, and the only a couple of reviews upon the experimental formation of the brand

new HA had been published in the 1970s (Webster, 1971).

It had been not really before anticipation of HM ferromagnetism within MnNiSb

through de Groot et al. in 1983, then scientific curiosity came back to Heusler compounds. The

HH XYZ compounds display a single magnet sublattice considering that the atoms around the

octahedral sites bring any magnet moment, which is suggested inside Fig. (1.6).

Mostly from the experiment, magnetic XYZ HH alloys can be found just for X = Mn

and rare earth metals. However, from experiment, it is found that a little magnetic moment is

observed for the Ni along with the late TMs. Certainly, by considering some basic principles,

situation like this can be overlooked. On the other hand, the majority of HA consisting of rare

earth elements which are discovered within the literature so far tend to be semiconducting or

semi-metallic frameworks or anti-ferromagnetic (AFM) with lower Néel temperature range

[24].

Merely, a few FM HH materials are portrayed in literature, as an illustration, NdNiSb

and VCoSb (Hartjes and Jeitschko, 1995; Heyne et al., 2005). The HH materials which contain

Mn atom are usually HMF along with higher TC. For the FH (X2YZ) materials, now the two

atoms are placed at the tetrahedral sites and hence situation is entirely different as compared

to the HH (XYZ) materials which result in an interaction between X atom and development of

the subsequent additional delocalized magnetic sublattice.

10

Fig. (1.4) HA based on Mn2 with respect to the position of Y element for each type, the inverse

Heusler, and the normal Heusler framework.

Fig. (1.5) Unit cell of (a) inverse Heusler framework CuHg2Ti as well as (b) the quaternary

edition LiMgPdSn.

11

Table 1.2 Various inequivalent Wyckoff positions and the general formula with space group

notations for the different HA (Graf et al., 2011).

Fig. (1.6) (a) XYZ HH materials and TMs occupy only the octahedral site and display magnetic

moment (b) X2YZ FH materials. The HH and FH have the one and two magnetic sublattice

respectively which means FH can be coupled in both FM and AFM phases while the HH has

only FM phase.

12

This is the reason that FH (X2YZ) materials display all types of a magnetic

phenomenon like ferromagnetism, ferrimagnetism and HM ferromagnetism today.

1.5.1 Half-Metallic Ferromagnets (HMFs)

In last three decades, different magneto-optical properties of a few HA inspired the

analysis of their electronic structure that results in a surprise outcome. For example, a number

of HA demonstrate metallic together with insulating properties simultaneously, an attribute

identified as HMF (De Groot et al., 1983; Kübler et al., 1983). De Groot and his associates

created an arrangement aiming out that three distinct sorts of HMF can be recognized.

The formal illustration of the density of states (DOS) is offered in the Fig. (1.7) which

show (a) A metal along with a limited DOS at the EF and (b) spin-projected depiction for the

metal. The Fig. 1.7 (c) demonstrates the DOS associated with the FM material for both

channels, the spin-up (majority) and spin-down (minority) are moved next to one another,

prompting to a quantifiable total magnetic moment (µtot), whereas, the Fig. 1.7 (d) illustrate

the HMFs which have metallic character for one spin-channel as well as insulator or SC for

the opposite spin-channel.

Basically, 100% spin polarization (SP) in the HMFs is merely achieved, at the absolute

temperature and half-metallicity often disappears when spin-orbit interactions are considered.

Many HA that contains just 3d TMs do not display any kind of spin-orbit interactions, they are

perfect applicants for HMFs.

1.5.2 The Slater-Pauling Rule (SPR)

The µtot associated with 3d TMs evaluated on the premise of counting the normal

valence electron number (𝑁𝑣𝑎𝑙) for each element present in the compound (Pauling, 1938;

Slater, 1936). This fact was discovered by Slater and Pauling. The µtot is provided by, in

multiple of Bohr magnetrons (µB) as:

µ𝑡𝑜𝑡 = 𝑁𝑣𝑎𝑙 − 2𝑛↓

where 2𝑛↓ signifies the quantity of electrons in the spin down (minority states). The minimal

in the spin down DOS pushes the quantity of d-electrons in the minority band being around

three.

13

Fig. (1.7) Schematic outline for the DOS (a) metal (b) spin projected metal (c) a ferro-magnet

(d) a HM ferromagnet (e) HM ferrimagnet

14

By ignoring the (s & p) electrons, the µ𝑡𝑜𝑡 inside localized section of the SP-curve is

determined in accordance with

µ𝑡𝑜𝑡 = 𝑁𝑣𝑎𝑙 − 6

It means that magnet moment for every atom is simply the typical quantity of valance

electron less than six. HMFs display energy band gap (EBG) in any one of the spin-channel

(spin-up or spin-down) DOS at the EF according to their definition because of this EBG, the

quantity of filled minority states should be a whole number, which is precisely satisfied for the

case µ = 𝑁𝑣𝑎𝑙 − 6 (Kübler, 2000; Wurmehl et al., 2005). This principle can result in a non-

integer values, if normal 𝑁𝑣𝑎𝑙 is not a whole number. Therefore, it is much simpler to use the

actual 𝑁𝑣𝑎𝑙 for each formula unit.

Regarding HH XYZ materials which have three atoms for every formula per unit cell,

the SPR becomes

µ𝑋𝑌𝑍 = 𝑁𝑣𝑎𝑙 − 18

and the HM materials which have less 𝑁𝑣𝑎𝑙 than the congenital HH materials, this rule is

modified by the Damewood et al. (Damewood et al., 2015a) as,

µ𝑋𝑌𝑍 = 𝑁𝑣𝑎𝑙 − 8

In the case of FH (X2YZ) materials, four atoms are placed inside each unit cell prompting to

the equation

µ𝑋2𝑌𝑍 = 𝑁𝑣𝑎𝑙 − 24

1.6 Applications of Heusler Alloys (HA) for Spintronic Devices

Summary of the different factors associated with HA will be talked considered, in this

evaluation section. The Fig. (1.8), condenses all the essential information regarding these types

of outstanding materials, varying through SCs, more than alloys as well as magnets to

topological insulators along with lots of technical programs within spintronic, thermoelectric,

opto-electronics and much more. Numerous intriguing studies will arise within the long term

that make the most of their own multiple’s benefits.

15

Fig. (1.8) Various distinctive important physical properties of the outstanding class of HA.

16

1.6.1 The Effect of Giant Magnetoresistance (GMR) and Tunneling Magnetoresistance

(TMR)

In 1986, the breakthrough of the giant magnetoresistance (GMR) influence the FM

multilayers and sandwiching of these layers by A. Fert (Baibich et al., 1988) & P. Grünberg

(Grünberg et al., 1986), changed the arena of information technology. In 2007, these two-

scientist privileged by a Noble prize for their exceptional breakthrough in Physics.

Nowadays, we are interacting with spintronic in our daily life due to the application of

GMR effect, the sort of spin-valves that can be utilized as a part of FM disks. The spin-valve

device contains a couple of magnetic levels, sandwiched with an extremely slim NM metallic

part.

Among the magnetic levels, one layer is "trapped" with AFM compound which is not

responsive to controlled FM fields, whereas the 2nd coating is “free” from the magnetization,

meaning that it can be balanced by rotating and using little magnetic fields. In contrast of GMR

spin-valves, the magnetoresistance increases 10%, if the metallic layer is replaced by an

insulating material. This increase is due to the tunneling of electrons from the insulating

material. Such materials are called tunneling magneto resistance (TMR) or tend to be referred

as magnetic tunnel junctions (MTJs).

The symbolic representation of the GMR and TMR is illustrated in Fig. (1.9) and see

review (Moodera et al., 1999) for the additional point of interest. Amazingly, a definitive

objective of spintronic, i.e. a tunneling gadget having a GMR impact associated with thousands

of percentages, could be attained simply by couple of distinct routes: The first path leads to

build insulating layer, and the second route guides to grow brand new HMFs with 100% SP.

At the very top of Fig. (1.9), GMR multilayers tend to be revealed in which the

magnetic coupling could be modified through different width from the nonmagnetic (NM)

spacer coating. While the bottom of Fig. (1.9) illustrates the TMR gadget in which the

tunneling current comes after opposite to the film surface.

17

Fig. (1.9) Outline of the fundamental spintronic gadgets.

18

1.6.2 Spin Polarization (SP)

Earlier groundbreaking research about the issue associated with spin-dependent

tunneling had been carried out within the 1970s through G. Michael. Tedrow as well as Ur.

Meservey (Tedrow and Meservey, 1973), by Michael. Jullière (Julliere, 1975), and also Utes.

Maekawa along with Ough. Gäfvert (Maekawa and Gafvert, 1982). Two decades later,

nevertheless, the primary substantial magnetoresistance within magnetic tunnel junctions had

been noticed at room temperature through T. Utes. Moodera (Moodera et al., 1995) as well as

Capital t. Miyazaki (Miyazaki and Tezuka, 1995). Pursuing the Jullière demonstration [219],

the TMR proportion of junction is identified with the SP of the electrodes based on the equation

⧍𝑅

𝑅𝑇𝑀𝑅=

2𝑃1𝑃2

1 + 𝑃1𝑃2

in which 𝑃1 and 𝑃2 are the polarization of the primary and secondary electrodes, respectively.

Also, the “SP” is characterized by

𝑆𝑃 = 𝑑 ↑ − 𝑑 ↓

𝑑 ↑ + 𝑑 ↓

whereas 𝑑 ↑ and 𝑑 ↓ presents the densities of the spin up and spin down states at the EF. The

Julliére model gives the basic estimation for the tunneling effect.

The very first theoretical work associated with half-metallicity within MnNiSb

triggered huge investigation curiosity, striving in the usage associated with HA within MTJs.

Actually, for the HH MnNiSb bulk material, a SP of just about 100% at the EF has been noticed

by method for spin polarized positron annihilation (SSPA) (Hanssen and Mijnarends, 1986).

However, the actual preparing of these thin-films of MnNiSb ended up being not

without challenges. Subsequently, diverse growth techniques, including co-sputtering and

molecular beam epitaxy (MBE), must be applied to get ready epitaxial films. At last, the crystal

arrangement was affirmed through XRD and the existence of the magneto crystalline

anisotropy. The assembly of HA into TMR appliances prompted an extraordinary boost in the

TMR proportion in the next years.

Nonetheless, the listing of guaranteeing applicants is lengthy, and numerous diverse

supplies happen to be examined, for example Co2Fe0.5Mn0.5Si, Co2FeAl0.5Si0.5 are among the

19

QH materials and Co2FeSi, Co2MnSi, Co2MnGe are the FH alloys. Consequently, a noticeable

advancement associated with the thin film high quality resulted in a definite enhancement from

the MTJs depending on Heusler materials.

This ended up, which not just an adequate crystallinity from the thin films performs a

significant part within MTJs, yet in which additionally the outer surface roughness, as well as

the user interface morphology in which electrode and the barrier are made of HA, includes an

excellent impact on the TMR esteem. In addition, the place of EF for actual half-metallic (EHM)

gap have a great importance and essential aspect within temperature reliance from TMR

percentage.

Accordingly, a big reduction in the TMR percentage can also be related to the little

energy splitting up between the EF and CBM. This is because of the thermal variations at

ambient conditions, which tend to be two times as large as this energy splitting up. Some key

features of the spintronics devices are the following:

➢ Higher values of TC

➢ Higher spin-polarization

➢ Manipulate involving atomic dysfunction

➢ Manipulate of the interface structure

These desired requirements regarding HMFs as well as their applications in spintronic

gadgets highly signifies that HA tends to be anticipating compounds, for a huge TMR because

of coherent tunneling along their own modified electronic properties as well as magnetic

attributes.

1.6.3 Current-Perpendicular-To-Plane (cpp) Giant-Magnetoresistance (GMR)

Besides the manufacture regarding TMR gadgets, current-perpendicular-to-plane (cpp)

GMR gadgets in which electrodes are made of HA, not too long ago surfaced in an area of

spintronics. Half-metallicity is frequently damaged at the electronic state on the interfaces, so

the cpp GMR devices have a great advantage over to the TMR devices because they are

insensitive at the digital surface.

20

The primary cpp-GMR gadgets contained a couple of Co2MnSi electrodes in which

each electrode is sandwiched with 3 nm Cr spacer (Yakushiji et al., 2006). It ought to be

mentioned that the selection of the spacer layer is critical problem.

The substantial spin dissemination length as well as reduced width are likewise

essential for the spacer coating to acquire wide cpp-GMR values. Such types of factors, joined

with a little lattice confound, prompted to the determination of silver as a perfect spacer

coating. Through an application perspective, a reliable cpp-GMR results 30% with area

temperature will be completely appropriate to make high performance gadgets.

1.6.4 Perpendicular Magnetic Anisotropy

In the magnetoresistance process (GMR or TMR), which are discussed in the previous

part permits to manage the electron circulation via FM nanostructure through their FM

condition. The opposite of this method is also available. The flow of spin-projected current can

easily affect the magnetic state when it flows through the magnetized Nano-structure. Spin-

transfer torque is a highly noticeable, amongst the better encouraging innovations these days,

to fulfill the actual growing need about quicker, scaled-down as well as non-volatile consumer

electronics.

Convoluting this improvement in the direction of scaled-down gadget dimensions is

the truth that power-consumption needs tend to be growing because transistor dimensions

reduce in size towards the sub-100 nm routine as it is illustrated in the Fig. (1.10).

Exchanging the current with a spin is also conceivable because of the mutual connection

among the spin of the inbound conducting carriers and the spin of the electrons in charge of

the area magnetization. Some important features of the spin-torque devices can be portrayed

in the following:

➢ Higher values of TC

➢ Higher spin-polarization

➢ Lower magnetic-damping

➢ Lower saturation-magnetization

➢ High perpendicular-anisotropy

21

Fig. (1.10) When conducting electrons move towards the magnet, their own spin preferentially

lines up within the magnet’s path. Since the electrons experience the nanomagnet, sandwiched

in between levels associated with NM materials near to the set alignment magnetic, the actual

path associated with their own spin is repolarized to complement from the nanomagnet.

Consequently, nanomagnet has the magnetic moment starts to precess, turns just like a

spinning-top on its pivot.

22

Above are the standard layouts for the compounds regarding prospective applications

inside spin-torque appliances. The look for brand new compounds with appropriately planned

properties is a dynamic field progressing research. Particularly tetragonally twisted HA are

typically emphases when innovative magnetic layers inside spin-torque gadgets.

1.6.5 Spin Injection

In spintronic, spin-injection treatment directed into degenerate SCs, for instance, GaAs

is additionally a region of extraordinary technological intrigue (Awschalom and Samarth,

2002). Truth to be told, the scientific utilizations of spin-injection are heap, which incorporate

the control of established data conveyed by spin, low-level formatting, and read-out of spin

qubits (Loss and DiVincenzo, 1998) as well as lucid control of spin associated with the

suggested spin field effect transistor (Schliemann et al., 2003).

The injected polarization of HA is considerably beneath the estimation of 100% that

would be normal for an HM. Conceivable clarifications for this trend involve a neighborhood

atomic mix-up and little EBG (≈ 200 meV) for the minority spin, for instance inside the

Co2MnGe (Picozzi et al., 2002). As a result, Heusler materials along with bigger EBG, for

example, Co2MnSi, might be proficient injectors (Ishida et al., 1998; Schmalhorst et al., 2004).

Given that spin-injection treatment studies investigate the actual SP in the interface, a

reasonable concept does not just need to think about the electronic framework from the

interface, but additionally the actual existence associated with atomic disorder along with the

results associated with non-zero heat. Certainly, these types of elements perform an important

part within interpretation spin-injection dimensions in brand new compounds.

1.6.6 Shape-Memory Compounds

These days, the FH Ni2MnGa framework is a standout amongst the most seriously

researched compounds attributable to its shape memory conduct along with its prospective

function in actuator gadgets, through which strains are manipulated by simply use of an outer

magnetic field. From this framework, under a FM changeover at TC of 376 K, the cubic phase

transition occurs (Webster et al., 1984).

23

Moreover, stoichiometric Ni2MnGa experiences any structural stage changeover

against the higher-temperature cubic L21 arrangement into a lower-temperature martensite

stage (Webster et al., 1984). Because of the structural transition feasibility, a shape memory

impact can be seen now through this L21 framework.

Shape memory compounds were broadened in order to a significant number of

materials, as an illustration, Ni2MnAl, Co2NbSn along with Fe2MnGa (Mañosa et al., 2004;

Zhu et al., 2009) and furthermore QH materials were researched inside this kind of

circumstance (Ito et al., 2008; Kainuma et al., 2008), e.g. magnetic field prompted shape

recuperation was accounted for the compressively distorted NiCoMnIn (Kainuma et al., 2006).

Stress greater than 100 MPa could be produced with this compound by applying the magnetic

field.

1.6.7 Superconductors

The group of HA incorporate not just metallic as well as semiconducting alloys, but

additionally superconducting materials. The initial superconducting HA Pd2RESn and also

Pd2REPb (where RE = rare earth metals) have been investigated simply by Ishikawa et al. in

1982 (Ishikawa et al., 1982). So far, several brand-new superconductors inside the Heusler

composition happen to be documented, their critical temperature, on the other hand, being too

low from an applications perspective. Typically, superconductivity can be discovered

frequently with FH materials which have 𝑁𝑣𝑎𝑙 = 27.

In the course of HH materials, absolutely no superconductor is identified, so these

persist into a non-centrosymmetric compound. One of the main exemption for the HH LaPtBi,

which has a basic exchange temperature around 0.9 K (Goll et al., 2008). About this type of

semimetal having a low transporter concentration, superconductivity had not been anticipated

and it is presently talked about within the framework associated with topological insulators.

Nevertheless, a reasonable comprehension of the cause of superconductivity, magnetism, as

well as their own concurrence in HA is yet absent.

24

1.6.8 Thermoelectric Compounds

As of late, HA materials has drawn excellent technological curiosity because of their

conceivable uses in the field of thermoelectric. Some important features of the thermoelectric

compounds can be portrayed in the following:

➢ Semi-metals with adjustable EBG

➢ Semi-metals with adjustable charge carrier concentration

➢ High Seebeck coefficient

➢ Low thermal conductivity

➢ Industrial processable

➢ Availability of resources

➢ Thermoelectrically compatible

➢ Low cost materials

As we already know that HH compounds along with 𝑁𝑣𝑎𝑙 = 18, display SC attributes.

The band structure information exposed narrow bands, resulting in the higher efficient bulk

along with a big thermo power (Uher et al., 1999). An incredibly favorable position of HA can

be likelihood of doping each of the 3 involved fcc sublattices exclusively keeping in mind, the

goal to enhance the thermoelectric properties.

Probably the most appealing attributes associated with HH compounds for

thermoelectric tend to be their higher Seebeck coefficient S of about 𝑆 ≈ 300 µ𝑉𝐾−1at the

ambient temperature and also their particular large electrical conductivity approximately

ranges from 1000 to 10000 Sc𝑚−1 (Kimura et al., 2009; Schwall and Balke, 2011; Uher et al.,

1999; Xie et al., 2008). The only real disadvantage could be the higher energy conductivity,

which possibly will be up to 10𝑊𝑚−1𝐾−1.

Numerous HH materials have been researched in the previous couple of years to

enhance their thermoelectric attributes (Bhattacharya et al., 2000; Mastronardi et al., 1999;

Uher et al., 1999; Xie et al., 2008). Lately, the actual manufacturing associated with Fe2VAl

thin films, along with higher Seebeck principles as well as reduced thermal conductivity,

brought on by the actual feed framework. These films had been documented permitting their

applications, in the thin film thermoelectric products.

25

1.6.9 Topological Insulators

For the topological insulators, a direct EBG is necessary at the middle position (Γ-point

of the BZ). There are 50 materials are reported in the HA which show the band inversion like

the topological insulator (e.g. HgTe). Topological insulators have several advantageous and a

continuous effort is still in progress for the development of topological insulators.

Specifically, the HH YPtSb, YPdBi, as well as ScAuPb tend to be near the edge. In

between, trivial or topological insulators are astoundingly fascinating materials claiming the

quantum transition which were produced by altering the definite lattice parameter or even little

variation of the atomic arrangement.

Some important features of the topological insulators can be portrayed in the following:

➢ SCs having adjustable EBG

➢ EBG in the bulk

➢ EBG in the quantum well framework

➢ Direct EBG at the Γ-point

➢ Dirac cones of odd numbers

➢ Huge spin orbit-coupling

➢ Parity alteration

➢ Band reversal

➢ Addition of brand-new qualities

➢ Having multiple functions

HH materials are an exceptionally tunable as well as the versatile course of compounds.

The numerous completely unique quantum phenomena like topological superconductivity and

quantized anomalous Hall Effect which also have the experimentally acknowledgment can

exist in the HH structure. Additionally, they unlock the new investigation and gives the

instructions in the direction of multifunctional topological gadgets regarding spintronic as well

as fault-tolerant quantum computing.

26

1.7 Heusler Moves Nano

There is no uncertainty, nowadays, how the development associated with

nanotechnology has already established a massive effect on a variety of research territories.

The basis behind this situation is the truth that nanocrystals compounds display physical

attributes which are very not the same as their own bulk partners. Limited size impacts that

result into the quantum containment which have crystal in the Nano range prompt the

development of innovative HMFs marvels. These HMFs may be used inside the huge range of

appliances associated with various applications.

Specifically, magnet nanoparticles have obtained massive attention regarding

appliances in several fields, for instance, drug delivery, data-storage gadgets, biomedical

imaging and catalysis (Hyeon, 2003; Raj and Moskowitz, 1990; Schladt et al., 2010; Sun,

2006). Given that a lower particle dimension refers to some bigger surface-to-volume

percentage, also numerous uncompensated spins can be found upon scaled-down

contaminants, consequently ensuing within improved values of µ𝑡𝑜𝑡.

The ball milling method is the typical strategy to manufacture the nanoparticles out of

the bulk compounds (De Santanna et al., 2008; Hatchard et al., 2008; Peruman et al., 2010;

Zhang et al., 2003a). As an example, FM Ni2MnGa nanoparticles have been well prepared by

firstly employing the ball milling approach besides post annealing method (Wang et al., 2007).

Just lately, ternary Heusler nanoparticles had been effectively synthesized through precursors

as well as their magnetic along with structural attributes have been explored (Kodama et al.,

1997; Wang et al., 2010). The immersion magnetization with lower temperatures is comparable

to the bulk worth that signifies, how the HM properties tend to be maintained within the

nanostructured compound.

1.8 Dissertation Scheme

HA sponsor an array of unpredicted unique physical features that cannot be obtained

through the properties from the exclusive atoms within the unit cell. Although different types

of HA exist, like FH, HH, QH, Inverse FH alloys, but our focus was only on the HH materials

among different types of HA. In this dissertation, a scientific contribution has been made to

study and discover the new HM HH XYZ materials to achieve higher EHM for the spintronic

applications.

27

The design of the selected elements from the periodic table of the investigated HH XYZ

materials is illustrated in the Fig. (1.11). A plethora of exotic HM properties of the new HH

XYZ materials is studied based on the first-principle calculations in this dissertation. The

structural, electronic, magnetic, thermal and HM properties of the series of HH CrTiZ (where

Z=Si, Ge, Sn, Pb), FeVZ (where Z= Si, Ge, Sn), YCrSb & YMnSb, YMnZ (where Z= Si, Ge,

Sn) and the HH XYZ materials where (X= Li, Na, K, Rb, Cs & Y=V, Nb, Ta & Z=Si, Ge, Sn,

S, Se, Te) are thoroughly discussed in the coming chapters of this dissertation. The ground

state properties like lattice parameters, the correct ground, and magnetic state, structural

stability, their equilibrium volume, total minimized energy, bulk modules and its pressure

derivative, total and partial magnetic moments, energy band gaps and many other important

aspects of the HH materials are explored. The computational calculations are performed by

using different DFT codes like WIEN2K, VASP, BoltzTrap, Phonopy for the study of the HH

XYZ materials in this dissertation. The dissertation scheme is distributed as follows:

➢ Chapter 1 covers the fundamentals of the HA and their applications in the spintronic

devices

➢ Chapter 2 provides the brief literature survey of the Heusler materials

➢ Chapter 3 gives the basic idea about computational parameters, techniques, and

details about DFT

➢ Chapter 4 presents an ab-initio study of new series of HH CrTiZ (where Z = Si, Ge,

Sn, Pb) materials in which HM ferromagnetism is explored

➢ Chapter 5 is all about the spin-polarized calculations of structural, electronic and

magnetic properties of the HH FeVZ (where Z=Si, Ge, Sn) alloys by using ab-initio

method

➢ Chapter 6 describes the theoretical investigations of HM ferromagnetism in new

HH YCrSb and YMnSb alloys using first-principle calculations

➢ Chapter 7 depicts about the physical properties of HH YMnZ (where Z= Si, Ge,

Sn) compounds via ab-initio study

➢ Chapter 8 demonstrate the structural chemistry and physical properties of the newly

designed HH XYZ materials with large spin-gaps

➢ Chapter 9 draws the conclusion and give a summary of this thesis and suggest the

future framework for the HH materials

28

Fig. (1.11) Selected elements from the periodic table for the studied HH XYZ materials in this

dissertation based on the color plan.

29

Chapter 2

Literature Review

Magnetism is referred to as an old phenomenon which has numerous cutting-edge

surprises. The man’s fascination with magnetism dates back hundreds of years, however, their

perception of it, is recent and still inadequate. In naturally existing materials, almost all

magnetic materials contain Fe and experimentally made magnetic compounds comprises of

one or more with the FM TMs like Fe, Co or Ni (Webster, 1969). In 1903, Fritz Heusler

synthesized Cu2MnAl alloy which acts as an FM even though none of involving component

aspects can be a magnet on its own (Heusler, 1904).

Due to the potential applications of the HMF materials from the perspective of

spintronic and magneto-electronics, they are under intensive investigation from the various

research groups in the last two decades (Hirohata and Takanashi, 2014; Žutić et al., 2004).

There are numerous distinctive advantages such as ultrafast processing speed of increased data,

enhanced integration densities, much lower consumption of electric power by the manipulation

and actively controlled of the spin degrees of freedom into the electronic appliances other than

conventional SCs (Prinz, 1998; Prinz, 1999; Wolf et al., 2001).

In 1983, by using the first-principles calculations, de Groot and his coworkers (De

Groot et al., 1983) from the electronic structure for the NiMnSb showed that it is fully HMFs.

The NiMnSb is the most researched compound (Watanabe, 1976) which show 100% SP at the

(EF). This means, the band structure of the NiMnSb display metallic character at one spin

channel whereas exhibit SC behavior at the opposite channel. The existence of EBG in one of

the spin channels gives 100% SP at the EF which ultimately leads the 100% SP current. In this

way, HMFs are potential contenders for the magneto-electronic appliances.

Other than HH and FH alloys (Galanakis, 2004; Zhang et al., 2003b; Zhang et al.,

2004), HM behavior is identified in several compounds as well like diluted magnetic SCs in

which impurity in the form of Mn is added in Si or GaAs (Akai, 1998; Stroppa et al., 2003),

the manganites i.e. La0.7Sr0.3MnO3 and some CrO2 and Fe3O4 oxide materials (Soulen et al.,

30

1998), also in CaAs which is called d0 ferromagnets (Coey, 2005), the pyrites i.e.

CoS2(Shishidou et al., 2001), the pnictides i.e. CrAs and the TMs chalcogenides in the wurtzite

or zinc-blende structure (Akinaga et al., 2000; Continenza et al., 2001; Galanakis, 2002a;

Mavropoulos et al., 2004; Mizuguchi et al., 2002; Nagao et al., 2004; Pask et al., 2003; Sanyal

et al., 2003; Shirai, 2001; Xie et al., 2003; Zhang et al., 2003c; Zhao et al., 2003), the double

perovskites i.e. Sr2FeReO6 (Kato et al., 2004), and in the europium chalcogenides i.e. EuN

(Horne et al., 2004).

Even though, in the practical manner, 100 % SP is also achieved at the EF with the

ambient conditions for the thin films obtained from La0.7Sr0.3MnO3 and CrO2 (Kato et al., 2004;

Soulen et al., 1998), but due to the fairly higher TC (Webster and Ziebeck, 1988a) of the HA,

they are considered more fascinated for the technological applications such as spin-filters

(Kilian and Victora, 2000), devices like giant-magnetoresistance (GMR) (Caballero et al.,

1998; Hordequin et al., 1998) or spin-polarized tunnel junctions (Tanaka et al., 1999) and so

called spin-injectors (Datta and Das, 1990).

A range of diverse magnetic phenomenon such as localized and itinerant magnetism,

Pauli paramagnetism, helimagnetism, ferromagnetism, antiferromagnetism, or heavy-

fermionic behavior (Gilleßen and Dronskowski, 2010; Toboła et al., 2003; Webster and

Ziebeck, 1988a; Ziebeck and Neumann, 2001) occurs in this fascinating family of HA which

consists of a large number of magnetic members.

The HH HM NiMnSb material has drawn lots of experimental curiosity. The

experiments like positron-annihilation (Hanssen and Mijnarends, 1986; Hanssen et al., 1990)

and infrared absorption (Kirillova et al., 1995) had successfully grown the HM single crystals

of NiMnSb. The high-quality films of NiMnSb are also produced but they do not show HM

behavior (Bona et al., 1985; Clowes et al., 2004; Mancoff et al., 1999; Zhang et al., 2004; Zhu

et al., 2001).

In contrast of 100% SP of single crystals of NiMnSb, high quality films of this

compound have only 58% SP at the EF achieved by Soulen et al. (Soulen et al., 1998). Such

types of SP measures are coherent to magnetoresistance calculated for NiMnSb based spin-

valve framework (Caballero et al., 1999; Kabani et al., 1990), the tunnel magneto resistance

junction (Tanaka et al., 1997) along with a superconducting tunnel junction (Tanaka et al.,

31

1999). The reason for losing HM characteristics for the HH NiMnSb epitaxial thin films is due

to the surface separatism associated with Mn and Sb atoms, and that is not even close to staying

ideal (Caruso et al., 2003; Komesu et al., 2000; Ristoiu et al., 2000a; Ristoiu et al., 2000b). In

addition to experimental research, NiMnSb lured additionally substantial interest amongst

numerous theoretical studies and many first-principles calculations verified the HM behavior

(Galanakis et al., 2000; Halilov and Kulatov, 1991; Kulatov and Mazin, 1990; Wang et al.,

1994). Larson and his coworkers show that the most stable structure of NiMnSb is the C1b

framework by the exchange of atoms (Larson et al., 2000).

The work done by the Orgassa et al. demonstrated that HM character kept maintained

by producing atomic disorder of some percentage in NiMnSb material although it causes

minority spin states within the semiconducting gap as well (Orgassa et al., 1999). Several

studies done on the surface properties of the different materials showed that interfaces or

surface of the HM materials loses the half-metallicity when layered with other SCs (Galanakis,

2002b; Galanakis, 2005; Galanakis et al., 2008a; Jenkins and King, 2002; Ležaić et al., 2005).

However, some researchers Wijs and de Groot along with Debernardi et. al. suggested that for

few layers of thin films, the possibility to regain HM persona for the HH NiMnSb material

(De Wijs and De Groot, 2001; Debernardi et al., 2003).

Lastly, Kübler (Webster and Ziebeck, 1988a) theoretically determined that NiMnSb

has the very accurate value of the TC is equal to 770 K that was very close to the experimental

result. The magnetic properties of these exceptional class of HA can be tuned by doping of

sp-electron substitution (Galanakis et al., 2008b; Özdoğan et al., 2009). The first series of

synthesized material from the HA was the FH materials (Suits, 1976; Webster, 1971; Ziebeck

and Webster, 1974). Kübler et al. were the first one to analyze the stability mechanism of the

FM and AFM phases of these HA (Kübler et al., 1983).

On the other hand, the presence of half-metallicity in the FH materials theoretically

predicted by the Japanese researchers. Ishida and collaborators were the pioneers to investigate

the ab-initio structural electronic calculations of the FH Co2MnSi and Co2MnGe materials

(Fujii et al., 1990; Ishida et al., 1982; Ishida et al., 1995) whereas FH Fe2MnSi and Fe2MnGe

materials investigated by Fujii et. al. (Ishida et al., 1995).

32

But polarized neutron diffraction experiment done by Brown et al. demonstrated that

the HM behavior is destroyed by the appearance of the small DOS around EF. Kübler et al.

verified this fact when he performed ab-initio computations on the FH Co2MnAl and Co2MnSn

materials (Kübler et al., 1983).

Until now, several HMFs are synthesized experimentally based on HA like Mn2-, Fe2-

and Co2- etc (Balke et al., 2006; Hongzhi et al., 2007; Luo et al., 2008a; Özdogan et al., 2006;

Shan et al., 2009) but there is still need to explore the HM properties theoretically as well as

experimentally for the useful spintronic applications.

2.1 Motivation for the work

As a detailed introduction chapter and literature survey of the HM HA gives so much

information about the application of the HM HA. The discovering, designing and functionality

of the new HM Heusler materials could be a meaningful work for the applications in the

spintronic devices. The simple structural framework of the Heusler materials which also have

lattice parameter comparable to numerous SCs have the large values of the magnetic moment

and TC, therefore are fundamental for the spintronic applications.

Therefore, it is very essential scientific outcome that the Heusler materials display

magnetic and semiconducting properties simultaneously. To discover new HM materials

experimentally is very hard as the confirmation of 100% SP is needed for the expected HMFs.

So DFT investigated band structure calculations play an essential part in this regard. The First-

principle estimations, particularly DFT have grown to be an extremely helpful technique

regarding predicting the physical properties of the different alloys.

The problem with the HMFs is that, the discovered HM properties are often disappear

due to the very small values of band gaps in the HA when the small lattice mismatch exists

due to strains in the HA also when they coupled with other conventional SCs. Consequently,

discovering brand new HMFs along with the larger values of EBG and EHM are vital regarding

useful for the spintronic devices.

33

In this dissertation, some new series of HMF HH materials are predicted by using first-

principles calculations. The structural, electronic, magnetic and thermal properties of the HH

CrTiZ (Z=Si, Ge, Sn, Pb), FeVZ (Z= Si, Ge, Sn), YCrSb and YMnSb, YMnZ (Z= Si, Ge, Sn,

Pb) materials are explored for the first time. Our proposed HM HH materials can be very useful

for the spintronic applications due to their large HM gaps, capable of providing 100% SP at

the EF with their equilibrium lattice constants and have adequate magnetic moment ranging

from of 1 µB to 4 µB.

34

Chapter 3

Basics of Density Functional Theory (DFT)

There are numerous fields inside the material sciences as well as in engineering where

it is very crucial to logical and innovative advancement is being familiar and managing the

properties associated with matter from the number of distinct atoms and molecules. Density

functional theory (DFT) is really a remarkably prosperous method of discovering results to the

essential formula, which explains the actual quantum conduct associated with atoms as well as

substances along the Schrödinger equation, with configurations associated with useful worth.

This method has quickly developed as being a specific artwork used through a number of

physicists as well as chemists, in the leading edge associated with quantum mechanized

concept to some device, that have specialty to frequently use, by many scientists in

biochemistry, physics, material science technology, chemical substance architectural, geology,

along with other professions (Sholl and Steckel, 2011).

The layout of this chapter is separated into two sections. The initial segment is about

the presentation of the fundamentals of density DFT which includes solving many body

Schrödinger equations and furthermore discuss the DFT in crystalline solids which is our

general concern about. The second part includes how to perform DFT estimations which

includes the little overview of WIEN2K software which is applied to run the DFT calculations.

3.1 Computational Material Science

Computational materials science is a field that is not necessarily associated with

computer coding. Materials researchers perform tests on the computers. DFT calculations that

are also known as first-principles calculations or ab-initio (which means from the beginning)

calculations. Ab-initio calculations offer three main segments;

➢ Theory (e.g DFT)

➢ Numerical methods and code

➢ Computer

35

The whole theory does not depend on the empirical parameters. It is just plain and

simple Quantum mechanics which is building up the whole world. In computational material

science, the computational scientist set up the experiments and let the computer apply the

theory and get a lot of nice properties like structural, vibrational, electronic, magnetic, and

thermal properties and much more describing any material. The beautiful thing about the

computational materials science is to illustrate the physical attributes of the matter by using

some theoretical methods rooted in the fundamental equations.

3.2 Many Particle Problem in Solids

The aim of DFT calculations to seek the ground state (most stable state of the

framework) for the set of particles and a useful approach to be carried out for the solution of

the many body Schrödinger equations.

ĤΨ ({ri }, {RI}) = EΨ ({ri }, {RI})

So, in the above equation, Ψ is a wave function which portrays the considered framework and

Ĥ and E expresses to the Hamiltonian and Energy operator which are applied to the wave

function. Also, the Hamiltonian operator can be described as

Ĥ = �̂� + �̂�𝑐𝑜𝑢𝑙𝑜𝑚𝑏

in which �̂� operator taking care of kinetic energy and �̂�𝑐𝑜𝑢𝑙𝑜𝑚𝑏 is the coulomb potential

operator which includes all the coulomb’s interactions between the two charges. The above

equation describes the basic quantum mechanics in which if the single electron state is selected

then our calculations will be simple which make the life easier. There are also bunch of nuclei

a and electrodes which makes the equation sort of very complicated to solve. Therefore,

making this equation a somewhat less difficult and the first thing to be carried out is to utilize

the Born-Oppenheimer approximation.

3.3 The Born Oppenheimer Approximation

According to this estimation, which can be stated as

mnuclei >> me.

36

This approximation says that nuclei tend to be very large plus heavy which makes them

slow to move whereas electrons are tending to be small and that is the reason they move very

fast. This means that the actual dynamics of the nuclei and electrons can be decoupled,

therefore the duration of time for the electrons must discover their ground state for just one

placement from the nuclei is a lot quicker compared to nuclei can proceed which means the

electrons begin to see the exterior potential associated with static nuclei, therefore by

decoupling the wave function

Ψ({𝑟𝑖 }, {𝑅𝑖}) → 𝛹𝑁 ({𝑅𝐼}) + 𝛹𝑒 ({𝑟𝑖 })

In the above equation 𝛹𝑁({𝑅𝐼}) represents the nuclear wave function and 𝛹𝑒 ({𝑟𝑖 }) is

termed as electronan ic wave function. It means, now the focus will be made only on to solve

the ground state of the electrons such as static ga roup of atomic placements therefore by

decreasing the list of parameters a little into the Hamiltonian,

Ĥ𝛹(𝑟1, 𝑟2, 𝑟3, … … … , 𝑟𝑁) = 𝐸𝛹(𝑟1, 𝑟2, 𝑟3, … … … , 𝑟𝑁)

So, the more detailed description of the Schrödinger equation becomes when the multiple

electrons are interacting with multiples nuclei making the equation more complex, and now

the Hamiltonian contains the three terms consisting of electronic variables, therefore

Ĥ = −ħ2

2𝑚𝑒∑ 𝛻𝑖

2

𝑁𝑒

𝑖

+ ∑ 𝑉𝑒𝑥𝑡

𝑁𝑒

𝑖

𝑟𝑖 + ∑ ∑ 𝑈 (𝑟𝑖 , 𝑟𝑗)

𝑗 >1

𝑁𝑒

𝑖=1

here, 𝑚𝑒 stands for the mass of the electron and one of three terms define the kinetic and

potential energy and second term shows the electrons interacting with the nuclei which see

themselves as an external potential and then the last term represents the electron-electron

repulsion. Let just pause and think of how big our problem this turns out and how fast this

escalates in terms of dimensions.

37

3.4 Why Density Functional Theory (DFT) Needed?

For the real materials, just take an example of carbon dioxide which has 22 electrons.

CO2: 6 + 16 = 22 electrons

Each electron in the CO2 molecule are described by three spatial dimension coordinates that

means solving the Schrodinger equation becomes a 66-dimensional problem. Consider another

example is of Pb nanocluster in which each Pb atom consists of 82 electrons. So, if the

nanocluster has 100 atoms then the specific nanocluster will contain 8200 electrons and

therefore Schrodinger equation becomes a 24,600-dimensional problem. So, by solving the

many body Schrodinger equation is for all practical materials a bit annoying. So, that is the

reason to approach the DFT.

3.5 Density Functional Theory (DFT)

To move from a wave function to electron density, which is true observable that in

principles, can be measured and defined from the wave function that reduces from 3N

dimensions to 3 spatial dimensions. So, the electron density is of only three dimensional,

𝑛 (𝑟) = 𝛹∗(𝑟1, 𝑟2, 𝑟3, … … … , 𝑟𝑁) 𝛹 (𝑟1, 𝑟2, 𝑟3, … … … , 𝑟𝑁)

So, that seems to be sort of a hint. Let’s go in that direction. Let’s try to solve the Schrodinger

equation in terms of considering the electron density intent. Now, make another approximation,

in which spouse that the Jth electron as a point charge, which is placed in all other electrons

field, that will simplify the many-electron problem to many-one electron problem.

So, situation now becomes like this

𝛹 (𝑟1, 𝑟2, 𝑟3, … … … , 𝑟𝑁) = 𝛹1(𝑟1) ∗ 𝛹2(𝑟2) ∗ 𝛹3(𝑟3) ∗ … … … ∗ ∗ 𝛹𝑁(𝑟𝑁)

which is a Hartree Product. Still, there is necessity to know about the molecules to

calculate. So that means, the electron density in terms of the single electron wave function

can be defined as

𝑛 (𝑟) = 2 ∑ 𝛹𝑖∗

𝑖

(𝑟)𝛹𝑖(𝑟)

which is another step to approaching at the heart of DFT.

38

3.6 Hohenberg and Kohn (at the heart of DFT)

So, the heart of DFT is based on two very fundamental theorems.

3.6.1 Theorem I

The 1st theorem conditions about the ground state energy from the Schrödinger

equation, which can be a unique functional for the density of electrons.

𝐸 = 𝐸 [𝑛(𝑟)]

The electron density is all which is needed to be defined the ground state energy. So that is the

good thing and 2nd theorem is about to find out the ground state density.

3.6.2 Theorem II

To precisely minimize the energy functional means that to moving down the well until

the ground state electron density has been found.

𝐸 [𝑛(𝑟)] > 𝐸0[𝑛0(𝑟)]

Now, let’s talk about a bit of energy functional.

𝐸[{𝛹𝑖}] = 𝐸𝑘𝑛𝑜𝑤𝑛[{𝛹𝑖}] + 𝐸𝑋𝐶[{𝛹𝑖}]

In which

𝐸𝑘𝑛𝑜𝑤𝑛[{𝛹𝑖}] = −ħ

𝑚𝑒∑ ∫ 𝛹𝑖

∗𝛻2𝛹𝑖

𝑖

𝑑3𝑟 + ∫ 𝑉(𝑟)𝑛(𝑟) 𝑑3𝑟 + 𝑒2

2∬

𝑛(𝑟)𝑛(𝑟′)

𝑟 − 𝑟′𝑑3𝑟𝑑3𝑟′

+ 𝐸𝑖𝑜𝑛

and the term, 𝐸𝑋𝐶[{𝛹𝑖}] represents the Exchange-correlation (XC) functionals, which include

all the quantum mechanical terms and the not known terms needs to be approximated. Some

basic XC functionals are the following

➢ Local density approximation (LDA),

➢ Generalized gradient approximation (GGA),

➢ modified Becke-Johnson (mBJ) approximation etc.

39

The energy functional can be divided into two parts. One that is known, and the other

is unknown. So, the known part is basically all the energy terms that are already described, like

the kinetic energy and all the potential energy terms which are connected just to the coulomb’s

reaction. The exchange-correlation functional that take cares of all the quantum mechanical

interactions between the electrons and about the not known terms that something exists, but

unfortunately, the information about them is lacking.

So in all calculations of DFT, this is something needs to be approximated, so the

simplest XC functional that one will stumble upon in the DFT is called the LDA, which is only

basic approximation of local electron density and then the GGA which is also taken into

account to the gradient of the electron density and there is a lot of developments going on all

the time on improving the XC functionals.

3.7 The Kohn-Sham Scheme

The Kohn and his post doctorate Sham have discovered that how to obtain the ground

state energy of the electron density in practice. They developed the scheme by considering the

exact state of single electron wave functions which are not interacting. So, single electron wave

functions are non-interacting systems. The interactions are sort of implicitly accounted for, in

these potentials.

[−ħ2

2𝑚∇2 + 𝑉(𝑟) + 𝑉𝐻(𝑟) + 𝑉𝑋𝐶(𝑟)] 𝛹𝑖(𝑟) = ∈𝑖 (𝑟)𝛹𝑖

So, the Hamiltonian for the single electron wave functions, 𝑉(𝑟) is the external potential and

then of the Hartree potential 𝑉𝐻(𝑟) that is just one electron interacting with the electron density

and then this exchange-correlation potential 𝑉𝑋𝐶(𝑟), which must be approximated.

3.8 Self-Consistency Scheme

In the DFT estimations, an iterative method also called self-consistency field (SCF) is

performed during the calculations. The SCF cycle consists of following steps:

• The 1st step, an initial guess of atomic density𝑛(𝑟)is made depending on the placement

of atoms.

40

• In 2nd step, the Hamiltonian operator is placed on the electronic system and set of Khon-

Sham equations are solved to calculate the electron wave functions 𝛹𝑖(𝑟).

• In 3rdstep, calculation of electron density is made depending upon the single electron

wave function. i.e 𝑛(𝑟) = 2 ∑ 𝛹𝑖∗(𝑟)𝛹𝑖(𝑟)𝑖

• In the last 4th step, a comparison is made between the 1st initial guess electron density

n(r) and the obtained electron density. If the values are same, then the true ground

density is achieved and if different then the calculations start again from the 2nd step

with the new value of electron density n(r)

So, one equation for each electron to obtain a set of wave functions and it is already

discussed, how this correlates with the electron densities. After that, recalculate the electron

density and if the electron density resulted, was the same one as the initial guessed value which

has been set, in the self-consistency loop, so that means the true ground state density is

achieved. If it is not the same, then replace the old electron density and put it as new trial and

then just loop through again.

That is how minimization of the electron density is done and try to search for the lowest

ground state and electron density by loop through this (SCF cycle). Now it is super easy to find

the ionic ground state. By electron density, the forces on ions can easily be calculated,

𝐹𝐼 = − 𝑑𝐸

𝑑𝑟𝐼= − < 𝛹𝑖 |

𝜗𝐻

𝜗𝑟𝑖| 𝛹𝑖 >

and then just move along the steepest distance of the ionic forces to obtain the ionic ground

state. So, in practice, an algorithm is used. After getting to the ground state, one can go even

further and move the ions, a bit away from their equilibrium position. Then, force constants

and vibrational frequencies are obtained, and the phonon dispersion curve can be calculated

for the ions. There are lot of possibilities.

3.9 Crystalline Solids and Plane-wave Density Functional Theory (DFT)

Now, moving towards the more specific case of crystalline solids. Now, the concern is

about the plane wave DFT. The crystal is a periodic arrangement of atoms. Consider the nuclei

which have some positive charge and represent the periodic potential U(r).

41

A free electron is represented by a plane wave (𝑒𝑖𝑘𝑟), but what happens with the wave

function when the electron is considered into the crystal. The Bloch finds the Bloch waves

𝛹𝑛𝑘(𝑟), by considering the electrons in a periodic potential.

𝛹𝑛𝑘(𝑟) = 𝑒𝑖𝑘𝑟 . 𝑢𝑛𝑘(𝑟)

So, Bloch waves are the plane waves which are modulated by some random

potential 𝑢𝑛𝑘(𝑟) which is also periodic with the lattice. Basically, they are perturbed free

electrons. So, these are the plane wave DFT which sort of comes out into the discussion. Now,

some important concepts in terms of DFT calculations or plane wave DFT are discussed.

3.9.1 Cutoff Energy

The first key parameter is cutoff energy. A very central concept in the DFT is reciprocal

space. Mathematically, it is just the Fourier transformation of the real axis where all the

dimensions are turned upside down.

𝛹𝑛𝑘(𝑟) = exp(𝑖𝑘. 𝑟) 𝑢𝑛𝑘(𝑟) = exp(𝑖𝑘. 𝑟) ∑ 𝐶𝑘

𝐺

exp (𝑖𝐺. 𝑟)

Basically, everything which is large in real space turns small in the reciprocal space

and the small things in real space extend far in the reciprocal space. The periodic function can

be expanded in terms of the Fourier series. So, the Bloch functional which is the electronic

wave function in the unit cell and the 𝑢𝑛𝑘(𝑟) is periodic with the lattice. By expanding it, the

wave vector turns out to be sort of reciprocal lattice vector. The Bloch wave are represented

as a summation of plane waves which has a wave vector of G + K. The kinetic energy of each

plane wave in the sum can be given as,

𝐸 = ℎ

2𝑚[𝐾 + 𝐺]2

Thus, the sum over an infinite number of reciprocal lattice vectors is needed. The

problem numerically is of course that one cannot deal with the infinite sums. In DFT

calculations, some sort of cut off energy must be defined so each plane wave in this sum has a

kinetic energy which is given by the above expression. So, for a larger reciprocal lattice and

vector, upsurge of kinetic energy is needed.

42

During the DFT calculations, for the considered plane waves, a cutoff energy is defined

which have the higher kinetic energy then this specific cutoff. This is an important input

parameter for the DFT calculations. To choose the suitable high enough cutoff energy, a

convergence test in terms of total energy is needed to be performed.

3.9.2 K-points

Another important concept is k-point sampling. In the reciprocal space, wave vectors

are plane wave vectors. They expand in the reciprocal space and the primitive unit cell is

termed as Brillouin Zone (BZ) or first BZ.

𝐾 = 2𝜋

𝜆[

1

𝑚]

Any k-vector which extends the primitive cell and reciprocal space, or it extends the

BZ. It can be written as the sum

𝑘′ = 𝑘 + 𝐺

The k-vector is just differing by some reciprocal lattice vector G which is basically the

same wave with some sort of face shifted. It means in terms of considering the plane wave

vector, only consider the first BZ. Without K-point sampling, numerically integrations cannot

be done, so in DFT terms of integral evaluation, only integrate over the first BZ.

It is also an important part of the DFT calculations that the researcher should map and

define the BZ in terms of k-points and the number of k-points must be sufficiently large so that

true, reliable and converged values of the energies can be obtained.

3.10 Pseudo-Potentials

Another important concept is the pseudo potentials in the DFT calculations. In terms

of the physical properties like chemical bonding and other characteristics of the material which

must be taken special care of, are mainly characterized by the outer electrons or so called the

valence electrons.

So, let’s make life a bit easier for ourselves. Instead of considering all the electrons of

the system, the DFT calculations can be made simpler by considering only the valance

43

electrons and freezing the inner electrons of the system while minimizing the electron energy

which makes the calculations much easier to do. A nice thing about the currently DFT code is

that they provide the pseudopotentials. It is not like the researcher must recalculate the Pseudo-

Potentials every time. There is often a library with the pseudopotentials for the use, of each

element in the periodic system.

3.11 WIEN2K

To examine the different physical properties, to develop the modern devices from the

solid materials at the atomic level, electronic structure calculations based on DFT are

performed, to the ideal crystal at ambient condition. This enables the quantum mechanized

discourse of the physics of the different physical properties, for instance, ground state

properties, volume optimization, electric, elastic, optical, chemical bonding, the dynamic

stability of the crystal, mechanical, the transition of phases, magnetic properties and so on. To

solve the equations of DFT, several procedures are designed.

There are numerous DFT simulations codes available but WIEN2K is probably the

speediest and trustable simulation package between other computational techniques. The

WIEN2K code is embedded in the DFT, which is already discussed in the earlier sections of

this chapter. WIEN2K includes numerous impartial F90 applications, that are connected

collectively by C-shell or Perl-scripts. WIEN2K utilizes the full-potential linearized

augmented plane wave method, which is probably the most accurate approach, developed by

the Blaha et al (Blaha et al., 2001b) and is founded on the Kohn-sham formalism regarding

DFT.

These days, greater than 500 research groups apply the WIEN2K simulation code

around the world to unravel the crystal properties on the nanoscale. These WIEN2K

computations operated on any kind of Unix/Linux systems through computers, work stations,

servers, supercomputers for the different crystal systems consisting up to 100 atoms per

formula unit cell. WIEN2K is very user-friendly simulation code based on the web graphical

user interface (w2web) along with a very good graphical user interface (GUI). The accuracy,

efficiency, and performance of the WIEN2K code are maintained as high as possible which

manage into a benchmark simulation package for the solids.

44

This dissertation contains the work on the HM HH XYZ materials which are fully

performed by using the state-of-art WIEN2K simulation code. Some other DFT simulation

packages like VASP, BoltzTrap, Phonopy are also used for the study of the HH XYZ materials

in this dissertation. This dissertation provides the general summary of an exceptional types of

HH alloys which have countless functionalities, ranging from semiconductors to metals and

HMFs which have lot of opto-electronics, thermoelectric and spintronic applications.

45

Chapter 4

Half-Metallic Ferromagnetism in New Half-Heusler Compounds:

An Ab-initio Study of CrTiZ (where Z= Si, Ge, Sn, Pb)

4.1 Introduction

Half metallic ferromagnets (HMFs) have attracted many researchers in the last decades

due to their unique properties and potential applications in spintronic devices (Jimbo et al.,

1993; Julliere, 1975; Ohno, 1998). Research on spintronic is currently very vigorous

worldwide since HMFs have the capability to use both charge and spin degree of freedom in

the solid materials to achieve multifunctional electronic devices (Prinz, 1998; Wolf et al.,

2001). The perspective of encryption and decryption of data from magnetic hard disk drives

makes these materials highly desired in the computer industry (Birsan and Palade, 2013a;

Carey et al., 2007). In addition, the SP at the EF allows these materials to be incorporated in

applications which include nonvolatile magnetic random access memories (MRAM) and

magnetic sensors (De Groot et al., 1983; Li et al., 2014; Wolf et al., 2001; Žutić et al., 2004).

The earliest of theoretical works carried out by de Groot et al. on NiMnSb and PtMnSb

HH compounds (De Groot and Buschow, 1986; De Groot et al., 1983) stimulated numerous

groups for exploring half metallicity in other compounds based on zinc blende SCs (Galanakis

and Mavropoulos, 2003; Xu et al., 2003; Yao et al., 2005a; Yao et al., 2005b; Zhang et al.,

2004) , FM metallic oxides (Lv et al., 2011; Song et al., 2009a; Szotek et al., 2004), transition

metal oxides (Lewis et al., 1997), perovskite manganite (Kato et al., 2002), transition metal

chalcogenides (Xie et al., 2003), dilute magnetic SCs (Saeed et al., 2010; Zhang et al., 2008),

FH compounds (Bai et al., 2011; Kandpal et al., 2007; Luo et al., 2009; Sharma et al., 2010a;

Xu et al., 2012; Zenasni et al., 2013) and HH compounds (Casper et al., 2012; Chen et al.,

2011; Lakdja et al., 2013; Nanda and Dasgupta, 2003; Rozale et al., 2013; Umamaheswari et

al., 2014).

46

Among these materials, HM HA are most prominent owing to their probability of

achieving higher value TC (Şaşıoğlu et al., 2004). Moreover, the structure of Heusler

compounds matches considerably with zinc blende and diamond structures which prevail in a

large variety of known SCs (Lin et al., 2014).

Additionally, HM HA show conduction of electrons in one spin direction around the

EF i.e. possess metallic behavior and are insulator or SCs in opposite spin orientation (Birsan

et al., 2012). Although in recent years some HH compounds like NiVM (M=P, As, Sb, S, Se

and Te) (Zhang et al., 2004), NiCrZ (Z=Al, Ga, In, P, As, Sb, S, Se and Te) (Galanakis et al.,

2008a; Luo et al., 2008b; Van Dinh et al., 2009), XMZ (X=Fe, Co and Ni; M=Ti, V, Nb, Zr,

Cr, Mo and Mn; Z=Sb and Sn) (Nanda and Dasgupta, 2003), XYZ (X=Li, Na, K and Rb;

Y=Mg, Ca, Sr and Ba; Z=B, Al and Ga) (Umamaheswari et al., 2014), XYZ (X(Nanda and

Dasgupta, 2003), Y=V, Cr, Mn, Fe, Co, and Ni; Z=Al, Ga, In, Si, Ge, Sn, P, As, and Sb) (De

Groot et al., 1986) have been predicted which possess HMFs nature by means of first-

principles calculations but a little work has been done experimentally on these compounds due

to the difficulty in synthesizing the chemical composition of HH materials like CoMnSb and

CrMnSb.

Nonetheless, it is very meaningful to investigate structural stability, electronic,

magnetic and HM behaviors of these compounds. According to our knowledge, no theoretical

or experimental research on the half-metallicity of CrTiZ (Z= Si, Ge, Sn, Pb) has been reported

yet. Motivated by this, structural, electronic and magnetic properties of these HH CrTiZ (Z=

Si, Ge, Sn, Pb) compounds are investigated by using density functional theory (DFT)

calculations.

4.2 Crystal Structure and Computational Details

HH compounds are intermetallic ternary with a 1:1:1 stoichiometry XYZ and

crystallizes into non-centrosymmetric cubic (MgAgAs) C1b configuration (Webster and

Ziebeck, 1988b) using space group of F-43m consisting on four percolate face centered cubic

sub lattices passed through the three atoms X, Y and Z, and a vacant site.

In the unit cell of this structure, the atoms X, Y, and Z are located at the corresponding

Wyckoff positions a1= (1

2,

1

2,

1

2), a2= (

1

4,

1

4,

1

4), a3=(0, 0, 0) sites, respectively, while (

3

4,

3

4,

3

4) site is

47

empty (Umamaheswari et al., 2014). In general X and Y are an alkali metal, transition metal

or rare-earth metal and Z is the main group element.

The X atom is placed at a1 and Z at a2 forming a rock salt lattice. On the other hand,

the Y atom is located at the center of the tetrahedron molded by X and Y atoms as shown in

Fig. (4.1). Generally, there are six modes in which X, Y and Z atoms can be distributed above

the three sub lattices. The interchanging of atoms at a1 and a2 results at equivalent positions

due to symmetry, which means that X, Y and Z atoms can be prescribed at (a1, a2, a3), (a3, a1,

a2), and (a2, a3¸ a1).

Due to this, to form C1b structure, there are three possible arrangements (Type 1, Type

2, Type 3) given in Table 4.1. Some experimental studies give the evident that the HH

compounds structure relies on the disorder of the atoms. For volume optimization, we utilized

self-consistent full-potential linearized augmented plane wave (FP-LAPW) method (Kohn and

Sham, 1965), which depends on DFT instigated into the WIEN2K simulation package (Blaha

et al., 2001a). We follow the Perdew–Burke–Ernzerhof (PBE) generalized gradient

approximation (GGA) for the electronic exchange–correlation interaction (Perdew et al.,

1996a). However, the DOS and the band structure were calculated by using mBJ potential.

A mesh of 12×12×12, consisting on 72 special k points that were taken in the BZ of the

irreducible wedge for the integrations within the modified tetrahedron method and for the wave

function broadening inside the atomic sphere, orbital momentum is taken lmax = 10. For the

convergence of the Eigen-value energy, the expansion of plane waves is organized by cut-off

parameter Kmax × Rmt = 8.0 where Kmax shows the uttermost value of the reciprocal lattice

vector used in plane wave function and Rmt represents the smallest muffin tin sphere radii. The

value of Gmax is set to 12 where Gmax is the largest vector value in charge density Fourier

expansion.

48

Table 4.1 Different configurations of atomic arrangements in HH structure.

Types X Y Z

Type 1 (¼, ¼, ¼) (0, 0, 0) (½, ½, ½)

Type 2 (¼, ¼, ¼) (½, ½, ½) (0, 0, 0)

Type 3 (½, ½, ½) (¼, ¼, ¼) (0, 0, 0)

Fig. (4.1) Crystal structure of HH XYZ compound with (MgAgAs) C1b for Type 1.

49

4.3 Results and Discussion

4.3.1 Ground State Properties

We employed ab-initio calculations to search HM compounds for spintronic

applications. In the present work, we have studied the structural, electronic and magnetic

properties of unreported ternary HH compounds CrTiZ (Z= Si, Ge, Sn, Pb). Because of no

experimental lattice constant has been reported, so we employed geometrical optimize

calculations to obtain theoretical equilibrium lattice constant of DFT investigated compounds

CrTiZ (Z= Si, Ge, Sn, Pb) in HH composition, the total energy varies with the empirical

Murnaghan’s equation as a function of volume for three possible phases (Type 1, Type 2 and

Type 3) in order to find out the correct arrangement of atoms in the crystal as shown in the Fig.

(4.2).

It is noted that all compounds are dynamically most stable in Type 1. So, structural,

electronic and magnetic properties are calculated for this type only. The theoretical lattice

constant of CrTiZ (Z= Si, Ge, Sn, Pb) for Type 1 is determined by minimizing the total energy

as a function of volume in the unit cell.

Magnetic ground state properties are also determined by minimizing the total energy

as a function of volume for both magnetic and NM states. The total energy curve with

deference to comparative volume in magnetic (FM) and NM phases are shown in the Fig. (4.3)

for all the compounds. In this structural optimization process, it is found that magnetic FM

calculation has a lower minimum total energy than NM type, indicating the magnetic state is

more stable in energy than NM form.

In addition, the value of energy difference ΔE is positive which is also indicating that

the magnetic state is preferable than the NM state as clearly shown in Fig. (4.3). The same

behavior is reported in the previous work (Umamaheswari et al., 2014). So, the structural,

electronic and magnetic properties are calculated for the Type 1 only. The theoretical lattice

constant of CrTiZ (Z= Si, Ge, Sn, Pb) for Type 1 is determined by minimizing the total energy

as a function of volume in the unit cell.

50

Fig. (4.2) Volume optimization at various atomic positions (Type 1, Type 2, Type 3) for the

HH (a) CrTiSi (b) CrTiGe (c) CrTiSn & (d) CrTiPb materials.

51

Fig. (4.3) Volume optimization for (a) CrTiSi (b) CrTiGe (c) CrTiSn (d) CrTiPb for magnetic

& NM states.

52

The predicted essential lattice constants, equilibrium volume, bulk modulus (B0), and

energy differences ΔE = ENM - EFM between the NM and FM states are given in Table 4.2.

Until now, an experimental or maybe theoretical value of CrTiZ has not been claimed to

compare with the present calculations.

The Formation energy (𝐸𝐹𝑜𝑟) of these compounds is significant to know the stability

of these putative compounds. The Formation energy is premeditated using the relation

𝐸𝐹𝑜𝑟 = 𝐸𝐶𝑟𝑇𝑖𝑍 − (𝐸𝐶𝑟 + 𝐸𝑇𝑖 + 𝐸𝑍)

where 𝐸𝐶𝑟𝑇𝑖𝑍 is the total energy of compound in a unit cell and 𝐸𝐶𝑟, 𝐸𝑇𝑖, and 𝐸𝑍 are total energy

of pure essential elements in the compound ECrTiZ and the calculated values are given in Table

4.2. These values of 𝐸𝐹𝑜𝑟 show that these compounds would not decompose as soon as they

have got been shaped.

4.3.2 Electronic and Magnetic Properties

For the prediction of the HMF and magnetic properties, electronic structure plays a

significant role. The electronic and magnetic properties of HH CrTiZ (where Z= Si, Ge, Sn,

Pb) compounds are discussed in this section. The band structures of CrTiZ (where Z= Si, Ge,

Sn, Pb) HH compounds revel that all CrTiZ (where Z=Si, Ge, Sn, Pb) compounds are HM in

nature because it is seen that minority spin (spin down) has metallic behavior at the EF which

is the indication of metallic nature.

On the other hand, there is EBG in the majority spin (spin up) showing the majority spin

is semi-conducting which clues to 100% SP near the EF as showing in Fig. (4.4). At the

optimized equilibrium volume and lattice constant, the Fig. (4.4) shows that all compounds

CrTiZ (where Z=Si, Ge, Sn & Pb) having metallic behavior for a spin up and semiconducting

for a spin down, which shows HM properties. In addition, (as given in Table 4.3) the particular

computed µtot of all the CrTiZ compounds is integral that is a usual quality connected with

HMFs (Felser et al., 2007).

The energy bands near the EF appears typically a result of the hybridization regarding

d-orbitals in the daptation of TMs. The band structure of the CrTiZ tends to be primarily

engaged using the 3d-Cr as well as 3d-Ti electrons near the EF.

53

Fig. (4.4) Electronic band structures of HH (a) CrTiSi, (b) CrTiGe, (c) CrTiSn & (d) CrTiPb

compounds for spin-up (↑) and spin-down (↓) channel.

54

It can be evidently identified that for all the materials there be found major splitting

among the majority and minority spin of the 3d-Cr and 3d-Ti states. The 3d-Cr along with 3d-

Ti are generally segregated into the t-2g state in the valance band (at low energy) and eg state

in the conduction band (at high energy).

Band structure also reveals that for the HH CrTiGe as a prototype, the upper part of the

valence band for a spin down lies at -0.17 (eV) and the lower part of conduction band for spin

up lies at 0.66 (eV) from the EF. By using these energies at the uppermost occupied band at L

point and the lowermost unoccupied band at the X point, the width of the EBG (indirect gap)

can be calculated which is 0.84 (eV) for the HH CrTiGe and EHM is 0.17 (eV) which can be

demarcated as the minimum energy requisite for an electron to flip the spin from the valance

band maxima to the EF. The majority spin EBG and as well as the EHM for other compounds is

provided within Table 4.2. The µtot of the compounds and individual magnetic moment of the

atoms are also given in Table 4.2.

We have also calculated spin-polarized total density of state (DOS) and partial density

of state (PDOS) for all the CrTiZ compounds at their equilibrium volume to understand the

origin of the ferromagnetism. Total and PDOS of CrTiZ (Z= Si, Ge, Sn, Pb) are presented in

the Fig. (4.5), which reveals that total and partial DOS of all the CrTiZ (Z=Si, Ge, Sn, Pb)

materials are HM since each alloy in the compute, the Cr and Ti sites rules portion of the plots.

For both spin up and down conditions it could be noticed from the total DOS that

uppermost part of valence bands originates from the hybridization associated with Cr and Ti

states. The spin splitting in these types of materials mostly come up from Cr-d states with a

small share coming from Ti-d states and the hybridization among Cr-d and Ti-d states.

Hence the magnetism comes up generally owing to the spin splitting of Cr-d like states.

The share regarding Z-atom is very small when compared to Cr and Ti. Because of interaction

between Cr-d like states and Ti-d like states, Because of interaction between Cr-d and Ti-d like

states, in the majority (spin-up) state, the d-t2g orbitals of Cr & Ti are fully occupied and d-eg

of Cr and Ti are partially occupied”. The hybridization is present among Cr-Ti within the 3d

orbital.

55

Table 4.2 Here, a (Å): lattice parameter, B (GPa): bulk modulus; ΔE (Ry): Energy difference

between FM and NM states and EFor (eV): Formation Energy

Table 4.3 Total magnetic moment µ𝑡𝑜𝑡 (µB) of compounds CrTiZ and local magnetic moments

(µB) of Cr, Ti, and Z atom. MI (µB) is the magnetic moment of the interstitial region, band gap

EBG (eV), and HM gap EHM (eV) in the spin up channel.

Material 𝐦𝐂𝐫

(µB)

𝐦𝐓𝐢

(µB)

𝐦𝒁

(µB)

𝐌𝐈

(µB)

µ𝐭𝐨𝐭

(µB)

𝐄𝐁𝐆

(eV)

𝐄𝐇𝐌

(eV)

CrTiSi 2.54 0.85 -0.02 0.64 3.99 0.86 0.12

CrTiGe 2.79 0.75 -0.06 0.53 4.00 0.84 0.17

CrTiSn 2.97 0.60 -0.05 0.49 4.00 0.91 0.31

CrTiPb 3.10 0.49 -0.04 0.45 4.00 0.94 0.33

Compounds a (Å) B0 (GPa) ΔE (eV) EFor (eV)

CrTiSi 5.7633 133.49 0.571 0.386

CrTiGe 5.9721 102.30 0.952 0.531

CrTiSn 6.2738 88.40 1.387 0.640

CrTiPb 6.3844 78.26 1.714 0.912

56

Fig. (4.5) Total and partial DOS of the HH (a) CrTiSi, (b) CrTiGe, (c) CrTiSn and (d) CrTiPb

materials, for spin- up (↑) and spin-down (↓).

57

Fig. (4.6) Total and orbital resolved partial DOS of the HH (a) CrTiSi, (b) CrTiGe, (c) CrTiSn

and (d) CrTiPb materials, for spin- up (↑) and spin-down (↓).

58

The reason for the absence of semiconducting gap in the majority spin is due to the

dominance of the Ti-t2g and Cr-t2g electrons round the EF for all the CrTiZ materials and the

cause of the origin of presence of semiconducting gap in the minority spin is due to the

depletion of Cr-t2g and Ti-t2g electrons which turns these occupied states into unoccupied states

and produces the semiconducting gap which is shown in Fig. (4.6) as a prototype for HH

CrTiGe alloy.

An understanding of half-metallicity along with the lattice constant is very crucial

regarding practical applications in spintronics. To analyze the sensitivity of half-metallicity,

the lattice constant must be changed in detail because by altering the lattice constant of the HM

materials could possibly have an impact on the HM nature. So, for this purpose, we focus on

the robustness of the ferromagnetism with respect to lattice distortion. The Fig. (4.7) shows

the computed µtot as a function of lattice parameter. We noted that integer value of the magnetic

moment remains unchanged up to the critical value of the lattice constant. These critical values

are 5.7 Å, 6.1 Å, and 5.9 Å for CrTiSi, CrTiGe, CrTiSn, CrTiPb, respectively.

59

Fig. (4.7) Origin of the semiconducting gap in the majority spin channel in the type T1 for the

HH CrTiGe as a prototype.

60

Fig. (4.7) The total magnetic moment (µtot) of the HM HH CrTiZ (where Z= Si, Ge, Sn, Pb) as

a function of lattice constant.

61

CHAPTER 5

Spin Polarized Calculations of the Structural, Electronic and

Magnetic Properties of New Half Heusler Alloys FeVZ (where Z =

Si, Ge, Sn) by GGA and mBJ Approaches

5.1 Introduction

In recent years, HM materials have been a focus of considerable attention from both

academic as well as industrial point of view. The interest in these materials stems from the fact

that these materials are capable of showing complete SP at the EF (De Groot and Buschow,

1986; Wolf et al., 2001; Žutić et al., 2004). In the HMFs, there is totally dissimilar behavior in

the two spin bands. In one spin orientation, these materials display a metallic character while

the other spin orientation shows a semi-conductive nature that leads to a 100% SP at EF

(Kandpal et al., 2007).

HM materials have attracted many technologists in the past decade owing to their

versatile electronic property which may lead to potential applications in the spintronic devices

such as nonvolatile magnetic random-access memories (MRAM) and magnetic sensors (De

Groot and Buschow, 1986; Wolf et al., 2001; Žutić et al., 2004), spin LED (Jonker et al., 2000),

spin FET (Schliemann et al., 2003), spin-tunneling devices (Lou et al., 2007; Miyazaki et al.,

1997).

Since the earliest of theoretical studies carried out by de Groot et al. (De Groot et al.,

1983) numerous HM compounds have been forecasted by different research groups (Xiao et

al., 2010). To-date, HM nature has been explored in dozens of materials such as dilute magnetic

SCs (Akai, 1998; Ogawa et al., 1999; Yao et al., 2005b), binary transition metal pnictides

(Jaiganesh et al., 2010), chalcogenides with zinc-blende structure (Tan et al., 2010), Full

Heusler (FH) compounds (Birsan and Palade, 2013b; Birsan et al., 2012; Birsan et al., 2013;

Fang et al., 2013; Huang et al., 2012; Kervan and Kervan, 2012; Kervan and Kervan, 2011;

Lei et al., 2011) and HH alloys (Casper et al., 2012; Chen et al., 2011; Lakdja et al., 2013;

Nanda and Dasgupta, 2003; Rozale et al., 2013; Umamaheswari et al., 2014; Yadav and

Sanyal, 2015; Zhang et al., 2003b).

62

The HH alloys have particularly attracted many researchers and material scientists to

predict the half-metallicity in various materials due to their high TC, structural resemblance to

the zinc-blende phase, magnetic behavior and other diverse properties. HH alloys provide a

chance for developing magnetic devices directly into SCs technology. Although a lot of

Heusler compounds have been theoretically anticipated to exhibit HM attributes, and recently,

many theoretical researchers have taken a keen interest in HH compounds until now to be in

our best knowledge HH FeVZ (where Z= Si, Ge, Sn) compounds have not received much

attention both theoretically and experimentally.

In the present study, the structural, electronic and magnetic properties of HH FeVZ (Z=

Si, Ge, Sn) compounds with C1b-type structure are investigated for the first time by performing

Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) (Perdew et al.,

1996a) while the electronic properties are probed using both GGA and the state-of-the-art mBJ

local density approximation functional calculations (Tran and Blaha, 2009). As the GGA

functional is known for underestimation of the band gap, so mBJ functional is employed which

has previously been shown to predict correct properties of magnetic materials.

For intestacy, GGA calculations of MnAs zincblende predict to display non-HM

properties (Sanvito and Hill, 2000), because conduction band minima touch or even crosses

the EF whereas experimental studies (Ono et al., 2002; Yokoyama et al., 2005) shows that it is

a truly HM compound which can be confirmed by mBJ calculations. Recently, Abdelaziz et

al. (Lakdja et al., 2013) also compares the results related to electronic and magnetic properties

of HH XCsBa alloys (where X= C, Si & Ge) with GGA and mBJ-GGA potential and concluded

that mBJ-GGA potential gives the accurate bandgap.

Although numerous feasible approaches are available in DFT calculations of SC gaps,

for instance, exact-exchange approach (Kotani, 1995; Sharma et al., 2005; Städele et al., 1997),

different GW methods (Faleev et al., 2004; Hybertsen and Louie, 1986), hybrid functionals

(Betzinger et al., 2010) which lead to the correct interpretation of the electronic properties, but

the mBJ potential (as an orbital independent, semi-local exchange correlation potential) has

been proved to produce accurate gaps for wide band gap insulators, sp-SCs, and 3d-TMs oxide.

Consequently, to discover the actual HM properties of the materials, it is very appropriate and

essential to make use of mBJ-GGA potential which significantly enhances the electronic

properties and its simple form as well as cheaper computationally cost makes mBJ functional

ideal for studying HM materials.

63

5.2 Computational Details

The structural optimization and the electronic calculations are performed by using the

self-consistent full potential linearized augmented plane wave (FPLAPW) method. FPLAPW

is employed into the WIEN2K code (Blaha et al., 2001b) based on density functional theory

(DFT). For the exchange correlation function, we used the PBE-GGA (Perdew et al., 1996a;

Perdew et al., 1996b). In this technique, space is consisting of muffin-tin (MT) spheres which

are non-overlapping and an interstitial region between these spheres. To separate the valance

and core electrons states, cut-off energy is set to -6 Ry. The spherical harmonic functions and

Fourier series, originate from a basis function, are employed for MT spheres and interstitial

region, respectively.

The cut-off parameter for the planewave was set to 𝐾𝑚𝑎𝑥 × 𝑅𝑀𝑇 = 9, where 𝐾𝑚𝑎𝑥 is

the maximum modulus for the reciprocal lattice vector. For the self-consistency cycles, energy

was set to 105 Ry per formula unit and by using the modified tetrahedron method (Blöchl et

al., 1994) for the BZ integration, 72 specific number of k-points are taken in the irreducible

partition of BZ (2000 k-points in the full BZ). The total energy calculation is also performed

with larger k-points and found negligible differences in the total energy computed using 2000k-

points. These kinds of variables assure excellent convergence for total energy.

5.3 Results and Discussions

5.3.1 Crystal Structure Stability

Ternary HH compounds, often referred as ternary intermetallic compounds having the

chemical formula XYZ with stoichiometry 1:1:1 crystalize in the face centered cubic C1b

structure with the space group F-43m (No. 216) (Nanda and Dasgupta, 2003). These HH

compounds can be derived from the L21 structure of a FH alloy X2YZ by omitting the one X

element, where X is the transition metal element and Y may be either transition metal or a rare-

earth metal and Z is from the main group element. Three phases α, β, and γ can be found for

the XYZ HH alloys because, in the unit cell of the HH alloy, three different atomic

arrangements are possible. Crystal structure of the HH FeVGe is shown in Fig. (5.1), consisting

of three interpenetrating, face-centered-cubic sub-lattices, which are occupied by Fe, V and Z

elements.

64

Table 5.1 Atomic arrangement of atoms X, Y, and Z in α, β and γ phases. The 4d position is empty.

Phase 4a (X) 4b (Y) 4c (Z)

α (1

4,

1

4,

1

4) (0, 0, 0) (

1

2,

1

2,

1

2)

β (0, 0, 0) (1

2,

1

2,

1

2) (

1

4,

1

4,

1

4)

γ (1

2,

1

2,

1

2) (

1

4,

1

4,

1

4) (0, 0, 0)

Fig. (5.1) The unit cell of cubic C1b-type structure for the HH FeVGe in α-phase

65

Atomic arrangement of the Studied HH FeVZ materials are described in Table 5.1. To

find out the lattice constant, bulk modulus and energy deviations as a function of volume,

geometrical optimization of HH alloys having generic formula FeVZ (X= Si, Ge, Sn) C1b -

type structure have been performed by using the Murnaghan's equation of state (Murnaghan,

1944a). Total energy as a function of volume is plotted in Fig. (5.2) for three possible phases

α, β, and γ, to reveal the accurate atomic arrangement of atoms in a unit cell which is very

essential because some studies show that nature of bond existing between the neighboring

atoms strongly influences the physical properties (Casper et al., 2012; Graf et al., 2011).

Therefore, the correct position of atoms is determined by minimizing the energy as a

function of volume at their equilibrium lattice constant. The three possible phases of the HH

FeVZ (Z= Si, Ge, Sn) alloys and position of these atoms for each phase (α, β & γ) are given in

Table (5.1). The Fig. (5.2) shows that α-phase is more favorable than other β and ɤ phases

because it has the lowest minimized energy. These results show that given compounds reside

in the α-phase.

To determine the magnetic ground state at the most stable structure (α-phase), both

spins polarized (magnetic) and spin un-polarized NM calculations are also performed. The HH

FeVGe as a prototype, for the FM and NM states as a function of volume, is shown in Fig.

(5.3), which is clearly indicating that the magnetic state has the lower energy as compared to

the NM state and therefore, is more favorable. Computed structural parameters such as

equilibrium lattice constant a(Å), total energy and magnetic moment at the three different

phases (α, β, γ) for the three HH FeVZ (where Z= Si, Ge, Sn) compounds in the FM state are

listed in Table 5.2, Moreover, the partial magnetic moments for the α-phase are also arranged

for the HH FeVZ (where Z = Si, Ge, Sn) in Table 5.3.

5.3.2 Electronic Properties

To explore the electronic properties of the FeVZ (where Z= Si, Ge, Sn) at equilibrium

volume, spin polarized calculations have been studied. The electronic and magnetic properties

of the FeVZ HH alloys are discussed in this section and we will compare our GGA outcomes

with the state-of-art mBJ-GGA results. It is already known fact that mBJ-GGA computations

only effects the electronic properties of the compounds that are underestimated or even

overestimated along with GGA or LDA calculations.

66

Fig. (5.2) Total energy as a function of volume for FeVGe in different phases (α, β, γ) of atomic

positions.

Fig. (5.3) Total energy as a function of volume for the HH FeVGe in α-phase for the magnetic

and NM states.

67

Table 5.2 Atomic optimization of the HH FeVZ alloys at the α, β and γ phases, a(Å) is the

lattice constant. Etot and µtot are the total energy and magnetic moment per formula unit

respectively.

Phase Material Lattice

Constant

(Å)

Energy

(Ry)

Magnetic

moment

(µB/unit cell)

Physical

Nature

α

FeVSi 5.46 -8642.44 1

HM FeVGe 5.58 -8642.48 1

FeVSn 5.90 -16802.51 1

β

FeVSi 5.61 -5024.32 3.45

Metallic FeVGe 5.72 -8642.37 3.55

FeVSn 6.13 -16802.37 3.97

γ

FeVSi 5.54 -5024.29 0.52

Metallic FeVGe 5.70 -8642.35 0.77

FeVSn 6.07 -16802.41 0.71

Table 5.3 Total and partial magnetic moments (µB) of the HH FeVZ (where Z=Si, Ge, Sn)

compounds in the α-phase at the equilibrium lattice constant.

Compound The magnetic moment of individual atoms (µB) µtot

(µB) Fe V Z

FeVSi 1.45 -0.45 0.012 1.0

FeVGe 1.84 -0.80 0.01 1.0

FeVSn 1.40 -0.41 0.011 1.0

68

The plots of the total DOS and partial DOS of the individual atoms of the HH FeVZ

(where Z= Si, Ge, Sn) compounds are only presented in α-phase at the optimized lattice

constant as shown in Fig. (5.4). We have not shown some states such as s and p states of Fe

and V because their contribution to the total DOS is very small. From Fig. (5.5), it can easily

be visualized that total DOS is mainly contributed by the 3d states of Fe and V while p state of

Ge near the EF makes the most contribution to the total DOS which is also in consistent with

previous HH transition-metal alloys [48, 49]. The d-orbital split up into two d-eg and d-t2g

orbitals. A small energy gap is found in the spin up channel due to the major contribution of

d-t2g orbitals of Fe and V atoms which have contributed more than d-eg orbitals of Fe and V.

The band d-t2g is dominated near the Fermi level (EF).

On the contrary, in the spin down channel, the p orbitals of the Z atom cross the EF,

leading to a metallic character for all three compounds. The most part of d-state of Fe in the

spin up channel is positioned around -2.0 to -1.2 eV, whereas, in the spin down channel, this

state is situated a little up around -1.8 to -0.8 eV, but d-states of V atom prevail in the energy

range from -1 to 0.3 eV. The p state of Z atom is quite symmetrical in the spin up directions

and crosses EF a little in the spin down the channel with a little share to the magnetism. It is

also revealed from the Fig. (5.5), that hybridization occurs between the 3d states of Fe and V

atoms. Among all the three atoms in a compound, the most part of the µtot is contributed by

Fe-atom.

The different values of the physical properties of the HH FeVZ (Z=Si, Ge,

Sn) such as, valence band maxima (eV), conduction band minima (eV), EBG (difference

between the valence band maxima to the conduction band minima) and EHM (which is the

minimum energy required to flip the electron spin across the EF from valence band maxima),

physical nature of the material and band transition calculated with both GGA and mBJ

potentials, are given in Table 5.4.

The spin up DOS has an EHM of 0.16, 0.21 and 0.02 eV for the HH FeVSi, FeVGe and

FeVSn materials respectively and show the semiconducting nature. So, in consequence, at the

equilibrium lattice constant for the HH FeVZ (Z = Si, Ge, Sn) alloys in α-phase, an ideal 100%

SP of the conducting electrons has been resulted because there appears a gap around EF in the

spin up state and at the same time DOS peak also crosses the EF in the spin-down state.

69

Fig. (5.4) Spin-dependent total and partial DOS of HM HH (a) FeVSi (b) FeVGe (c) FeVSn at

equilibrium lattice constant at the α-phase. EF is set at zero. The top portion (spin-up) displays

the majority-spin channel and the lower portion (spin-down) is for the minority spin channel.

Solid and dotted lines show the DOS’s of GGA & mBJ-GGA potential respectively.

70

Table 5.4 Different physical properties of HH FVX (Si, Ge, Sn) at the equilibrium lattice

constant in the α-phase. VXC is the exchange correlation potential, VBM is the maximum value

of the valance band, and CBM is the minimum value of the conduction band, EBG is the energy

band gap, EHM is a half-metallic gap. The transition between the bands and nature of compound

is also given

Material VXC VBM

(eV)

CBM

(eV)

EBG

(eV)

EHM

(eV)

Magnetic

moment

(µB)

Band

transition

Physical

State

FeVSi

GGA

0.10

0.67

0.57

-----

0.92

W X

Nearly

HM

mBJ -0.16 0.72 0.88 0.16 1.00 W X HM

FeVGe

GGA -0.05 0.79 0.84 0.04 1.00 L X HM

mBJ -0.21 0.61 0.82 0.21 1.00 T X HM

FeVSn

GGA

0.07

0.72

0.65

-----

0.98

T X

Nearly

HM

mBJ -0.23 0.60 0.83 0.23 1.00 T X HM

71

Computed results also suggest that p-state of Z-atom has the lowest part in the valance

band in both majority and minority spin states. In the locality of the EF, d-state of Fe and p-

state of Z atom point out the certain dominance showing the origin of the µtot will arise from

Fe and Z atoms. Also, the negative magnetic moment for V represents the AFM alignment of

the magnetic moment of V with Fe. There is large splitting near EF due to the Fe and Z-atoms

and splitting causes the appearance of the energy gap in the minority spin channel (in the spin-

up state). It also reveals that Fe and Z-atoms governed the energy gap in the spin up state.

Band structure calculations must be carried out very carefully because, for the

prediction of HM ferromagnetism and magnetic properties of the HH compounds, electronic

structure plays an important role. The band structures for all the magnetic compounds of FeVZ

with PBE-GGA and mBJ-GGA potentials are calculated and presented in Figs. (5.5-5.7), at

their equilibrium lattice constants in the α-phase. Left side shows the spin up (majority-spin)

state and the right side shows the spin down (minority-spin) state. It can clearly be noticed that

for all the HH FeVZ compounds, the minority spin state shows no semiconducting gap and is

of a metallic nature, whereas the majority spin state shows the semiconducting behavior.

When GGA potential is employed to calculate band structures for the FeVGe HH

compound, which shows that it is truly HM because electronic states in the minority spin

channel depicting the metallic behavior, however, in the majority spin channel, there exist an

EBG of 0.84 eV and electronic state do not cross EF. The band structures of FeVSi and FeVSn

compound calculated with PBE-GGA potential show that these compounds are nearly half

metals because in the spin-up state very little part of the valance band crosses the EF.

To improve these results obtained from PBE-GGA, mBJ-GGA potential is employed.

From PBE-GGA calculations, only HH FeVGe is an HM compound but when calculations are

made from mBJ-GGA potential, it is observed that valance bands are now shifted downwards,

and conduction bands are shifted upwards for all the FeVZ compounds. The values of both

EBG and EHM are also increased and now, all these compounds are truly HM materials.

5.3.3 Magnetic Properties

The total and partial magnetic moment µtot and magnetic moment of the individual

atoms (in the units of µB) for the HH FeVZ (where Z=Si, Ge, Sn) per formula unit cell for the

α-phase are summarized in Table 5.4.

72

Fig. (5.5) Spin polarized band structure of the HH FeVSi for the α-phase at equilibrium lattice

constant. Solid and dashed lines denote for the GGA and mBJ-GGA potential respectively.

Arrow head points the spin up and spin down direction.

73

Fig. (5.6) Spin polarized band structure of the HH FeVGe for the α-phase at equilibrium lattice



74

Fig. (5.7) Spin polarized band structure of the HH FeVSn for the α-phase at equilibrium lattice



75

To understand the semiconducting gap, Fig. (5.8) illustrates the spin-polarized band

structure of the HH FeVGe (up-state) in the α-phase at the equilibrium lattice constant. Band

1 is of the s-state of the Ge, which has the lowest part in the valance band for both majority

and minority spin states. Bands 2-4 and 12-14 are because of the p-state of Ge whereas bands

3-6 are because of d-states of the Fe and 7-11 consists of d-states of V.

The d-orbitals further splits up into double degenerated d-eg(2) and triplet degenerated

d-t2g(3) states due to the crystal field effect. Bands 7-9 at Г are because of the d-t2g states of

the Fe atom below EF. Above EF, bands 10 and 11 located at X are due to the d-eg states of the

V atom. Bonding and antibonding states are formed because these triplet d-t2g states of Fe

interact with the sp states of V atom. It means that triply degenerated d-t2g state of Fe and

doublet degenerated the d-eg state of V in the spin up channel should be occupied as in the spin

down channel, but by the exchange interaction, electrons get depleted in these occupied states

and become unoccupied and govern the semiconducting gap.

5.3.4 Half-Metallic (HM) Robustness

The HM robustness is the transition of a material from HM to pure metallic nature.

Finally, for the useful applications of HH alloys in the spintronic, HM stability for the FeVSi,

FeVGe, and FeVSn compounds is explored over a wide range of lattice constant. As thin films

or multiple layers of HM materials are used to grow on a suitable substrate for spintronic

devices, therefore, the lattice constant of the deposited thin films may change, and this can

destroy the half-metallicity of the HH materials. Hence, it is very essential to know how far

lattice constant of the HH FeVSi, FeVGe, FeVSn materials should be varied so that they keep

their half-metallicity.

Due to this reason, the relationship between the µtot and the spin magnetic moment of

Fe, V, and Z atoms and its reliance on the lattice parameters are shown in Fig. (5.9). It can be

revealed that as lattice parameter of FeVZ (Z= Si, Ge, Sn) compounds are extended or

contracted from their theoretical equilibrium lattice constant, the hybridization between the Fe

and V atoms changes. For all the three compounds, when the lattice parameter is boosted, it

increases the magnetic moment of the Fe and decreases the magnetic moment of the V but the

µtot per unit cell changes slightly and remains approximately at 1 µB, which is an integral

multiple of Bohr magnetron.

76

Fig. (5.8) Band structure of the HH FeVGe compound with mBJ potential of α-phase at

equilibrium lattice constant. The different colors show the s, p and d orbitals of atoms.

77

Fig. (5.9) Magnetic moment as a function of lattice constant of the HH (a) FeVSi, (b) FeVGe

& (c) FeVSn materials

78

The HH FeVSi, FeVGe, and FeVSn materials retain their HM property within the

lattice constant range of 5.25Å to 5.75Å, 5.18Å to 5.8Å and 5.20Å to 5.90Å, respectively. i.e,

EF remains in the gap and these alloys keep their half-metallicity when the lattice constants of

FeVSi, FeVGe, and FeVSn are contracted and extracted up to 3.84% to 5.31%, 3.91% to 5.91%

and 3.94% to 11.8% respectively, from their theoretical equilibrium lattice constant.

79

CHAPTER 6

Theoretical Investigations of Half-Metallic Ferromagnetism in

New Half-Heusler YCrSb and YMnSb Alloys Using First-Principle

Calculations.

6.1 Introduction

To meet the essentials of the advance technological applications, the search for the best

materials in general and for spintronic applications is a challenge. Spin-polarized FM materials

are generally supposed to be the best replacements for conventional materials (Bhat et al.,

2015). The quest for brand-new materials in the field of spintronic has guided towards HA in

the last three decades due to their ability to be strong candidates for spin based electronic

materials. The important part regarding spintronic is a way to obtain spin-polarized charge

carriers.

HMFs are a type of brand new material because of their distinctive characters and tend

to be probably the most essential components designed for spintronic (Umamaheswari et al.,

2014). HMFs have attracted considerable interest within last three decades due to their unique

property of possessing a semi-conducting behavior in one spin direction with a narrow gap at

the EF producing 100% polarization at the EF and metallic behavior in other spin direction.

HMFs will be appealing materials that can result in high performance applications in

spintronics devices, as a source of spin polarized charge carriers injected, such as spin field-

effect transistor (spin-FET), spin light emitting diode (spin-LED) along with tunneling devices

(Huang et al., 2014).

HMFs with HH structure offer the great possibility of integrating magnetic devices into

SC technologies and potential applications in spintronics due to their structural resemblance to

the zinc-blende phase and relatively high value of TC. In 1983, de Groot et al.(De Groot et al.,

1983) initially predicted the HM ferromagnetism by exploring the band structure calculations

of Mn-based materials in semi-Heusler NiMnSb, which is right now more successful to be

synthesized experimentally with single crystalline nature.

80

Several studies relevant to HMFs are already expected theoretically and many of HMFs

are validated experimentally. Half-metallicity is located in Heusler compounds (Alijani et al.,

2011; Chatterjee et al., 2010; Jaiganesh et al., 2010; Ko et al., 2010; Liu et al., 2008; Luo et

al., 2011) and several other kinds of materials which include FM metallic oxides (Jedema et

al., 2001; Li et al., 2009; Soeya et al., 2002; Song et al., 2009b), nanostructures (Son et al.,

2006) binary TM pnictides (chemical compounds) as well as chalcogenides acquiring zinc-

blended and rock-salt structural arrangements (Ahmadian and Alinajimi, 2013; Dong and

Zhao, 2011; Galanakis and Mavropoulos, 2003; Gao et al., 2007; Liu, 2003).

Numerous studies have already been conducted on these types of materials and plenty

of them have become HMFs. But often an experimental synthesis of these materials at the room

temperature is difficult, as half-metallicity is lost due to very small EHM and very large

magnetic moments arises. Small EHM and large magnetic moment mean high stray field. The

EHM would frequently vanish in each of these HH materials when strain mismatch rises at the

interface with the traditional SCs.

In addition, HM materials having a large magnetic moment are not ideal for spintronic

practical applications, since the big magnetic moment indicates higher stray fields as well as

large energy deficits. This deficiency inspires us to find brand new HM alloys that have a

modest magnetic moment and larger EHM. The outcomes offered by this study might clarify

the applications of these HH materials in the arena of spintronics. Structural, electronic and

magnetic properties of HH YCrSb and YMnSb are explored in this study for the sake of their

novel applications.

6.2 Computational Details

To cope with the exchange and correlation potential, all computations are executed

within density function theory (DFT) using the generalized gradient approximation (GGA)

available as Perdew–Burke–Ernzerhof (PBE) functional (Perdew et al., 1996a). A cycle of the

self-consistent scheme is performed to find out the structural and electronic properties of

YCrSb and YMnSb HH materials by solving the Kohn–Sham equations (Sham and Kohn,

1966) through utilizing the full-potential linearized augmented plane wave method (FPLAPW)

(Andersen, 1975) as implemented within the WIEN2K simulation code (Schwarz et al., 2002).

A k-point mesh of 15×15×15 is chosen for the calculations of these HH materials each

with muffin-tin sphere radius of 2.5 a.u, for Y, Cr(Mn) and Sb atoms, respectively, and the

81

value of RMT × Kmax is set to be 9. Expansion of site-centered potentials and densities is taken

with the angular momentum up to lmax = 10. The particular BZ integration is completed from

the standard tetrahedron approach (Jepson and Anderson, 1971). For the two consecutive

computations, the actual convergence criterion in this self-consistent information about ionic

relaxations is 10-5 eV/unit cell.


6.3.1 Structural Arrangements and Stability

The HH alloy with general formula XYZ has only one magnetic sublattice, where X

and Y are the transitional metals and Z is the main group element. HH materials belong to a

family relating to traditional SCs, for instance, Si or GaAs and crystalize into the non-

centrosymmetric cubic MgAgAs-C1b structure (space group F-43m, No. 216) having 1:1:1

stoichiometry, which is ternary arranged different from the CaF2 and can be derived from the

tetrahedral ZnS type structure (Graf et al., 2011).

The Wyckoff positions of the three interpenetrating fcc lattices are 4a(0, 0, 0), 4b(𝟏

𝟐,

𝟏

𝟐,

𝟏

𝟐), and 4c(

𝟏

𝟒,

𝟏

𝟒,

𝟏

𝟒), and the 4d(

𝟑

𝟒,

𝟑

𝟒,

𝟑

𝟒) site is empty. In essence, X, Y and the Z atoms can occupy

these Wyckoff positions 4a, 4b and 4c sites, respectively. Three unique phases (XI, XII, XIII)

are possible for X, Y and Z atoms by changing these atomic positions in a unit cell, for instance

XI, XII, and XIII phases can be organized at distinct Wyckoff positions (Helmholdt et al., 1984).

Atomic layout for each phase is presented in Table 6.1. For an illustration, the crystal structures

of HH YCrSb alloy for three possible atomic arrangements are shown in Fig. (6.1).

Exploration of XYZ materials within three feasible arrangements is essential because

a few experimental types of research display that the composition associated with HH materials

rely on the atomic disorder (Aliev, 1991; Helmholdt et al., 1984; Ishida et al., 1997). The

crystalline framework of C1b-type structure associated with this kind of material can be

reviewed properly from Refs. (Gruhn, 2010; Umamaheswari et al., 2013). In our latest

information, there is no experimental nor theoretical report so far, relating to both YCrSb and

YMnSb HH materials. Murnaghan’s equation of state (Murnaghan, 1937) is utilized to find

out the lattice constants. Prior to studying electronic and magnetic properties, stabilities of the

crystal structure of YCrSb and YMnSb are checked by optimizing the total energy as a function

of volume for all the three possible states.

82

Table 6.1 The Site preferences of X, Y and Z atoms in three atomic arrangements XI, XII and

XIII in the C1b HH structure. The 4d site is empty.

Phase 4a (0,0,0) 4b(𝟏

𝟐,

𝟏

𝟐,

𝟏

𝟐) 4c (

𝟏

𝟒,

𝟏

𝟒,

𝟏

𝟒)

XI Z X Y

XII X Y Z

XIII Y Z X

Fig. (6.1) Conventional unit cells of HH YCrSb alloy in the MgAgAs (C1b) structure for the

three distinct XI, XII and XIII atomic arrangements.

XI

Structure

XII

Structure

XIII

Structure

83

Variations of total energy with volumes of HH YCrSb and YMnSb compounds for all

the three possible XI, XII and XIII phases are shown in Fig. (6.2). It is obvious that XI

structures for both the compounds obtain the least minimized total energies compared with

those of the other XII and XIII feasible structures. Consequently, it is concluded that XI

structure is the most preferred phase because of its least minimized total energy and all further

computations are performed at this specific ground state phase.

The outcomes are ascribed to the following reasons: (a) within the XI structure, Cr sorts

the nearest neighbor (NN) surrounds with both Y and Sb, although Sb has both Cr and Y as

NN pairs for the XII structure; (b) the size of Y is than that of Cr. Therefore, a strong bond is

established between Cr and Y resulting in the minimum total energy in the XI structure.

In the XIII structure, Sb is not in the NN arrangement with the Cr. The optimized lattice

constants of the HH YCrSb and YMnSb materials for stable XI phase are 6.673 Å and 6.565

Å, respectively. For these two studied compounds with the FM state, the computed lattice

constant, total energy, bulk modulus B (in unit GPa) and first order derivative of the modulus

B´ evaluated by using unit cell volume at zero pressure for the three unique phases are detailed

in Table 6.2. Yet, no experimental data for the bulk moduli nor the lattice constant of the

studied compounds are available to be compared with the theoretical results.

Spin-polarized (magnetic phase) and non-spin polarized (NM phase) calculations are

also carried out for each of YCrSb and YMnSb compounds within the stable XI structure. The

variations of total energy with volume are presented in Fig. (6.3) respectively for the NM, FM

and AFM states, which clearly indicate that FM state is energetically more favorable than NM

and AFM states. Furthermore, the total energy difference between the NM and FM phases

(ΔEFM-NM) in stable XI-structure is given the Table 6.3.

As can be seen, the values of ΔEFM-NM are negative for both the studied compounds,

implying that the FM phase of such materials is much steadier than NM phase. Therefore, the

next discussion provides the actual FM phase. To confirm that the studied materials can

possibly be synthesized experimentally, formation energy (𝐸𝑓𝑜𝑟) is also taken into

consideration for the YCrSb and YMnSb materials which can be explained by using the

following equation:

84

Fig. (6.2) Variations of computed FM total energy with volume per unit cell for the three

feasible atomic arrangements XI, XII and XIII of both HH (a) YCrSb (b) YMnSb with MgAgAs

(C1b) structure.

85

Table 6.2 Values of optimized lattice constant aopt (Å), the bulk modulus B (GPa), the pressure

derivative of the bulk modulus B, the total energy (Ry) of the HH YCrSb and YMnSb

materials.

Table 6.3 Calculated values of formation energy (𝐸𝑓𝑜𝑟) (in eV) per formula unit, spin-up

energy band gap EBG (eV), half-metallic gap EHM (eV), the energy difference between FM &

NM states ΔEFM-NM (eV) and the spin-polarization SP (%) for YCrSb and YMnSb HH

materials.

(X)4a:(Y) 4b:(Z) 4c EBG

(eV)

EHM

(eV)

ΔEFM-NM

(eV)

𝑬𝒇𝒐𝒓

(eV)

SP (%)

YCrSb 0.78 0.43 -1.68 -3.557 100

YMnSb 0.40 0.13 -1.19 -6.770 100

Table 6.4 Calculated values of total and local magnetic moment (µB) of the individual atom

and interstitial site for HH YCrSb and YMnSb materials.

Compound Y

(µB)

Cr

(µB)

Sb

(µB)

Interstitial

(µB)

µ𝐭𝐨𝐭

(µB)

YCrSb 0.17336 3.41594 -0.06046 0.47179 4

YMnSb -0.00442 2.94109 -0.02969 0.09358 3

Compound Structure aopt

(Å)

B

(GPa)

B´ Etot (Ry) Half-

metallicity

YCrSb

XI 6.673 64.6 4.71 -21840.5260 Yes

XII 6.839 57.8 4.44 -21840.5081 No

XIII 7.068 44.25 4.07 -21840.4419 No

YMnSb

XI 6.565 68.10 4.78 -22056.0804 Yes

XII 6.760 60.86 4.61 -22056.059 No

XIII 7.038 42.33 4.20 -22055.9851 No

86

Fig. (6.3) Variations of calculated total energy with volume of HH (a) YCrSb (b) YMnSb

materials in stable XI phase for NM, FM and AFM states

87

𝐸𝑓𝑜𝑟 = 𝐸𝑌𝐶𝑟(𝑀𝑛)𝑆𝑏 − 𝐸𝑌 − 𝐸𝐶𝑟(𝑀𝑛) − 𝐸𝑆𝑏

where 𝐸𝑌𝐶𝑟(𝑀𝑛)𝑆𝑏 is the total energy of the YCrSb and YMnSb materials calculated by the

first-principles calculations and 𝐸𝑌, 𝐸𝐶𝑟(𝑀𝑛), 𝐸𝑆𝑏 are energies of the corresponding individual

atoms. Usually, negative formation energy signifies the stableness of the compound. Formation

energies for the YCrSb and YMnSb HH materials are listed in Table 6.3. The lower value of

formation energies for the studied compounds indicate that these materials can be synthesized

experimentally.


The electronic structure affects an essential part to identify the HM properties

associated with HH materials. Band structures of the HH YCrSb and YMnSb alloys are shown

in Figs. (6.4) and (6.5), respectively. The left panel demonstrates the spin-up (majority) state,

and the right panel indicates the bands for the spin-down (minority) state.

The different colors in Figs. (6.4 & 6.5) represent different physical meanings. They

show the contributions of s, p and d orbitals of Y, Mn/Cr and Sb atoms to electronic band

structure. They reveal the information about which orbital of the atoms in the alloy is

contributing more near the EF and which atom orbital is in the core state. They also represent

each eigenvalue along the k-path which we have previously selected during the SCF cycle.

Obviously, it can be noted that half-metallicity has semiconducting EBG around the EF

in the majority spin (spin-up) state Figs. (6.4 (a) & 6.5 (a)), and that the band cross the EF and

thus displays metallic nature in minority spin (spin-down) state Figs. (6.4(b) and 6.5(b)). For

both HH YCrSb and YMnSb materials in the majority spin channel, there are clear gaps

between EBG and EHM in the majority band. The EBG is the energy band gap which is the spacing

between the valance band maximum and the conduction band minimum, and the EHM is the

shortest distance twixt the most occupied valance band energy and the EF.

This parameter EHM possess specific significance for the half metallicity of the FM

material rather than EBG along the EF. The presence of non-zero flip gap (EHM) for both the

compounds in the majority spin channel indicates that they are true HMFs. The values of EBG,

EHM, and EF calculated for both HH YCrSb and YMnSb materials are presented in Table 6.3.

88

Fig. (6.4) Spin-resolved band structures of HH YCrSb (a) spin up (b) spin down. EF is set to

zero.

Spin-up Spin-dn

d0n

89

Fig. (6.5) Spin-resolved band structures of the HH YMnSb (a) spin up (b) Spin down. The

Fermi level, EF is set to zero.

Spin-up Spin-dn

90

It can also be seen that the band transition for the YCrSb is direct (Γ-Γ) while an indirect

band transition is found for the YMnSb (Γ-X) HH material. It can also be noted that bands near

the EF, are triply degenerate at Γ for the majority spin channel.

The number of states for each period of energy which is occupied by the specific energy

levels is usually explained by the DOS of the system. To examine the electronic natures of the

YCrSb and YMnSb materials, total and partial DOS within the magnetic phase designed for

spin-up and spin-down channel are also measured by utilizing the PBE-GGA. The DOS

graphics are displayed in Fig. (6.6) to analyze the EBG in the majority spin state of the studied

materials at the equilibrium lattice constant. The spin-dependent total and orbital electronic

DOS of the HH YCrSb and YMnSb are presented in Fig. (6.6).

Large spin splitting in these materials occurs from Cr/Mn (d-t2g) states with a small

contribution from Y (d-t2g) states. The contribution by the Sb atom near the EF is quite small

in comparison with by the Cr/Mn (d-t2g) and Y (d-t2g) atoms. Also, Sb atom has symmetrical

state below the EF having energy around -10 eV. A solid hybridization among the d-orbitals of

Y, Cr, and Mn atoms is found, which divides the d orbitals of these atoms into d-eg and d-t2g

states. A semiconducting gap is found for the majority-spin channel. It can be visualized that

states near the EF for both majority and minority spin states are mostly contributed due to the

Cr/Mn (d-t2g) and Y (d-t2g) atoms, which are comparable to various other TMs based on HH

materials (Huang et al., 2014; Huang et al., 2015).

To clarify the origin of the semiconducting gap, d-d hybridization nearby the EF can be

revealed inside Fig. (6.7). The Cr and Mn atoms are enclosed by Sb atoms, seeing them at NN

and Y as next neighbor. Both Cr and Mn 3d states split up into the triplet associated with d-t2g

states and a doublet associated with eg states because of the crystal field theory. In the majority

spin channel, the d-t2g and eg states of Mn and Cr ought to be occupied like in the minority spin

states but electrons are depleted in the majority spin state due to the exchange interaction.

These states turn out to be unoccupied and develop the semiconducting gap. Furthermore, the

electronic SP at the EF can be expressed by the following relation (Monir et al., 2015),

𝑆𝑃 = 𝑑 ↑ (𝐸𝐹) − 𝑑 ↓ (𝐸𝐹)

𝑑 ↑ (𝐸𝐹) + 𝑑 ↓ (𝐸𝐹)

where 𝑑 ↑ (𝐸𝐹) and 𝑑 ↓ (𝐸𝐹) are the densities of states at the EF for the majority and

minority spin states, respectively.

91

Fig. (6.6) Spin-polarized densities of state for the total and individual atoms at the equilibrium

lattice constant for the XI phase of the HH (a) YCrSb (b) YMnSb materials.

92

Fig. (6.7) Schematic representations of origin of a semiconducting gap in the majority

spin state in the stable XI structure for the HH YCrSb material.

93

The studied HH YCrSb and YMnSb materials have 100% SP (see Table 6.3), proving

that electrons at the EF are fully spin-polarized. That confirms the HM characteristics.


The origin of magnetic moment for the HH alloy is described in this section. The total

and individual magnetic moment of the atoms per unit cell in the unit of multiples of Bohr

magnetron for the YCrSb and YMnSb for the XI structural phase are presented in Table 6.4.

The structures of HH materials can be decomposed right into a zinc blende (ZB) substructure

along with variants within the occupancy from the interstitial lattice sites. There are three main

mechanisms (Huang et al., 2015) which govern the magnetic properties due to HM in the ZB

structure: (a) the d-states of the Cr and Mn atoms (here it can even be Y-atom) split into triply

(t2g) and doubly (eg) due to the crystal field effect, (b) bonding and antibonding states are

formed when the sp3-type state of Sb interacts with these triplet states, (c) populations of the

electrons change in the majority and minority spin channel due to the exchange interaction.

The local magnetic moments of the crystal are formed by the remaining electrons of the Cr and

Mn atoms.

Due to the resemblance of HH alloy composition to the ZB structure, the magnetic

moment arranged in Table 6.4 can be ascribed to the Mn and Cr atoms. As the HH materials

contain only one magnetic sublattice consisting of the atoms on the octahedral sites (Graf et

al., 2011), which is also indicated in Table 6.4, the Cr and Mn atoms mainly contribute to the

µtot for the studied HH materials and occupy the octahedral sites in the stable XI structure.

It can also be understood from the electronic arrangements. Electronic configurations

for the Cr and Mn are (3d)54s and (3d)54(s)2, respectively. For pure metals, Cr and Mn,

electronic spins form the magnetic moments according to the first Hund’s rule but when these

types of TMs (Cr, Mn) are made into alloys, the availability of 3d-electrons will change

because of diverse electro-negativity. In the stable XI structure, Sb is the NN for the Cr and

Mn in the HH YCrSb and YMnSb materials because of this a small charge is transferred from

Cr and Mn to Sb by leaving lots of d-electrons at Cr and Mn atoms that govern the magnetic

moments for these HH materials respectively.

94

6.3.4 Location Associated with Half-Metallicity

In the experimental fabrication of HH alloys on a substrate to make device applications,

lattice mismatch may happen due to the influence of various factors. For this “strain

engineering” technique (Lu et al., 2001) is usually used to obtain the required electrical and

physical properties of HH alloys through developing layered alloys by lattice mismatched

substrates. Therefore, it is essential to further investigate the lattice parameter strain

engineering by exploring the robustness belonging to the HM through changing the lattice

constants of these two studied materials.

The µtot and the spin moments of the Y, Cr, Mn and Sb atoms with respect to lattice

parameter are shown in the Fig. (6.8). When the lattice parameters of HH YCrSb and YMnSb

materials are expanded, the hybridization between Y and Cr/Mn decreases, which leads to the

rise in the spin moment of Cr/Mn and decrease in Y. The EF found inside the gap and the

number of majority spin states change a little in all these lattice variations. In addition, it is

also observed that by varying the lattice constants in a wide range, there is slightly change in

the overall µtot, and the overall µtot remain 4 and 3 µB for the HH YCrSb and YMnSb materials,

respectively.

It is also discovered that for the optimized equilibrium lattice constant for the stable XI

phase, the magnetic moments have integer values for both compounds, which is viewed as the

character associated with HMF. Thus, these types of substrates may be handled as ideal

applicants for the spintronic devices. Through the computations, the HM can be found to reach

up to compression and expansion of -10.1% to 3.6% for the HH YCrSb and for -12.3% to 2.7%

for the HH YMnSb material. This verifies that magnetic properties, can be tuned for these

substrates, by expanding and compressing their lattice parameters.

95

Fig. (6.8) Lattice parameter dependences of the µtot, and the spin moments of Y,

Cr/Mn and Sb atoms for the HH (a)YCrSb and (b) YMnSb, respectively.

96

Chapter 7

Physical Properties of Half-Heusler YMnZ (where Z = Si, Ge, Sn)

Compounds Via Ab-Initio Study

7.1 Introduction

Recently, HM magnets have drawn a plenty of attention due to their attainable uses in

spintronics and magneto-electronics (Hirohata and Takanashi, 2014; Žutić et al., 2004). Highly

spin-polarized magnetic materials had been popular to enhance the overall performance

associated with spintronics products for example spin filter as well as spin-valves (Inomata et

al., 2016) and have several advantages over conventional SC electronic devices such as

reduced energy usage, the higher processing speed of data, non-volatility as well as elevated

integration densities (Wolf et al., 2001). Numerous appealing materials, such as half-metals

(De Groot et al., 1983; Tanveer et al., 2015), SC (Tobola et al., 1998), magnetic shape memory

alloy(Ullakko et al., 1996), topological insulator (Chadov and Qi, 2010) and spingapless SC

(Ouardi et al., 2013) like properties happen to be present in HA.

Recently half-metallicity has been found by numerous research groups in the based on

zinc-blende SC compounds (Ahmad and Amin, 2013; Arif et al., 2012), dilute magnetic alloys

(Amin and Ahmad, 2009; Amin et al., 2011), HH alloys (Ahmad and Amin, 2013; Hamidani

et al., 2009; Huang et al., 2014; Tanveer et al., 2015), QH alloys (Rasool et al., 2016; Wang et

al., 2017a) and in the FH alloys not only theoretically (Deka et al., 2016; Gupta and Bhat,

2014; Hu and Zhang, 2017; Qi et al., 2015; Rauf et al., 2015; Yousuf and Gupta, 2017) but

also experimentally (Bae et al., 2012; Checca et al., 2017; Vivas et al., 2016). Heusler based

materials are more prominent because they have the probability of achieving higher value of

TC and their structure resemblance to the zinc-blende and diamond structures which prevail in

a large variety of known SC compounds.

Fritz Heusler in 1903, discovered that compound having composition Cu2MnAl acts

like a HM material. HM materials demonstrate absolutely distinct actions within two bands i.e.

semiconducting regarding electrons in one spin band showing a gap at the EF and exhibits

conventional metallic character in complete reverse spin alignment for the other band.

97

Considering that just one spin band is conducting, it is possible to picture a tool in

which the digital conduction might be merely switched off and on with a permanent magnetic

field inside a spin valve or even magnetic tunnel junction, similar to the electrical field-effect

products, in which the conduction is actually switched off and on, with an entrance electrode

(Behin-Aein et al., 2010). The spin–orbit coupling will be disregarded due to its tiny share for

the magnet attributes.

The presence of energy Egin majority spin band results in a 100% SP at the EF and

therefore the completely spin-polarized current ought to be achievable within these HM HA

making the most of the actual effectiveness and performance associated with magneto-

electronic devices (De Boeck et al., 2002a; De Boeck et al., 2002b) and capable of presenting

amazing attributes such as shape-memory alloys as well as tunable topological insulators

having a higher possibility of spintronics, power systems, half-metals, multi-feroics, high

temperature ferri and ferromagnets and magneto-caloric programs(Felser et al., 2015).

Materials regarding state-of-the-art applications turn out to be progressively complicated and

nowadays electronic industry mostly depends on elemental SC Si and Ge.

Latest developments in physics, chemistry, and material science empowered the

realistic layout of the fresh usages regarding various advanced technology. FH alloys and HH

alloys which show HM properties possess a plethora of probable prospective applications

within spintronics, data storage, magnetocaloric and as permanent magnets. So far, considering

the ab-initio electronic structure calculations, numerous compounds were anticipated proposed

to be HMFs. A breakthrough discovery in the half-metallicity with most materials owned by

HH family has drawn substantial interest from the scientists (Kübler et al., 1983).

Yet, HM properties are hard to be maintained at ambient conditions except if there is a

big EHM and this gap need to be effective towards diverse lattice constants. To design the shape

memory combination, not only the reduced value of cohesive energy is required to strain

effortlessly but also the reduced value of formation energy (Efor) guarantees that these

compounds could be experimentally synthesized. As compared to the FH alloys, a very few

HM HH composites can be synthesized experimentally. Although, some ternary HH

compounds like YPtBi and YAuPb are found to be non-trivial topological insulators with zero

EBG while YAuSn, YPtSb, YNiBi, YPdSb, and YPdBi are found to be trivial band insulators

(Al-Sawai et al., 2010).

98

In one of our previous theoretical work, YMnSb and YCrSb also show HM properties

(Sattar et al., 2016a). This research is aimed to investigate the magnetic, electronic and

transport properties of HH YMnZ (Z= Si, Ge, Sn) alloys to identify at which lattice constant

range the HM character is maintained along with high magnetization. The study has predicted

some important results above and beyond 100% SP and half-metallicity in these alloys. The

present investigation also aims to evaluate theoretically the thermoelectric efficiency of HH

YMnZ alloys by calculating the Seebeck coefficient, electrical conductivity, and thermal

conductivity.

Due to increase in demand of thermal-electrical energy conversion, the thermoelectric

properties of various materials such as clathrates, filled-skutterudites, layered cobalt oxides,

and HH alloys have been studied (Mohankumar et al., 2015). Particularly, in HA, the

thermoelectric properties of many HH materials have been investigated theoretically and

experimentally (Hu and Zhang, 2017; Mikami et al., 2013; Xu et al., 2011; Yadav and Sanyal,

2015; Yousuf and Gupta, 2017). The advantage of HA is that one can play with the

thermoelectric properties by doping easily.

In the light of the above, in this chapter, structural stability, electronic, magnetic and

transport properties of the YMnZ materials are investigated based on ab-initio calculations

with the HH structure which has the general formula XYZ and crystallizes in the space group

F-43m (No. 216). We have theoretically investigated to identify at which lattice constant range

the HM character is maintained along with high magnetization. The present investigation also

aims to evaluate theoretically thermoelectric efficiency of YMnZ HH alloys by calculating the

Seebeck coefficient, electrical conductivity, and thermal conductivity. The present work is

totally original.

The remaining chapter is sorted out as follows: In section 7.2, method and

computational points of interest are discussed. In section 7.3, the crystal structure and stability

of HH alloys are portrayed and the fundamental results are elaborated.

7.2 Computational Insights

Geometrical optimization and also electronic structural computations are performed by

using the density functional theory (DFT) which has been carried out by means of self-

consistent full potential linearized augmented plane wave (FP-LAPW) method accomplished

through Wien2K simulation code (Blaha et al., 2001b).

99

The exchange-correlation outcomes have been explained with the parameterization

from the generalized gradient approximation (GGA). In order to explore the electronic and

magnetic properties with accurate Eg, the state-of-art mBJ local density approximation method

offered by Tran and Blaha (Tran and Blaha, 2009) is utilized. In present calculations, the value

of Rmt×Kmax is selected to 9 that decides the good convergence for the matrix size in which

Kmax is the plane wave cutoff energy and Rmt is equivalent to the minimum value of muffin-tin

sphere radii. For the denser BZ sampling, a k-point mesh of 21×21×21 in the first BZ (10000

k-points in full BZ) is chosen. For the convergence requirements, total energy and force have

been preserved as 10-5 eV and 10-4eV/Å, respectively.

7.3 Results and Discussions

7.3.1 Structural Properties

Both theoretical and experimental (Fecher et al., 2005; Miura et al., 2004a; Miura et

al., 2004b; Picozzi et al., 2004; Pierre et al., 1997; Wurmehl et al., 2006) research work about

Heusler compounds acknowledge that their structural arrangement has a significant effect on

their physical properties. This kind of robust relationship among the structural arrangement of

HA and their useful properties require an intensive structural depiction when their physical

attributes are usually reviewed.

The HM YMnZ alloys are characterized in the HH with a face-centered cubic (fcc) C1b

phase having space group of F-43m (Feng et al., 2014) which are directly relevant to zinc-

blende and diamond structure. The crystalline framework (C1b) of this kind of materials can

be reviewed properly in the literature (Gruhn, 2010; Sattar et al., 2016b).

Possibly, there are three unique sorts of atomic placement in the conventional cubic

unit cell X-type1: 4a(0,0,0), 4b(½, ½, ½), and 4c(¼, ¼, ¼); X-type2: 4c(¼, ¼, ¼), 4a(0,0,0),

4b(½, ½, ½), and X-type3: 4b(½, ½, ½), 4c(¼, ¼, ¼) and 4a(0,0,0) as suggested by the T. Graf

et al (Graf et al., 2011) and placed in Table 1. Just to illustrate, the conventional cubic unit cell

of the HH YMnSi material in the three different types is pointed out in Fig. (7.1). In our finest

details, there is not a single experimental or hypothetical review performed on these alloys.

Thus, we calculated the lattice constant by using Murnaghan equation of state

(Murnaghan, 1944b) within GGA with a specific goal to discover the ground state properties.

For the initial first stage, to search for stabilize structural layout along with the correct magnetic

state with an objective to determine the exact ground state of the HH YMnZ alloys.

100

Fig. (7.1) The conventional cubic unit cell of the HH YMnSi at the diverse atomic

arrangement X-type1, Xtype2, and X-type3.

101

Table 7.1 Inequivalent atomic arrangement inside the C1b-type framework in which atoms

placed on Wyckoff positions 4a and 4b make a ZnS-type sublattice whereas the octahedral

holes occupied by the atoms on 4b.

Phase 4a (0,0,0) 4b (½, ½, ½) 4c (¼, ¼, ¼)

X-type1 X Y Z

X-type2 Z X Y

X-type3 Y Z X

Table 7.2 Computed total energy (Ry/f.u.) at three unique structural phases (X-type1, X-type2,

X-type3) with NM, magnetic (FM) and AFM states of the HH YMnZ (Z=Si, Ge, Sn) materials.

Also, predicted lattice parameter a (Å), bulk modulus B (GPa) and the formation energy Efor

(Ry) of these studied materials is given in the preferred FM state.

Compound Structure Etot (Ry/f.u.) a (Å) B

(GPa)

Efor

(Ry)

NM FM AFM FM FM FM

YMnSi X-type1 -9668.590462 -9668.83599 -9668.688 6.4098 68.79 0.8761

X-type2 - 9668.53982 -9668.67907 -9668.614 6.6618 49.28 -

X-type3 -9668.57475 -9668.79779 -9668.641 6.3085 72.47 -

YMnGe X-type1 -13286.87857 -13286.9691 -13286.946 6.4890 68.15 0.8187

X-type2 -13286.7079 -13286.8299 -13286.798 6.7398 47.37 -

X-type3 -13286.8674 -13286.9327 -13286.905 6.4025 66.86 -

YMnSn X-type1 -21446.916512 -21447.0261 -21447.001 6.8482 57.44 -

X-type2 -21446.976111 -21447.0440 -21447.027 6.6752 62.54 0.8314

X-type2 -21446.802887 -21446.9325 -21446.902 7.0291 42.26 -

102

For this, we performed minimization of energy as a function associated with a lattice

constant towards three distinctive conceivable site occupation for each NM, FM as well as

AFM structures. The acquired results are demonstrated in Figs. (7.2 & 7.3).

Computed optimized lattice constant ɑ (Å) combined with bulk modulus B (GPa) and

the total energy Etot (Ry) within their distinctive structural phases (X-type1, X-type2, and X-

type3) as well as various NM and magnetic states (FM, AFM) for the HH YMnZ materials are

listed in Table 7.2. The X-type1 structure with an FM ground state for both studied compounds

have the most reduced energy among the three conceivable structures in the respective different

magnetic configurations and is presented as the ground state structure which is clearly visible

in the Figs. (7.2 & 7.3).

As the atomic radii of Sn is greater than the Si/Ge and Z (Si, Ge and Sn atoms) share

the same group in the periodic table, the optimized lattice constant of HH YMnSi is smaller

than the HH YMnGe and YMnSn alloy, as a result, bulk modulus reduces due to the weak

hybridization among the atoms. Our results are the DFT predictions as there is no experimental

or theoretical evidence present regarding the lattice constant and bulk modulus for these

studied compounds.

To examine the stableness of these DFT investigated HH YMnZ studied compounds,

the estimation of the formation energy (EFor) is important which decides whether a compound

can be synthesized experimentally or not. It can be defined as the adjustment in energy when

the compound is shaped through its constituent components to their compound form and can

be measured as,

EForYMnZ = Etot

YMnZ - EY - EMn – EZ

where EtotYMnZ are the first-principles calculated equilibrium total energies of the HH YMnZ

compounds per formula unit. The EY, EMn, EZ are the equilibrium total energies for each atom

of the natural distinct elements Y, Mn and Z (Si, Ge, Sn) within their individual stable state,

respectively. It is observed that Y take the hcp structure, while Mn crystallizes in bcc along

with the Si, Ge and Sn prefers fcc diamond structure.

103

Fig. (7.2) Total energy to be functionality connected with volume inside three unique atomic

positions X-type1, X-type2 and X-type3 for the HH (a) YMnSi, (b)YMnGe and YMnSn alloys.

These curves represent the FM state.

104

Fig. (7.3) Total energy to be functionality connected with volume inside ternary magnetic

states (NM, FM, and AFM) for the HH (a) YMnSi, (b) YMnGe and (c) YMnSn alloys.

105


In this segment, the electronic and magnetic properties for both studied HH

materials are examined through GGA and GGA-mBJ for the comparison between them.

The GGA-mBJ predicts energy EBG with favorable accuracy and work of Guo et al. (Guo

and Liu, 2011) on FM materials are in phenomenal concurrence with experimental

outcomes.

Spin-dependent band structure on the optimized relaxed lattice constant with high

symmetry guidelines regarding the first BZ in the stable X-type1 structural phase of HH

YMnSi and YMnGe alloys have been computed and exhibited in Figs. (7.4 &7.5) whereas

the band structure of the HH YMnSn is shown in Fig. (7.6) at their equilibrium lattice

constant with the most stable phase of X-type2.

For GGA computations, it is clearly visible from these plots that the physical nature

of YMnSi is of metallic and YMnGe and YMnSn are half-metal. The GGA-mBJ

estimations reveal that spin-down states (minority bands) stay metallic but in the spin-up

states (majority-bands), valence band maxima (VBM) shifts downwards to the reduced

energy area and conduction band minima (CBM) is moved upwards towards the greater

energy region comparatively to the EF and thus displaying the EBG.

To demonstrate the character associated with the electronic structure, we have

additionally plotted the computed spin-polarized total as well as the partial DOS. The Fig.

(7.7) demonstrate the computed spin-dependent total DOS and atom projected partial DOS

for the two HH YMnSi and YMnGe materials with the X-type1 structure and for the HH

YMnSn material with the X-type2 structure at the optimized lattice constants.

It can be viewed from the Fig. 7.7 (a, b & c) that the overall general features of the

DOS for the three studied materials are comparable because of the likeness of their crystal

framework and chemical ambiances. It has been observed that DOS acquired from GGA

and mBJ adopts almost the similar pattern with a difference of gap.

It can be easily visualized from the total DOS that HH YMnZ are HM materials

because EF falling in the semiconducting gap in the spin-up channel with EBG is found of

0.4214 eV, 0.5761 eV and 0.5903 eV for the HH YMnSi, YMnGe and YMnSn compounds

respectively and shows the 100% SP for both HH materials. On the other hand, there is an

intersection at the EF for the spin down channel which strongly suggests that these materials

are true HMFs.

106

Fig. (7.4) Spin-projected band structure with the HM HH YMnSi alloy. Black solid lines

show the GGA and red dotted lines are for the GGA+mBJ

Spin-up Spin-dn

107

Fig. (7.5) Spin-projected band structure with the HH YMnGe compound. Black solid lines

show the GGA and red dotted lines are for the GGA+mBJ.

Spin-up Spin-dn

108

Fig. (7.6) Spin-projected band structure with the HH YMnSn compound. Black solid lines

show the GGA and red dotted lines are for the GGA+mBJ.

Spin-up Spin-dn

109

Besides, the partial DOS of the HH YMnSi and YMnGe materials are for the most

part involved by the Mn d-states with a little share of Y d-states electrons and it can be

obviously observed that for both materials a substantial exchange splitting exists among

the spin-up and spin-down channel due to the d-states of Mn and Y atoms.

These d-states of Mn and Y atoms are separated into eg states at the low energy and

presence of t2g states declare at the high energy due to the hybridization between them. The

s-bands are not shown in Fig. 7.7 (a, b & c) because these bands are very low in energy and

thus easily can be distinguished from other bands. It is also clear from the plot that the

lower energy region of the valance band is related to the p-bands of Z atoms. For both spin-

channels, the s and p-states are almost alike. Furthermore, it is noted that the partial DOS

of Mn 3d-orbitals represents the same tendency. It is also observed that the maximum peak

of DOS around EF is mainly linked to Mn 3d-states. This affirms that the bonding state, for

the most part, exists at the greater valence transition element Mn, as the contribution of

partial DOS for Y d-orbital is quite small when compared to the Mn d-orbitals. Symmetrical

states are found for the Y atom below and above the EF. States below and above the EF for

both spin channels are because of d-states of Mn and Y atoms, as several other TMs HH

alloys studies (Huang et al., 2014; Huang et al., 2015) suggest that states around the EF for

both spin channels are mostly contributed by the d-orbitals of the TMs.


For the HH YMnZ studied materials, the estimated total magnetic moment per unit

cell at their optimized lattice parameter is precisely 4.00 μB. The integer value associated

with magnetic moment shows the halfmetallicity of the HH alloys. The computed total

magnet moments atomic-resolved and share regarding interstitial locations inside the

crystal (interstitial magnetic moments) in the HH YMnZ compounds at their optimized

lattice constant with the stable structure X-type1are listed in Table 7.3.

It is observed that the maximum contribution in the µtot comes from Mn which is

the result of the immense exchange splitting among the majority as well as minority spin

states of Mn. It is furthermore pointed out that partial moments of the Y and Z(Si, Ge, Sn)

atoms are extremely little and their share for the overall magnetic moment is quite little

which can be noticed from the Table 7.3 as well.

110

Fig. (7.7) The total and partial DOS of the HH (a) YMnSi, (b) YMnGe and (c) YMnSn

compounds using GGA+mBJ.

111

The expression of the SP of a magnetic material can be provided by

𝑆𝑃 = 𝑁 ↑ − 𝑁 ↓

𝑁 ↑ + 𝑁 ↓

in which 𝑁 ↑ and 𝑁 ↓ are the number of spin-up and spin down states and 𝑃𝑁 measures the

spin imbalance of valence electrons. Alternately, at the EF, the electron SP can be expressed

as

𝑆𝑃 = 𝑑 ↑ (𝐸𝐹) − 𝑑 ↓ (𝐸𝐹)

𝑑 ↑ (𝐸𝐹) + 𝑑 ↓ (𝐸𝐹)

in which 𝑑 ↑ (𝐸𝐹) and 𝑑 ↓ (𝐸𝐹) are the spin dependent DOS at the EF for the spin up and

spin down channel, respectively. In this study, the HH YMnZ materials calculated with

GGA-mBJ have 𝑆𝑃 (%) = 100% . It means that the electrons at the EF are completely

polarized, thus confirming that these two studied compounds possess HM characteristics.

The calculated values of SP (%) are also listed in Table 7.3.

The magnetic moment of Z and Y atoms are quite small and almost negligible when

compared to the magnetic moment of Mn and do not play a considerable role to the µtot of

the materials. A very minor negative interstitial magnetic moment of the interstitial region

is also discovered as suggested by the Table 7.3. It is notable that during the experimental

synthesis of the materials like the non-equilibrium melt-spun as well as ball milling process

for the spintronics appliances, the lattice parameter is broadly impacted.

112

Table 7.3 The computed µtot (µ/f.u.) and local magnetic moments (µatomic/f.u.) of the HH

YMnZ (Z=Si, Ge, Sn) materials with X-type1 phase at the two exchange-correlation

potential (VXC) are given. Band gap energy: EBG (eV) and half-metallic gap: EHM (eV) is

also described at the Electronic conductivity (metallic, HM, or semiconducting).

Material VXC EBG

(eV)

EHM

(eV)

µtot

(µB)

µY

(µB)

µMn

(µB)

µZ

(µB)

µI

(µB)

Electronic

conductivity

YMnSi GGA 0.24 ----- 3.98 -0.02 3.92 -0.02 0.10

Nearly

HM

GGA+mBJ 0.42 0.16 4.00 -0.02 3.98 -0.02 0.06 HM

YMnGe GGA 0.32 0.05 4.00 -0.07 4.06 -0.03 0.04 HM

GGA+mBJ 0.57 0.36 4.00 -0.04 4.04 -0.02 0.02 HM

YMnSn GGA 0.33 0.23 3.98 -0.06 4.01 -0.02 0.06 HM

GGA+mBJ 0.59 0.50 4.00 -0.07 4.11 -0.02 -0.1 HM

113

The lattice constant can be changed considerably because of the uncontrolled

change in the strain. So, the lattice constant deviates from its optimized equilibrium value.

Furthermore, when the multilayers of the materials are prepared by molecular beam epitaxy

(MBE) or by some different techniques, the strain due to the substrate likewise is not

avoidable. Therefore, for the future hypothetical investigation as well as the experimental

synthesis of these HH YMnZ HM materials, it is very meaningful and useful to explore the

effect of lattice constant variation on these studied materials to ensure the half-metallicity

for the extensive variety of lattice parameter.

For the studied materials YMnZ, the computed total as well as a local magnetic

moment of these elements (Y, Mn, and Z) as a function of lattice constant are displayed in

Fig. 7.8 (a, b & c). It can be noticed that the magnetic moment of Mn atoms slightly

improves by the increase of the lattice parameter, even though the magnetic moment of Y

reduces. The actual change within Mn as well as Y magnetic moments changes one another

and keeps the entire magnetic moments being an integer.

It means that spin moment of Mn and Y atoms improve together with expanding

lattice parameter continues till a µtot within the unit cell. Once the lattice constant is

broadened, the improvement associated with the partial spin magnetic moment is a

consequence of the adjustment from atomic-like character ensuing through the decline

associated with hybridization in between nearby atoms. According to the SPR, for the HH

materials, the relationship between the µtot and final amount associated with 𝑁𝑣𝑎𝑙 inside the

unit cell is

µtot = (Z - 18) µB

But for the HM HH materials such as in the present study, the amount of valence

electrons is less than 18 and EBG is in the majority-spin state instead of minority spin state.

In this manner, the above the principle is not applicable and the suitable relationship will

be adopted. The µtot is a number of uncompensated spins results in

µtot = (Nmaj - Nmin) µB = (2Nmaj - Nval) µB

In which Nmaj and Nmin are the quantities of the majority and minority spin state,

respectively (Galanakis, 2002a). For all the three studied materials, the majority-spin bands

tend to be occupied with a total of 9 electrons for each unit cell.

114

In this manner, the suitable relation for such materials is,

µtot = (18 – Nval) µB

where µtot is equivalent to twice the quantity of possessed majority electrons minus the Nval.

In the case of HH YMnZ materials, the number of valence electrons is equivalent to 14 in

which Mn atom contribute 7, whereas 3 from Y atom and 4 from Z= (Si, Ge & Sn) atom.

Therefore, the magnetic moment is exactly 4 µB per unit cell. This µtot agrees with our DFT

calculated results. It also means that the majority band takes the 9 electrons for each unit

cell whilst the minority channel consists of 5 electrons providing the magnetic moment of

4 µB for each unit cell.

To examine the reliance of conducting behavior and magnetic properties on the

optimized lattice constant, we performed calculations to find out the aggregate magnetic

moment to be a functionally connected with lattice parameter for the wide range of 6.0 Å

to 7.4 Å. The half-metallicity preserve itself for the lattice constant range of around 6.3 Å

to 7.1 Å for YMnSi whereas for the YMnGe this HM range is in between 6.2 Å to 7.0 Å

and for the HH YMnSn half-metallicity is maintained from lattice constant range of 6.4 Å

to 7.1 Å. The graph between the µtot versus lattice constant is plotted in Fig. 7.8 (a, b & c).

Varieties of valence band maxima (red circles) and conduction band minima (black

squares) are also presented in the Fig. 7.8 (a, b & c) in the spin-up channel to related with

lattice parameter. It can be spotted that HM region is almost the same for these studied

materials.

The HH YMnSi, YMnGe, and YMnSn continue to retain the HM behavior with all

the lattice constants inside the array of 6.3-7.1 Å, 6.2-7.0 Å and 6.4-7.1 Å respectively.

This kind of outcome affirms in which the lighter component has the steady half-metallicity

regarding the variety of the lattice parameter (Özdogan et al., 2006). The EBG in the spin-

up band (majority channel) is given by the difference amongst VBM to CBM. It is visible

(Fig. 7.8) that EBG increases with the increasing lattice constant in the majority spin-band.

7.3.4 Thermoelectric Properties

In the present era, where the generation of the energy mainly presides over fossil

fuels, requires efficient and easily manipulated substitutes that are eco-friendly in nature

(Yousuf and Gupta, 2017). The interest in supportable energies has started a substantial

investigation into various sorts of power change advancements during the past ages.

115

Fig. (7.8) The computed total magnetic moment (µtot) for the HH (a) YMnSi, (b) YMnGe

and YMnSn materials corresponding to the variation of lattice constant. The dashed vertical

line shows the optimized equilibrium lattice constant.

116

Thermoelectric compounds, which can straight forwardly transform waste material

heat into feasible electrical energy, have obtained a growing number of consideration for

appealing applications within power collection (Snyder and Toberer, 2008).

To affirm the current outcomes, the electronic transport properties, and the

electronic conductivity along with, thermal conductivity, Seebeck coefficient and power

factor have been computed by applying the Boltzmann transport equation (Wooten, 1972)

as applied inside the BoltzTrap code (Madsen and Singh, 2006). This is an established fact

that the relaxation time for the scattering in BoltzTrap code is treated as constant.

In the present research, we estimated the thermoelectric variables to be functionally

connected with temperature shifting from 300 K to 800 K. The averaged value of the

electrical conductivity of HH YMnZ materials is plotted as a function of the temperature

in Fig. 7.9 (a), demonstrating distinctive patterns of the present HH materials and

uncovering a robust reliance on temperature. Moreover, at 300 K, it is obvious that

electrical conductivity associated with YMnSi offers higher value (7.55×1019 (Ω.m.s)-1)

compared to the estimations of YMnGe (i.e. 7.22×1019 (Ω.m.s)-1) and (i.e. 7.0×1019

(Ω.m.s)-1) YMnSn. Past 300 K, the electrical conductivity of all the studied materials has

expanded with temperature (till 800 K). The expansion of temperature prompted to an

increment of the carrier concentration number and in addition portability of carriers, which

at long last outcome in more prominent electrical conductivity. The studied materials tend

to be p-sort HH, henceforth the registered conductivity is essentially prompted by the hole

carrier concentrations.

Fig. 7.9 (c) demonstrates the averaged value of Seebeck coefficient (S) versus

temperature fluctuating from 300 K to 800 K. We acquired a positive value of S for all the

studied materials showing the dominance of holes over electrons. The Seebeck coefficient

(S) of HH YMnZ materials are incremented to 800 K with the expansion of temperature.

Essentially, we note two imperative issues concerning the impact of these studied HH

materials on the Seebeck coefficient: Firstly, at low temperature the value of S (YMnSi) >

S (YMnGe) > S (YMnSn) because of contrast of several carrier concentration for all the

studied materials. Secondly, interchanging Si by Ge/Sn (is much like include more

electrons or lessen the holes concentrations) sometimes appears as changing the carrier

concentration that triggers an extensive anisotropy in the estimated S of YMnZ materials.

The YMnSi has the greatest value of S (at 800 K) since it consists of more hole

concentration for a little scale in comparison with the YMnGe and YMnSn.

117

Fig. (7.9) (a) Electrical conductivity, (b) thermal conductivity, (c) See beck coefficient and

(d) Figure of merit as a function of temperature.

118

Temperature reliant on averaged thermal conductivity associated with HH YMnZ

materials are expressed within Fig. 7.9 (c). Because restricted through the formalism put in

place within BoltzTraP code, we talk about right here just the electronic thermal

conductivity and disregard the part associated with lattice thermal conductivity.

Wiedemann-Franz rule clarifies in which thermal conductivity associated with metals as

well as a SC is dependent on temperature along with electrical conductivity.

Inside the regarded temperature extend, thermal conductivity associated with HH

YMnZ materials rises directly. For the most part, thermal conductivity fluctuates based on

the variance as indicated by the amount of carrier concentration, electrical conductivity as

well as mobility. Each one of these guide lines differs using the variance associated with

the temperature. At optimum temperature, k (YMnSi) > k (YMnGe) >k (YMnSn) summing

17×1014 (W/m.K.s) as well as 16×1014 (W/m.K.s) and ×1014 (W/m.K.s) respectively,

thermal conductivity merely reveals heat circulation inside the materials. By changing the

Si element with Ge and Sn, we demonstrate a capacity to reduce the actual thermal

conductivity, which is the most imperative parameter for assessment of compounds in term

of modern significance.

Fig. 7.9 (d) provides power factors based on the electrical conductivities as well as

Seebeck coefficients as an element of temperature for YMnZ materials. The power

component of HH YMnZ materials fluctuates persistently within a temperature variation

from 300 K to 800 K. By evaluating each studied material, HH YMnSi has the most

noteworthy computed value of power factor. The explanation behind this high-power factor

in the HH YMnSi material is the greater value of S as well as thermal conductivity. Like

other thermoelectric variables such as electrical and thermal conductivities and Seebeck

coefficient, the power factor also shows a similar pattern (YMnSi) > (YMnGe) > (YMnSn).

Based on these types of results, YMnSi can be probably the most noticeable material for

thermoelectric applications.

119

Chapter 8

Structural Chemistry and Physical Properties of the Newly

Designed Half-Heusler XYZ Alloys with Large Spin Gaps

8.1 Introduction

Spintronics is a versatile domain which involves physics, physical chemistry, as

well as engineering, and it is the new research region for material scientists. Various new

materials should be discovered to meet distinct requirements. To find out the HMFs and

FM SCs along with TC greater than ambient conditions is always a priority for the material

science researchers (Felser et al., 2007). Logic circuits based on the spin of electrons

possess a long hold anticipation for a spintronic application. Even so, the constrained

variety of compounds designed for different system parts offers apparent difficulties for the

layout of the spintronic appliances. Compounds regarding spintronic purposes demand

appropriate mix of magnet moments and large values of band gaps also capable of being

operative at room temperature. It is observed that HH materials are ideal prospects

pertaining to spintronic applications because their crystal structure resemblance to the zinc-

blend phase and present large values of TC also they can maintain the half-metallicity under

small lattice mismatch.

In the last three decades, the half-metallicity has been widely investigated

particularly in the HA due to its unique feature that their electronic band structure is of

metallic nature in any one of two spin channels and show EBG or insulating behavior in the

other spin channel resulting in a complete (100%) SP at the EF. This sort of substantial SP

can be enabled to improve the functionality of the spintronic devices for example spin

valve, spin diode, and spin filter (Žutić et al., 2004).

HMFs are considered most suitable electrode materials designed for injecting a

spin-polarized current into SCs (Van Roy et al., 2000), MTJs (Tanaka et al., 1999), and for

GMRs devices (Hordequin et al., 1998). The significant amount of potential HH materials,

their multifunctional properties and latest recognition that HM Heusler has a tendency to

stay HM when layered with additional HH or FH (Azadani et al., 2016) boosts the

opportunity of discovering, tailoring, and synthesizing compounds suitable for distinct

practical applications to next generation spintronics devices.

120

Generally, the remarkable class of intermetallic materials which is in intense

investigations from last decade are the Heusler materials having general formula X2YZ

with L21 (2:1:1stichometry) and HH materials with C1b framework (1:1:1 composition) --

display exactly the same vast variety of properties similar to the perovskites, such as

topological insulators (Chadov and Qi, 2010; Feng et al., 2010; Yan and de Visser, 2014),

Kondo behavior (Ślebarski et al., 2001), non-centrosymmetric superconductivity

(Winterlik et al., 2008) as well as traditional, tunable magnetic properties, non-collinear

magnetism, semiconductivity, magnetoresistance effects, Li-ion-conductivity along with

other physical properties.

The surprising results about the Heusler materials were firstly reported by Fritz

Heusler in 1903 when he discovered that Cu2MnAl has FM behavior at the room

temperature even though none of the involving component Cu, Mn, or Al displays

magnetism. HA sponsor a plethora of surprising unique properties, that cannot be

discovered through primary properties of the atoms within the crystal framework.

Today, more than 1000 compounds have been identified in this fascinating class of

Heusler family which synthesized through 40 different combinations of the elements and

still, new materials with intriguing properties are continuous discovered for numerous

technological applications such as thermoelectric SCs (Sakurada and Shutoh, 2005;

Sootsman et al., 2009) optoelectronics SCs (Kieven et al., 2010) and piezoelectric SCs (Roy

et al., 2012).

A systematic research on the structural stability of HH (C1b) family is essential to

furnish direction for potential findings. Despite the fact that, a lot of first-principles

calculations anticipated several HH materials show half-metallicity (Galanakis et al., 2006;

Graf et al., 2011), though, a detailed investigation on the structural stability, electronic and

magnetic properties of HH family is essential, because it is not apparent which of the

numerous HM HH alloys that can be predicted, usually are stable.

To explore half-metallicity in the materials, it is a more effective way to implement

first-principles computations to design HM compounds first for the spintronics applications

and then synthesize them experimentally rather use costly trial-and-error experimental

plan. Employing a priori details with the structural stableness permits experimentalists to

pay attention to favorable properties to synthesize half-metals with ease.

121

The use of acoustic phonon spectra is the easiest method to deal with the stableness

regarding anticipating HM compounds. A recent study of the HH LiCrS and LiCrSe at their

optimized lattice constant show that both compounds show half-metallicity at the bulk and

Cr-S, Cr-Se at (001) surfaces (Hussain, 2018). Another theoretical research suggests that

ternary intermetallic compounds LiMnZ (Z = N, P) using an HH framework reveal HM

character at their elongated lattice constants and their magnet moments are anticipated to

the highest up to 5µ𝐵 per f.u. (Damewood et al., 2015b).

The work of Xiaotian et. al. (Wang et al., 2017b) on the XCrZ (X = K, Rb, Cs; Z

= S, Se, Te) shows that these HH materials have a largest magnetic moment of 5 µ𝐵 and a

semiconducting gap of more than 2 eV. Lately, studies on alkali-metals chalcogenides NaX

and LiX where (X= S, Se & Te) also predicts the HM properties and show very large EBG

with magnetic moments of 1 µ𝐵 when they crystalizes in zinc-blend and wurtzite structures

(Sadouki et al., 2018a; Sadouki et al., 2018b).

Based on the previously mentioned details, it is essential to discover new HM HH

alloys with larger EBG and high magnetic moment. In this computational investigation, HM

properties are systematically investigated and explored. We addressed, the series of 90 HH

XYZ compounds where (X= Li, Na, K, Rb, Cz; Y= V, Nb, Ta & Z= Si, Ge, Sn, S, Se, Te)

by the help of First principle calculations. We have produced a database of the structural,

electronic and magnetic properties, that will help us to recognize possibly practical

electrode/spacer supplies intended for long-term spintronics applications.

The computational methods, simulation guidelines, and code utilized in this DFT

calculations are presented in section 8.2. In section 8.3, we examine the three possible

types of structural arrangement (Wang et al., 2017b) for the HH alloys for each material to

figure out the energetically most stable structural framework using the lowest minimized

energy and discover the ground magnetic state of these studied materials.

8.2 Computational Methods

The ground state properties for all the 90 HH XYZ materials are performed by using

the Perdew–Burke–Ernzerh of (PBE) scheme (Perdew et al., 1996a) which is variant of the

generalized gradient approximation (GGA) to DFT whereas the electronic and magnetic

properties of all the HH XYZ materials are performed by using the TB-mBJ local density

approximation (Tran et al., 2007) implemented in the WIEN2K simulation code.

122

The TB-mBJ functional gives the accurate values of the band gaps compared to

PBE and computationally very less expensive. We have also used the Vienna Ab-initio

Simulation Package (VASP) to determine the correct magnetic ground state (FM, AFM)

and to check the vibrational stability at the gamma point and to perform phonon full

spectrum calculations for the some interesting HH XYZ materials. Phonopy software is

also used to determine the force constants between the lattice when the atoms are slightly

distorted from their equilibrium position. The force constants help to determine the phonon

frequency and the dynamic stability of the crystal structure. Mean field approximations

(MFA) are mapped into the Heisenberg spin model. The Monte Carlo simulations are also

carried out to use the Heisenberg spin model to determine the values of TC.


8.3.1. Ground State Properties

The general formula for ternary HH materials is XYZ where X, Y are usually an

alkali or TMs and Z is the main group element. Here, in this chapter, X represents the alkali

metals (Li, Na, K, Rb & Cs) whereas Y shows the group-V elements (V, Nb, & Ta) and Z

is for the sp-elements (Si, Ge, Sn, S, Se & Te). The unit cell of the HH XYZ materials

features a face-centered cubic (fcc) structure which has a Structurbericht representation of

C1b and space group of 216 (F-43m) according to the International Tables of

Crystallography consisting on three inequivalent interpenetrating fcc sublattices filled by

X, Y and Z atoms respectively.

Physical properties of the HH compounds are greatly influenced by the atomic

placement inside the unit cell. There exist three unique possible phases of atomic

arrangements in type1 (T1), type2 (T2) & type3 (T3) by interchanging the distinct Wyckoff

positions of X, Y & Z atoms in the C1b structure (Wang et al., 2017b). The illustration of

the unit cell of the HH XYZ materials of these three types is displayed in Fig. (8.1).

Geometrical optimization has been performed to determine the most stable type

among the three different types (T1, T2 & T3) for all the HH XYZ materials before

calculating the electronic properties. The lattice constants are determined by using the PBE-

GGA potential as there are no prior reports found on our studied HH XYZ materials. The

lattice constant can be changed considerably because of the uncontrolled change in the

strain. So, the lattice constant deviates from its optimized equilibrium value.

123

Fig. (8.1) Conventual unit cell of the HH XYZ materials in three different atomic

arrangement types T1 [4c (1

4,

1

4,

1

4), 4d (

3

4,

3

4,

3

4), 4a(0, 0, 0)], T2 [4a(0, 0, 0), 4d (

3

4,

3

4,

3

4), 4c

(1

4,

1

4,

1

4)] and T3 [4b (

1

2,

1

2,

1

2), 4d (

3

4,

3

4,

3

4), 4a(0, 0, 0)].

124

So structural parameters of these materials are derived by optimizing the energy

extracted from their respective optimized volume around their equilibrium lattice constant and

then their data points are fitted to Murnaghan’s equation of state (Murnaghan, 1944b). Fifty-

six of the studied HH XYZ materials have the lowest values of energies at T1 phase and thirty-

two energetically preferred to T3 phase as a stable ground state. Atomic arrangement of T2

phase is found to be a ground state for only two HH LiNbSn and LiTaSn materials out of the

90 HH XYZ materials.

We further calculated the correct magnetic ground state of the studied HH XYZ

materials by volume optimization at their respective ground phase (T1, T2 or T3). For the

illustration purpose, only HM HH NaVTe is selected to describe the variation of volume versus

total energy curve at the three possible T1, T2 & T3 phases along with magnetic ground state

(FM & AFM) in the Fig. (8.2) out of the 90 DFT investigated HH XYZ materials.

It can be clearly depicted from the Fig. (8.2) that most stable phase of the HH NaVTe

is a T1 phase with FM configuration. For the complete details about the lattice parameters,

electronic behavior, values of magnetic moments, energies of the FM, AFM states, EBG and

EHM at their preferred type and magnetic ground state of all the 90 HH XYZ materials at the

three possible phases (T1, T2 & T3) are provided as supplementary information in the

Appendix-I at the end. The number of materials which preferred to structural stability among

three unique different atomic positions in the C1b unit cell of the HH structure, with the correct

magnetic ground state along with the electronic properties of all the 90 DFT investigated HH

XYZ materials are presented in Fig. (8.3). From this figure, one can easily see that how many

numbers of materials have the stable ground phase (T1, T2 or T3) with correct magnetic (NM,

FM or AFM) configurations and their electronic properties for all the 90 DFT investigated HH

XYZ materials. After structural stability, we determined the magnetic ground phase (NM, FM

or AFM) at their preferred stable ground phases (T1, T2 or T3). We identified 14 HH materials

as a NM material, 55 HH are energetically favorable to the FM and 21 materials prefers to the

AFM ground state. Furthermore, the electronic properties of the 90 HH XYZ materials are also

calculated, out of which, 44 materials are found to be metallic in nature (NM metallic = 9, FM

Metallic = 14 & AFM metallic = 21). Also, 7 HH materials found to be SCs, in which 2

materials are magnetic SCs and 5 are NM SCs.

125

Fig. (8.2) Volume optimization of the HH HM NaVTe material at the (a) three different atomic

arrangement types (T1, T2 & T3) (b) FM and AFM ground state.

126

Additionally, half-metallicity was found in total 39 HH XYZ materials. The electronic

properties are discussed here are calculated in the most stable phase of the HH XYZ materials

with their correct magnetic ground state. Out of 90 HH XYZ materials, 21 HH materials

comparatively have the lowest energy at the AFM state rather than FM state confirms that their

magnetic ground state is AFM.

If we generalize, the series of HH XYZ materials which energetically preferred T1 as

a stable ground phase are the HH XYZ where (X= Li, Na, K & Y=V, Nb, Ta & Z= Si, Ge, Sn,

S, Se, Te) and the series of HH XYZ (X= K, Rb & Y= V, Nb & Z= S, Se) along with the series

of HH LiYZ where (Y=Nb, Ta & Z =Si, Ge, S, Se, Te) followed by the series of RbTaZ where

(Z=, Si, Ge, S, Se). On the other hand, the series of the materials which prefer T3 phase as a

most stable ground state are CsYZ where (Y= V, Nb, Ta & Z= Si, Ge, Sn, S, Se, Te) and XYZ

where (X= K, Rb, & Y=V, Nb, & Z = Si, Ge, Sn, Te) along with RbTaZ where (Z=S, Te).

Only the NM HH LiNbSn and LiTaSn materials which show the metallic character have the

lowest energy in the T2-phase.

It can be noted that the alkali metals with smaller atomic radius (e.g. Li, Na, K) tend to

prefer in the T1 stable phase while when the size of the atomic radius increases of each element

(Rb, Cs) or coupled with TMs in the XYZ material then they energetically prefer to be sable

in the T3 phase. The well-known empirical procedures also verify the energetical stable phases

of the HH XYZ materials that the most electronegative elements like (Si, Ge, Sn, S, Se & Te)

and the most electro positive elements (alkali metals Li, Na, K, Rb, Cs) forming the NaCl like

sublattice whereas the elements which have intermediate electronegativity e.g. (V, Nb & Ta)

prefer to occupy the tetrahedral sites (Zeier et al., 2016).

Among 90 HH XYZ materials, seven materials are also found to be a SC. The HH

LiVSi and LiVGe are the magnetic SC at their stable phase T1 with FM configuration. Both

FM SC materials show a semiconducting gap at both the spin channels (up & down) with a

magnetic moment of 2 µ𝐵. Reaming five CsNbS, CsNbSe, and series of three HH materials

CsTaX (where X=S, Se & Te) are NM SC with µtot of 0 µ𝐵.

127

Fig. (8.3) Summary of the 90 HH XYZ materials, at their preferred stable ground state among

three different types T1, T2 & T3 phases and magnetic ground state (NM, FM, AFM).

Illustration of the electronic properties of the each HH materials is also presented at their

preferred stable type and magnetic ground state.

128


In this section, the electronic structure and magnetic properties, are discussed, which

are very important and core of the present work. These properties are performed for all the 90

HH XYZ materials on their respective most stable and meta stable phases (T1, T2 or T3) with

their correct magnetic configurations (NM, FM or AFM) at their equilibrium lattice constants.

The complete information about their equilibrium lattice constant, electronic properties

at all the T1, T2 and T3 phases, µ𝑡𝑜𝑡, the EBG (eV), the EHM (eV), the info about their vibrational

stability at the gamma point and the values of NM, FM and AFM energies of all the 90 HH

XYZ materials at their respective stable and meta-stable ground state and magnetic ground

state can be found in Appendix-I along with the supporting information.

The energy difference between the valance band maxima (VBM) and conduction band

minima (VBM) forms the EBG whereas the EHM is termed as the minimum energy required by

the electrons to flip the spin gap. Our DFT investigated HM HH XYZ materials show very

large values of the EBG and EHM. In Fig. (8.4), the values of the energy (a) band gap EBG (eV)

and (b) half-metallic gap EHM (eV) of all the 90 HH XYZ materials are presented only on their

respective energetically most stable ground phase in the 3D plot.

As suggested by the general formula of HH XYZ materials, alkali-metals (X= Li, Na,

K, Rb, Cs) are assigned on the X-direction, the group-V elements (Y = Si, Ge, Sn, S, Se, &

Te) on the Y-axis and the main group elements (Z = Si, Ge, Sn, S, Se, & Te) on the Z-direction.

The color bar indicates the width of the EBG and EHM. As out of 90 HH XYZ materials, 46 HH

materials show the metallic nature, thus they have the zero values of EBG and EHM energies

which is indicated by the dark blue color. The values of the EBG and EHM increases from blue

to yellow successively.

Furthermore, the vibrational stability at the gamma point of the crystal structure for all

the 90 HH XYZ materials are also explored thoroughly. Among these, 39 are HM HH XYZ

materials. only 28 HM HH XYZ materials have the vibrational stability at the gamma point. It

means that their phonon frequencies are positive and show optic modes at the gamma point.

Remaining 11 HM HH XYZ materials show the acoustic modes and have the imaginary

(negative) phonon frequency greater than f/i = 1 THz.

129

Fig. (8.4) Colors show the width of the (a) EBG (b) EHM of 90 HH XYZ materials. The species

X, Y, and Z which represent the HH XYZ materials which are signifying on the three

coordinates. Blue and yellow colors represent the successively increasing values of these

energy band gaps.

(b) (a)

130

If the crystal has a very large values of imaginary (negative) frequency then it means

that it is vibrationally unstable and may be in a structural phase transition phase (meta stable

state). So, these 11 HM HH XYZ materials which are vibrationally unstable at the gamma

point are discarded for the further discussion and our focus will be only on the 28 vibrationally

stable HM HH XYZ materials with FM phase for the further analysis.

8.3.3 Mixing Energy

To determine either our DFT calculated HM HH XYZ materials can be experimentally

synthesized with the C1b structural framework, the mixing energy of the 28 vibrationally stable

HM HH XYZ materials is calculated with their respective stable phases (T1 or T3) with FM

ground state at their equilibrium lattice constants. The mixing energy of these 28 vibrationally

stable HM HH XYZ materials is calculated by the following formula,

𝐸𝑚𝑖𝑥 = 𝐸𝑋𝑌𝑍𝑓𝑐𝑐

− ( 𝐸𝑋𝑓𝑐𝑐

+ 𝐸𝑌𝑓𝑐𝑐

+ 𝐸𝑍𝑓𝑐𝑐

)

where 𝐸𝑋𝑌𝑍𝑓𝑐𝑐

is the total energy (eV/atom) of the HH XYZ materials with C1b crystal structure

and 𝐸𝑋𝑓𝑐𝑐

, 𝐸𝑌𝑓𝑐𝑐

and 𝐸𝑍𝑓𝑐𝑐

are the energies of the each X, Y or Z species of the HH XYZ materials

in the fcc structure. The mixing energies of these 28 vibrationally stable HM HH XYZ

materials are displayed in a 3D plot of the Fig. (8.5).

Now, we examine the variation in mixing energies of our selected vibrationally stable

28 HM HH XYZ materials at their respective stable phases (T1 or T3) with FM ground state.

It is obvious from the blue circles that HM HH XYZ materials with X = (Li, Na, Rb, Cs), Y

=V and Z = (Si, Ge, Sn, S, Se) tend to have lower values of the mixing energies which is a

good indicator that these 28 vibrationally stable HM HH XYZ materials can be synthesized

experimentally and may be more stable than its constituting elements at the zero temperature.

Only HM HH NaVTe along with magnetic SCs LiVSi & LiVGe have the negative

values of Emix (eV/atom). The list of mixing energy of the 28 vibrationally stable HM HH XYZ

materials with FM ground state along with 2 FM SCs is also presented in Table 8.1. The trend

can be easily seen from the Table 8.1 that the values of the mixing energy for the 28

vibrationally stable HM HH XYZ materials increases when the atomic size of the Y element

increases where (Y= V, Nb, Ta).

131

Fig. (8.5) Mixing energy (eV/atom) of the 28 vibrationally stable HM HH XYZ materials at

their respective stable state with FM configurations. Blue shades show the mixing energy less

than 0.2 (eV/atom). Each coordinate of the 3D plot symbolizes the X, Y & Z species of the

associated 28 HM HH XYZ materials.

132

The understanding of the mixing energy offers essential significance for the prospective

applications associated with HH materials. It is expected that the 28 HM HH XYZ materials

with FM phase which have lower values of the mixing energy (blue circles in Fig. 8.5)

especially the HM HH LiVSn, NaVZ (Z = Si, Ge & Te) with their stable phase T1, whereas

HM HH RbVSe, CsVZ (Z= Sn, S) materials with T3 phase have a greater prospect from the

spintronic application point of view because their mixing energy is around -0.1 to 0.2

(eV/atom). Thus, they have the greater chance to be stable materials and can be synthesized

experimentally when decomposed into respective constituent elements at zero the temperature.

8.3.4 Curie Temperature (TC)

For the practical spintronic applications, TC is an additional essential requirement to

use the FM HH XYZ materials as spin injectors. The TC of the interesting 28 HM HH XYZ

materials is also calculated by using the mean field approximation (MFA) and mapping the

total energy of FM and AFM states of the HH XYZ materials into a Heisenberg model.

The construction of Heisenberg spin model is made from the expression (Hu et al., 2018),

𝐸𝑠𝑝𝑖𝑛 = 𝐸0 +1

2 ∑ 𝐽𝑖𝑗

𝑖𝑗𝑆𝑖𝑆𝑗,

in which 𝐸0 is the reference energy, the magnetic moment of the ith atom is interpreted by 𝑆𝑖

and 𝐽𝑖𝑗 represents the values of the exchange constant obtained from the DFT calculations at

absolute temperature. The magnetic exchange interactions are considered for the nearest

neighbors (𝑛𝑛 = 8) inside the unit cell. The exchange coupling 𝐽𝑖𝑗 can be obtained as follows,

𝐸0 = 1

2 (𝐸𝐹𝑀 + 𝐸𝐴𝐹𝑀)

𝐽𝑖𝑗 = 1

8 |𝑆|2 [𝐸𝐹𝑀 − 𝐸𝐴𝐹𝑀]

where 𝐸𝐹𝑀 and 𝐸𝐴𝐹𝑀 are the energy of the crystal assuming the unit cell has the ideal FM and

AFM spin configurations.

133

Fig. (8.6) The Curie temperature (TC) of the 28 HM HH XYZ materials at their respective

stable state with FM configurations which are also vibrationally stable at the gamma point. The

color bar shows the values of the calculated TC (K) with +/- 25 K tolerance. Each coordinate

of the 3D plot symbolizes the X, Y, Z species of the associated HM HH XYZ material.

134

The values of the TC for the 28 vibrationally stable HM HH XYZ materials along

with 2 FM SCs are presented in the Table 8.1 and their 3D plot is illustrated in the Fig.

(8.6). From the Table 8.1, our selected 28 vibrationally stable HM HH XYZ materials have

the lower values of TC, at the range of room temperature. The quite low values of the TC

ranging from the 100 K to 300 K as it is indicated by the color plan of the Fig. (8.6). Dark

blue circles show the value of TC = 100 K. Most of our explored HM HH alloys are in the

range of 150 K to 250 K (light blue to green). Only HM HH RbNbS, RbNbZ (Z = Si, Sn,

Te) and CsNbTe have the maximum value of TC = 300 K (yellow circles).

For the practical spintronic applications, HMFs are needed which have negative

(low) values of the mixing energy and high values of the TC. Now, by looking at the Table

8.1, the materials which have the high values of TC also have higher values of the mixing

energy (greater than 0.2 eV/atom) and the HM HH XYZ materials which have lower values

of mixing energy have the TC below or around room temperature.

For instance, HM HH NaVTe although have the negative mixing energy of -0.123

eV/atom but its Tc temperature is just 100 K. The HM HH XYZ materials in which

transition metal Y= Nb, Te have the greater values of the TC but their mixing energy is

high, only the HH XYZ materials with Y=V have the lower values of mixing energy, which

indicates that HH XYZ materials with Y= V have the greater chances to be experimentally

synthesized.

Out of 28 vibrationally stable (at gamma point) HM HH XYZ materials, only HM

HH NaVSi, RbVSe and CsVTe along with FM SCs LiVSi and LiVGe materials have the

moderate and acceptable values for both mixing energy as well as TC. Remaining HM HH

XYZ materials are discarded for the further discussion in this chapter because they have

the mixing energy greater than 0.2 (eV/atom) and our focus will be only on HM HH NaVSi,

RbVSe and CsVTe along with FM SCs LiVSi and LiVGe materials.

8.3.5 Band Structure and Density of States

In our DFT investigated 90 HH XYZ materials, seven materials are found to be a

SCs. Among them, HH LiVSi and LiVGe are the magnetic SCs with the magnetic moment

of 2 µB with their stable phase of T1 at their optimized lattice constant. The NM SCs

includes the series of CsNbZ (Z= S, Se) and CsTaZ (Z= S, Se, Te) in the HH C1b

composition with their optimized lattice constant which are all energetically preferred to

T3 as a stable phase.

135

Table 8.1 Equilibrium lattice parameter: a (Å), electronic conductivity (SC and HM)

represent the semiconductor and HM characteristics, µ𝑡𝑜𝑡 is equivalent to total magnetic

moment, EBG & EHM are the energy band gap and HM gap, FM & AFM along with EFM &

EAFM shows the magnetic ground state and energy of the FM and AFM states respectively,

TC & Emix show the Curie Temperature and mixing energy of the each 30 interesting HH

XYZ materials at their preferred ground state (T1 or T3) with vibrationally stability

checked at the γ-point.

XYZ Preferred

Types

a

(Å)

Electronic

Behavior µ𝑡𝑜𝑡

(µB)

EBG

(eV)

EHM

(eV)

Mag-

netic

State

Stabl

e

EFM

(eV)

EAFM

(eV)

TC

(K)

+/-

25K

𝐸𝑚𝑖𝑥

(eV/

atom)

LiVSi T1 5.85 SC 2.00 1.43 ---- FM Yes -63.25

-62.72

200 -0.11

LiVGe T1 5.93 SC 2.00 1.06 ---- FM Yes -60.23

-59.61

250 -0.11

LiVSn T1 6.37 HM 2.00 0.89 0.47 FM Yes -54.94

-54.66

150 0.05

NaVSi T1 6.25 HM 2.00 1.11 0.52 FM Yes -55.56

-55.15 200 0.21

NaVGe T1 6.32 HM 2.00 1.16 0.50 FM Yes -53.12

-52.80

150 0.21

NaVTe T1 6.84 HM 4.00 4.18 0.54 FM Yes -52.55

-52.38

100 -0.12

KVSi T3 6.55 HM 2.00 1.49 0.21 FM Yes -48.80

-48.26

250 0.56

KVGe T3 6.64 HM 2.00 1.59 0.15 FM Yes -46.74

-46.41

150 0.53

RbVTe T3 7.27 HM 4.00 3.73 0.83 FM Yes -48.01

-47.35

250 0.14

CsVSn T3 7.32 Nearly

HM

1.99 0.66 0.15 FM Yes -42.91

-42.58

150 0.78

136

Table 8.1 (continued)

XYZ Preferred

Types

a

(Å)

Electronic

Behavior µ𝑡𝑜𝑡 (µB)

EBG

(eV)

EHM

(eV)

Mag-

netic

State

Stable EFM

(eV)

EAFM

(eV)

TC

(K)

+/-

25K

𝐸𝑚𝑖𝑥

(eV/

atom)

CsVS T3 6.93 HM 4.00 3.92 0.68 FM Yes -49.97

-49.46

200 0.012

CsVSe T3 7.13 HM 4.00 3.66 0.66 FM Yes -48.62

-48.04

250 0.111

KNbSi T1 6.79 HM 2.00 1.13 0.54 FM Yes -52.38

-52.03

150 0.595

KNbGe T1 6.86 HM 2.00 1.15 0.46 FM Yes -50.14

-49.79

150 0.604

KNbSn T1 7.25 HM 2.00 1.10 0.34 FM Yes -47.53

-47.24

150 0.685

RbNbSi T3 6.77 HM 2.00 1.24 0.57 FM Yes -49.37

-48.68

300 0.831

RbNbSn T3 7.19 HM 2.00 1.19 0.33 FM Yes -45.83

-45.14

300 0.828

RbNbTe T3 7.41 HM 4.00 3.82 0.75 FM Yes -47.59

-46.90

300 0.402

CsNbSi T3 6.87 HM 2.00 0.47 0.11 FM Yes -49.23

-48.64

250 0.907

CsNbGe T3 6.96 HM 2.00 0.62 0.14 FM Yes -47.12

-46.52

250 0.915

CsNbSn T3 7.28 HM 2.00 0.69 0.16 FM Yes -45.72

-45.09

250 0.94

CsNbTe T3 7.55 HM 4.00 3.23 0.39 FM Yes -47.16

-46.45

300 0.49

NaTaSn T1 6.71 HM 2.00 1.18 0.17 FM Yes -56.88

-56.68

100 0.55

KTaSi T1 6.70 HM 2.00 1.34 0.50 FM Yes -56.60

-56.42

100 0.74

KTaGe T1 6.80 HM 2.00 1.41 0.69 FM Yes -54.08

-53.82

150 0.77

KTaSn T1 7.17 HM 2.00 1.31 0.54 FM Yes -51.29

-50.91

200 0.88

RbTaSi T1 6.89 HM 2.00 1.36 0.66 FM Yes -53.13

-52.72

200 0.92

RbTaGe T1 6.99 HM 2.00 1.39 0.55 FM Yes -50.82

-50.32

200 0.97

RbTaSn T3 7.16 HM 2.00 1.05 0.35 FM Yes -49.09

-48.56

250 1.03

RbTaTe T3 7.37 HM 4.00 3.70 0.24 FM Yes -48.91

-48.37

250 0.75

137

For an illustration purpose, only the electronic band structure of the FM SC LiVGe

along with HM HH CsVSe and DOS of HM HH RbVTe are selected among all the 28

vibrationally stable HM HH XYZ materials to illustrate the electronic properties. Their

band structure and DOS are presented in the Figs. (8.7-8.9).

For the FM SC HH LiVGe material, Fig. (8.7), one can see the semiconducting gap

in both spin channels. In the majority (spin-up) channel and minority (spin-down) channel,

FM SC HH LiVGe material have the semiconducting gap of 0.63 eV and 1.65 eV

respectively. In the spin-up channel, band gap is direct while in the spin down channel, the

indirect band gap is found.

In the Fig. (8.8), the band structure of the HM HH CsVSe (as an example) is shown

to illustrate the HM properties of the 28 found HM HH XYZ materials. In the spin up

channel (majority bands), metallic characteristics are found while on the opposite spin

channel (minority bands), there is a large indirect EBG of 3.7 eV found at the equilibrium

lattice constant which leads to the 100% SP at the EF. The VBM found to be situated at Γ

and the conduction band minima CBM is situated at the X of the wave vectors (k-points) of

the BZ.

The value of the spin-flip gap or EHM is EHM = 0.7 eV which can be defined as the

minimum energy required to flip the gap for the HM HH CsVSe material. The values of

these EBG and EHM can be clearly seen in the Fig. (8.8) for the HM HH CsVSe alloy. The

EHM has much greater importance in the HM properties around the EF rather than EBG. The

non-zero value of the EHM in the spin down channel is the clear indication that the HH

CsVSe is true HM at the EF.

The density of state (DOS) explains the different energy levels occupied by the

electrons for the specific number of states at each energy level. For the analyses of the

electronic nature of the 90 HH XYZ material, only DOS of the HM HH RbVTe is selected

to explain the HM properties at its equilibrium lattice constant. The Fig. (8.9) presents the

total and partial DOS of the individual atoms which are present in the HM HH RbVTe

material. The DOS calculations for this material are performed at the optimized lattice

constant calculated by the DFT with the stable T3 phase and FM configurations. Some state

of elements like s & p of Rb and V are not offered in the DOS plot because they do not add

any contribution to the total DOS of the RbVTe.

138

Fig. (8.7) Band structure of the HH SC LiVGe material with FM ground phase in the spin

up and spin down channel. The horizontal dashed line represents the EF which is fixed at

zero eV.

139

Fig. (8.8) Band structure of the HM HH CsVSe material in the spin up and spin down the

channel. The horizontal dashed line represents the EF which is fixed at zero eV.

140

Fig. (8.9) Spin projected total and partial density of state (DOS) of HM HH RbVTe material

at the equilibrium lattice constant. The vertical dashed line in the middle shows the Fermi

level and fixed at EF = 0 eV.

141

On the contrary, in the spin up channel the p orbitals of Te cross the EF along with

the d-t2g orbitals of Rb and V, leading to a metallic character for all three compounds. The

p-state of Z atom is quite symmetrical in the spin up directions and crosses EF a little in the

spin down channel with a little share to the magnetism. It is also revealed from the Fig.

(8.9), that hybridization occurs between the 3d states of Rb and V atoms.

8.3.6 Vibrational Properties

Vibrational properties perform a significant part within most of the physical

properties associated with solids, like the electric conductivities, superconducting

temperature, Debye temperature, thermal properties as well as stableness of the structure.

After performing the volume optimization and extracting the most stable ground

structure of the each HH XYZ material, we further tested their dynamic stability of the

structure by two-step phonon calculations. First, we calculated the vibrational properties of

our DFT investigated 90 HH XYZ materials at their preferred stable phase at the gamma

point. If it behaves well at the gamma point and has the interesting properties, then we

carried out the phonon calculations for the selected HH XYZ materials. Out of 90 HH XYZ

materials, 63 HH XYZ materials found to be vibrationally stable at the gamma point

whereas 27 HH XYZ materials show imaginary frequencies greater than 1 THz.

Furthermore, among 27 unstable HH XYZ materials, 10 materials are unstable at

the FM phase which are KVZ (Z = S, Se, Te), RbVZ (Z = Si, Ge, S, Se), CsVZ (Z= Si, Ge,

Te) and while remaining 17 HH XYZ materials like LiVS, NaVZ (Z= S, Se), KVSn,

RbVSn, NaNbZ (Z= Se, Te), KNbZ (Z=S, Se, Te), RbNbZ (Z= S, Se), KTaZ (Z= S, Se,

Te) and RbTaZ (Z = S, Se) have the AFM ground state. It can be noted that the majority

(17 of 21) of the HH XYZ materials which have AFM as a ground state are vibrationally

unstable at the gamma point.

To ensure the structural stability of the FM HM HH NaVSi and FM SC HH LiVSi

and LiVGe materials other than gamma point of the first Brillion zone, we have calculated

the phonon full spectrum calculations as well. These two FM SC materials vibrationally

well behaved for all the k-points within the BZ at their equilibrium lattice constant. For the

illustration purpose, only the result of the phonon spectrum of SC HH LiVGe material is

shown in the Fig. (8.10) because both have the similar phonon dispersion curve due to the

resemblance of the crystal structure.

142

Fig. (8.10) Phonon full spectrum curve for the (a) HM HH NaVSi and (b) FM SC LiVGe

143

The three acoustical and six optical branches of vibrational modes at nay q-point

can be seen in the dispersion curve as our DFT calculated HH XYZ materials contains three

atoms in the primitive unit cell. As there are no imaginary frequencies are found and all

frequencies are positive at the symmetry path of the Brillion zone which confirms the

dynamical stability of the SC HH LiVGe materials.


There is a unique feature related to the HM system that the µtot of the system should

be an integer and integral multiple of Bohr magnetron. The SPR for the conventional HH

XYZ materials which have three atoms in the primitive unit cell, is given by

µ𝑡𝑜𝑡 = (𝑍𝑣𝑎𝑙 − 18)µ𝐵

where µ𝑡𝑜𝑡 is the total magnetic moment of the HH XYZ material and 𝑍𝑣𝑎𝑙 represents the

total number of valance electrons inside the unit cell. In our investigated HH XYZ system,

the values for the 𝑍𝑣𝑎𝑙 is smaller than the usual TMs related to HH XYZ materials.

A researcher, Damewood et al. (Damewood et al., 2015a) has modified the SPR for

the systems which have the smaller values of 𝑍𝑣𝑎𝑙

µ𝑡𝑜𝑡 = (𝑍𝑣𝑎𝑙 − 8)µ𝐵

The value of 𝑍𝑣𝑎𝑙 is 10 and 12 for the series of HH HM XYZ (Z= Si, Ge, Sn) and

XYZ (Z= S, Se & Te) respectively. Our DFT investigated 39 HM HH XYZ (Z= Si, Ge, Sn)

and the series of XYZ (Z= S, Se & Te) materials have also a µ𝑡𝑜𝑡 of 2 µB and 4 µB

respectively and obeys the modified SPR.

The µ𝑡𝑜𝑡 of the selected 28 vibrationally stable HH XYZ materials along with the

two FM SCs are shown in the Table 8.1. Our all DFT investigated 28 vibrationally stable

HM HH XYZ materials show the 100% SP at the EF at their preferred ground stable phase

with the FM configurations.

144

CHAPTER 9

Overview of the Results

This dissertation provides an extensive overview of an exceptional class of HH

materials which have countless functionalities, ranging from SCs to metals and HMFs with

plenty of technological applications in spintronics, thermoelectric, and opto-electronics.

The structural, electronic, and HM properties of the DFT investigated HH

compounds CrTiZ (Z = Si, Ge, Sn, Pb) investigated by using the first-principles DFT

calculations. Spin-polarized ferromagnetism explored in three different atomic

arrangements (Type 1, Type 2, Type 3) and halfmetallicity has been found in all these

compounds at their optimized lattice constants in Type 1 with EHM ranging from 0.12 to

0.33 eV. As other HH materials which are based on TMs, the hybridization between d-d

orbitals of Cr and Ti atoms causes the semiconducting gap in the majority-spin state for all

the CrTiZ (Z= Si, Ge, Sn, and Pb) materials in the Type 1. Furthermore, the outcome

suggests that the half-metallicity is availably robust contrary to the lattice distortion which

gives the possibility to grow these compounds on various substrates and especially the HH

CrTiSn and CrTiPb materials are suitable for spintronics applications because of their

larger EHM. Due to a large integral magnetic moment (4 µB/unit cell) of all these HH

materials, they might perform as electrodes to insert spin-electrons into II-VI magnetic SCs.

A detailed investigation of new series of potentially HH FeVZ (where Z= Si, Ge,

Sn) compounds performed by employing GGA mBJ exchange-correlation energy

functional of density functional theory. Our GGA results indicate that FeVGe is HM, while

FeVSi, FeVSn are metallic. On the other hand, the mBJ calculations reveal that FeVSi,

FeVGe, and FeVSn compounds are excellent HM having integer magnetic moment of 1 µB

and EHM of 0.16 eV, 0.21 eV, and 0.23 eV respectively. We found that the ferromagnetism

arises from Fe-d states along with a small contribution of p-states of Z-atoms. The band-

gap appearing in the spin up channel is due to strong d-d hybridization of TMs (Fe and V).

The HH FeVSi, FeVGe, and FeVSn retain their HM nature when their lattice parameters

are changed in the range of 3.84–5.31%, 3.91–5.91% and 3.94–11.8% respectively and

145

therefore, they could be considered as a potential candidate for the useful spintronic

applications.

The structural, electronic, and magnetic properties of HH YCrSb and YMnSb

materials with three different atomic arrangements (XI, XII, and XIII) are investigated by

using FP–LAPW method. The calculated formation energies confirm that these compounds

are chemically stable. Results reveal that both YCrSb and YMnSb are true HMFs having

integral magnetic moments of 4 µB and 3 µB, respectively. The µ𝑡𝑜𝑡 of the studied materials

are mainly contributed by the Cr and Mn atoms respectively. The d–d hybridization

between the transition-metal elements Y and Cr/Mn sorts the semiconducting gap inside

the majority spin as some other transition-metal centered HH materials. The HM gaps are

0.43 eV and 0.13 eV are found for the HH YCrSb and YMnSb compounds, respectively.

The electronic structure and DOS calculations indicate that both HH YCrSb and YMnSb

materials show semiconducting nature in majority spin channel and in contrast, conducting

trend observed in minority spin channel. It is found that HH YCrSb and YMnSb preserve

their half-metallicity for lattice constant ranges of 5.77 Å 6.85 Å and 5.92 Å–6.81 Å,

respectively and retain 100% SP at the EF.

The structural, electronic and magnetic properties of the HH YMnZ (Z = Si, Ge,

Sn) alloys are explored in three different atomic arrangements (X-type1, X-type2, and X-

type3) by using GGA and GGA+mBJ exchange-correlation energy potential. The HH

YMnSi and YMnGe compounds are energetically more favorable in the X-type1 phase

while HH YMnSn prefers the X-type2 structure. Furthermore, it is also noted that these

materials prefer FM state than the NM and AFM state. The computed GGA results show

that HH YMnSi is metallic whereas HH YMnGe and YMnSn materials show the HM

properties. In contrast, the GGA+mBJ estimation indicates that all three studied materials

are truly HM with total integer magnetic moment of 4 μB. It is made clear that GGA+mBJ

provides much better spin magnetic moments and band gaps as compared to those

computed with GGA. Furthermore, the half-metallicity is witnessed to be robust based on

the extended array of lattice parameter. Consequently, HH YMnZ materials are anticipating

alloys for the upcoming spintronics appliances. The transport properties of the YMnZ

materials have been curtained utilizing BoltzTrap simulation code. The computed figure of

merit computed an extensive variety of temperature demonstrates that HH YMnSi exhibits

preferred thermoelectric conduct over HH YMnGe and YMnSn materials.

146

Finally, half-metallicity explored for the new series of 90 hypothetical HH XYZ

materials (where X=Li, Na, K, Rb, Cs & Y= V, Nb, Ta and Z= Si, Ge, Sn, S, Se Te) by

using first-principles calculations. The T2 ordering never is most favorable in the HH XYZ

materials except for two HH LiNbSn and LiTaSn materials; the debate is in between T1

and T3 phases. All the HH XYZ materials energetically prefer either T1 or T3 phase as a

ground state. The examined 90 HH XYZ materials, 15 HH materials are found to be NM,

54 HH are energetically favorable to the FM and 21 materials prefer to the AFM ground

state. These 21 AFM HH XYZ materials are metallic in nature and do not possess HM

properties while remaining HH materials are stable at the FM state. Out of 90 HH materials,

39 materials are found to be HM at their equilibrium lattice constant with the most stable

state with FM configurations while remaining materials show HM properties in their meta

stable phase. Out of 39 HM HH XYZ materials, 28 materials are vibrationally stable at the

gamma point while remaining 11 HM HH materials show the imaginary phonon frequency

greater than 1THz. The HM HH NaVTe has the lowest negative mixing energy while others

have lower values of mixing energy, while HM HH RbVSe and CsVTe materials have the

greater values of the Curie temperature. The reason for the gap is due to the 3d orbital

splitting of the TMs (V, Nb & Ta) according to the crystal field theory with p-d

hybridization of the main group elements (Si, Ge, Sn, S, Se, Te). The phonon dispersion

curve for the RbVSe and CsVTe show the soft modes while FM SC LiVSi, LiVGe and

NaVSi do not have any soft modes indicating the dynamical stability of these materials.

The lower values of mixing energy and higher value of the Curie temperature along with

dynamical stability, make the two FM SCs LiVSi and LiVGe along with HM HH NaVSi

materials potential contenders for the spintronic applications.

147

9.1 Future Directions

Numerous intriguing theoretical as well as experimental studies will arise in near

future, which will exploit the plenty of benefits of the HM properties for the HH XYZ

materials that are presented in this dissertation.

➢ This dissertation contains the work on the structural, electronic and

magnetic properties for the different newly designed HH CrTiZ (where

Z=Si, Ge, Sn, Pb), FeVZ (where Z= Si, Ge, Sn), YCrSb & YMnSb, YMnZ

(Z= Si, Ge, Sn) and the 90 HH XYZ alloys (where X= Li, Na, K, Rb, Cs &

Y=V, Nb, Ta & Z=Si, Ge, Sn, S, Se, Te) which are presented for the first

time. So, there is a still scope for the more work for these mentioned HH

XYZ materials.

➢ Several other physical properties like optical, mechanical, thermoelectric,

elastic, Curie temperature should be determined for the presented HM HH

XYZ alloys in this dissertation. The most importantly their dynamical

stability should be checked from the phonon dispersion curve.

➢ So far, no experimental research is performed for all the HH XYZ materials

which are presented in this dissertation, therefore, our DFT investigated HM

HH XYZ materials provide a useful information that these HM HH XYZ

materials can be synthesize experimentally and are potential contenders for

the spintronic applications.

148

References

Ahmad, I and Amin, B. (2013). Robust Half-Metallicity in Ga 1-Xmnxp and Ga 1-

Xmnxas. Computational Materials Science, 6855-60.

Ahmadian, F and Alinajimi, R. (2013). First-Principles Study of Half-Metallic

Properties for the Heusler Alloys Sc 2 Crz (Z= C, Si, Ge, Sn). Computational

materials science, 79345-351.

Akai, H. (1998). Ferromagnetism and Its Stability in the Diluted Magnetic

Semiconductor (in, Mn) As. Physical Review Letters, 81(14): 3002.

Akinaga, H, Manago, T and Shirai, M. (2000). Material Design of Half-Metallic Zinc-

Blende Cras and the Synthesis by Molecular-Beam Epitaxy. Japanese Journal of

Applied Physics, 39(11B): L1118.

Al-Sawai, W, Lin, H, Markiewicz, R, Wray, L, Xia, Y, Xu, S-Y, Hasan, M and

Bansil, A. (2010). Topological Electronic Structure in Half-Heusler Topological

Insulators. Physical Review B, 82(12): 125208.

Aliev, F. (1991). Gap at Fermi Level in Some New D-and F-Electron Intermetallic

Compounds. Physica B: Condensed Matter, 171(1): 199-205.

Alijani, V, Winterlik, J, Fecher, GH, Naghavi, SS and Felser, C. (2011). Quaternary

Half-Metallic Heusler Ferromagnets for Spintronics Applications. Physical

Review B, 83(18): 184428.

Amin, B and Ahmad, I. (2009). Theoretical Investigation of Half Metallicity in

Fe/Co/Ni Doped Znse Material Systems. Journal of Applied Physics, 106(9):

093710.

Amin, B, Arif, S, Ahmad, I, Maqbool, M, Ahmad, R, Goumri-Said, S and Prisbrey,

K. (2011). Cr-Doped Iii–V Nitrides: Potential Candidates for Spintronics. Journal

of electronic materials, 40(6): 1428-1436.

Andersen, OK. (1975). Linear Methods in Band Theory. Physical Review B, 12(8):

3060.

Arif, S, Ahmad, I and Amin, B. (2012). Theoretical Investigation of Half‐Metallicity in

Co/Ni Substituted Aln. International Journal of Quantum Chemistry, 112(3):

882-888.

Awschalom, DD and Samarth, N. (2002). Optical Manipulation, Transport and Storage

of Spin Coherence in Semiconductors. In Semiconductor Spintronics and

Quantum Computation, pp. 147-193: Springer.

149

Azadani, JG, Munira, K, Romero, J, Ma, J, Sivakumar, C, Ghosh, AW and Butler,

WH. (2016). Anisotropy in Layered Half-Metallic Heusler Alloy Superlattices.

Journal of Applied Physics, 119(4): 043904.

Bae, T, Lee, S, Hong, J, Lee, DR and Roh, J. (2012). Effects of Magnetic Seed-Layers

on the Structural and Magnetic Properties of Co 2 Mnsi Heusler Alloy. Materials

Chemistry and Physics, 136(2): 577-581.

Bai, J, Raulot, J, Zhang, Y, Esling, C, Zhao, X and Zuo, L. (2011). Crystallographic,

Magnetic, and Electronic Structures of Ferromagnetic Shape Memory Alloys Ni 2

Xga (X= Mn, Fe, Co) from First-Principles Calculations. Journal of Applied

Physics, 109(1): 014908.

Baibich, MN, Broto, JM, Fert, A, Van Dau, FN, Petroff, F, Etienne, P, Creuzet, G,

Friederich, A and Chazelas, J. (1988). Giant Magnetoresistance of (001)

Fe/(001) Cr Magnetic Superlattices. Physical Review Letters, 61(21): 2472.

Balke, B, Fecher, GH, Kandpal, HC, Felser, C, Kobayashi, K, Ikenaga, E, Kim, J-J

and Ueda, S. (2006). Properties of the Quaternary Half-Metal-Type Heusler

Alloy Co 2 Mn 1− X Fe X Si. Physical Review B, 74(10): 104405.

Bayar, E, Kervan, N and Kervan, S. (2011). Half-Metallic Ferrimagnetism in the Ti 2

Coal Heusler Compound. Journal of Magnetism and Magnetic Materials,

323(23): 2945-2948.

Behin-Aein, B, Datta, D, Salahuddin, S and Datta, S. (2010). Proposal for an All-Spin

Logic Device with Built-in Memory. Nature nanotechnology, 5(4): 266-270.

Betzinger, M, Friedrich, C and Blügel, S. (2010). Hybrid Functionals within the All-

Electron Flapw Method: Implementation and Applications of Pbe0. Physical

Review B, 81(19): 195117.

Bhat, IH, Yousuf, S, Bhat, TM and Gupta, DC. (2015). Investigation of Electronic

Structure, Magnetic and Transport Properties of Half-Metallic Mn 2 Cusi and Mn

2 Znsi Heusler Alloys. Journal of Magnetism and Magnetic Materials, 39581-

88.

Bhattacharya, S, Pope, A, Littleton IV, R, Tritt, TM, Ponnambalam, V, Xia, Y and

Poon, S. (2000). Effect of Sb Doping on the Thermoelectric Properties of Ti-

Based Half-Heusler Compounds, Tinisn 1− X Sb X. Applied Physics Letters,

77(16): 2476-2478.

Birsan, A and Palade, P. (2013a). Band Structure Calculations of Ti2fesn: A New Half-

Metallic Compound. Intermetallics, 3686-89.

150

Birsan, A and Palade, P. (2013b). Band Structure Calculations of Ti 2 Fesn: A New

Half-Metallic Compound. Intermetallics, 3686-89.

Birsan, A, Palade, P and Kuncser, V. (2012). Half-Metallic State and Magnetic

Properties Versus the Lattice Constant in Ti2cosn Heusler Compound: An Ab

Initio Study. Solid state communications, 152(24): 2147-2150.

Birsan, A, Palade, P and Kuncser, V. (2013). Prediction of Half Metallic Properties in

Ti2cosi Heusler Alloy Based on Density Functional Theory. Journal of

Magnetism and Magnetic Materials, 331109-112.

Blaha, P, Schwarz, K, Madsen, G, Kvasnicka, D and Luitz, J. (2001a). Vienna

University of Technology. Vienna, Austria.

Blaha, P, Schwarz, K, Madsen, G, Kvasnicka, D and Luitz, J. (2001b). Wien2k. An

augmented plane wave+ local orbitals program for calculating crystal

properties.

Blöchl, PE, Jepsen, O and Andersen, OK. (1994). Improved Tetrahedron Method for

Brillouin-Zone Integrations. Physical Review B, 49(23): 16223.

Bona, G, Meier, F, Taborelli, M, Bucher, E and Schmidt, P. (1985). Spin Polarized

Photoemission from Nimnsb. Solid state communications, 56(4): 391-394.

Bradley, A and Rodgers, J. (1934). The Crystal Structure of the Heusler Alloys.

Proceedings of the Royal Society of London. Series A, Containing Papers of a

Mathematical and Physical Character, 144(852): 340-359.

Caballero, J, Park, Y, Childress, J, Bass, J, Chiang, W-C, Reilly, A, Pratt Jr, W and

Petroff, F. (1998). Magnetoresistance of Nimnsb-Based Multilayers and Spin

Valves. Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and

Films, 16(3): 1801-1805.

Caballero, J, Reilly, A, Hao, Y, Bass, J, Pratt Jr, W, Petroff, F and Childress, J.

(1999). Effect of Deposition Parameters on the Cpp-Gmr of Nimnsb-Based Spin-

Valve Structures. Journal of magnetism and magnetic materials, 19855-57.

Carey, MJ, Childress, JR and Maat, S. (2007). Magnetoresistive Sensor Based on Spin

Accumulation Effect with Free Layer Stabilized by in-Stack Orthogonal Magnetic

Coupling: Google Patents.

Caruso, A, Borca, C, Ristoiu, D, Nozieres, J and Dowben, P. (2003). A Comparison of

Surface Segregation for Two Semi-Heusler Alloys: Ticosb and Nimnsb. Surface

science, 525(1-3): L109-L115.

151

Casper, F, Graf, T, Chadov, S, Balke, B and Felser, C. (2012). Half-Heusler

Compounds: Novel Materials for Energy and Spintronic Applications.

Semiconductor Science and Technology, 27(6): 063001.

Chadov, S and Qi, X. (2010). S. Chadov, X. Qi, J. Kübler, Gh Fecher, C. Felser, and Sc

Zhang, Nat. Mater. 9, 541 (2010). Nat. Mater., 9541.

Chatterjee, S, Singh, V, Deb, A, Giri, S, De, S, Dasgupta, I and Majumdar, S. (2010).

Magnetic Properties of Ni2+ Xmn1-Xin Heusler Alloys: Theory and Experiment.

Journal of Magnetism and Magnetic Materials, 322(1): 102-107.

Checca, N, Caraballo-Vivas, R, Torrão, R, Rossi, A and Reis, M. (2017). Phase

Composition and Growth Mechanisms of Half-Metal Heusler Alloy Produced by

Pulsed Laser Deposition: From Core-Shell Nanoparticles to Amorphous

Randomic Clusters. Materials Chemistry and Physics, 196103-108.

Chen, J, Gao, G, Yao, K and Song, M. (2011). Half-Metallic Ferromagnetism in the

Half-Heusler Compounds Gekca and Snkca from First-Principles Calculations.

Journal of Alloys and Compounds, 509(42): 10172-10178.

Clowes, S, Miyoshi, Y, Bugoslavsky, Y, Branford, W, Grigorescu, C, Manea, S,

Monnereau, O and Cohen, L. (2004). Spin Polarization of the Transport Current

at the Free Surface of Bulk Nimnsb. Physical Review B, 69(21): 214425.

Coey, J. (2005). D0 Ferromagnetism. Solid State Sciences, 7(6): 660-667.

Continenza, A, Picozzi, S, Geng, W and Freeman, A. (2001). Coordination and

Chemical Effects on the Structural, Electronic, and Magnetic Properties in Mn

Pnictides. Physical Review B, 64(8): 085204.

Damewood, L, Busemeyer, B, Shaughnessy, M, Fong, C, Yang, L and Felser, C.

(2015a). Stabilizing and Increasing the Magnetic Moment of Half-Metals: The

Role of Li in Half-Heusler Limn Z (Z= N, P, Si). Physical Review B, 91(6):

064409.

Damewood, L, Busemeyer, B, Shaughnessy, M, Fong, CY, Yang, LH and Felser, C.

(2015b). Stabilizing and Increasing the Magnetic Moment of Half-Metals: The

Role of Li in Half-Heusler Limn Z (Z= N, P, Si). Physical Review B, 91(6):

064409.

Datta, S and Das, B. (1990). Electronic Analog of the Electro‐Optic Modulator. Applied

Physics Letters, 56(7): 665-667.

152

De Boeck, J, Van Roy, W, Das, J, Motsnyi, V, Liu, Z, Lagae, L, Boeve, H, Dessein, K

and Borghs, G. (2002a). Technology and Materials Issues in Semiconductor-

Based Magnetoelectronics. Semiconductor science and technology, 17(4): 342.

De Boeck, J, Van Roy, W, Motsnyi, V, Liu, Z, Dessein, K and Borghs, G. (2002b).

Hybrid Epitaxial Structures for Spintronics. Thin Solid Films, 412(1): 3-13.

De Groot, R and Buschow, K. (1986). Recent Developments in Half-Metallic

Magnetism. Journal of Magnetism and Magnetic Materials, 541377-1380.

De Groot, R, Mueller, F, Van Engen, P and Buschow, K. (1983). New Class of

Materials: Half-Metallic Ferromagnets. Physical Review Letters, 50(25): 2024.

De Groot, R, Van der Kraan, A and Buschow, K. (1986). Femnsb: A Half-Metallic

Ferrimagnet. Journal of magnetism and magnetic materials, 61(3): 330-336.

De Santanna, Y, De Melo, M, Santos, I, Coelho, A, Gama, S and Cótica, L. (2008).

Structural, Microstructural and Magnetocaloric Investigations in High-Energy

Ball Milled Powders. Solid State Communications, 148(7): 289-292.

De Wijs, G and De Groot, R. (2001). Towards 100% Spin-Polarized Charge-Injection:

The Half-Metallic Nimnsb/Cds Interface. Physical Review B, 64(2): 020402.

Debernardi, A, Peressi, M and Baldereschi, A. (2003). Structural and Electronic

Properties of Nimnsb Heusler Compound and Its Interface with Gaas. Materials

Science and Engineering: C, 23(6-8): 743-746.

Deka, B, Kundu, A, Ghosh, S and Srinivasan, A. (2016). Effect of Electron-Electron

Correlation and Site Disorder on the Magnetic Moment and Half-Metallicity of

Co 2 Fega 1− X Si X Alloys. Materials Chemistry and Physics, 177564-569.

Dong, S and Zhao, H. (2011). First-Principles Studies on Magnetic Properties of

Rocksalt Structure Mc (M= Ca, Sr, and Ba) under Pressure. Applied physics

letters, 98(18): 182501.

Faleev, SV, van Schilfgaarde, M and Kotani, T. (2004). All-Electron Self-Consistent G

W Approximation: Application to Si, Mno, and Nio. Physical Review Letters,

93(12): 126406.

Fang, Q-L, Zhang, J-M, Xu, K-W and Ji, V. (2013). Electronic Structure and

Magnetism of Ti 2 Fesi: A First-Principles Study. Journal of Magnetism and

Magnetic Materials, 345171-175.

Fecher, GH, Kandpal, HC, Wurmehl, S, Morais, J, Lin, H-J, Elmers, H-J,

Schönhense, G and Felser, C. (2005). Design of Magnetic Materials: The

153

Electronic Structure of the Ordered, Doped Heusler Compound Co2cr1− Xfexal.

Journal of Physics: Condensed Matter, 17(46): 7237.

Felser, C, Fecher, GH and Balke, B. (2007). Spintronics: A Challenge for Materials

Science and Solid‐State Chemistry. Angewandte Chemie International Edition,

46(5): 668-699.

Felser, C, Wollmann, L, Chadov, S, Fecher, GH and Parkin, SS. (2015). Basics and

Prospective of Magnetic Heusler Compounds. APL materials, 3(4): 041518.

Feng, L, Liu, E, Zhang, W, Wang, W and Wu, G. (2014). First-Principles Investigation

of Half-Metallic Ferromagnetism of Half-Heusler Compounds Xyz. Journal of

Magnetism and Magnetic Materials, 35192-97.

Feng, W, Xiao, D, Zhang, Y and Yao, Y. (2010). Half-Heusler Topological Insulators:

A First-Principles Study with the Tran-Blaha Modified Becke-Johnson Density

Functional. Physical Review B, 82(23): 235121.

Fujii, S, Sugimura, S and Asano, S. (1990). Hyperfine Fields and Electronic Structures

of the Heusler Alloys Co2mnx (X= Al, Ga, Si, Ge, Sn). Journal of Physics:

Condensed Matter, 2(43): 8583.

Galanakis, I. (2002a). Surface Half-Metallicity of Cras in the Zinc-Blende Structure.

Physical Review B, 66(1): 012406.

Galanakis, I. (2002b). Surface Properties of the Half-and Full-Heusler Alloys. Journal

of Physics: Condensed Matter, 14(25): 6329.

Galanakis, I. (2004). Appearance of Half-Metallicity in the Quaternary Heusler Alloys.


Galanakis, I. (2005). Electronic and Magnetic Properties of the (1 1 1) Surfaces of

Nimnsb. Journal of magnetism and magnetic materials, 288411-417.

Galanakis, I and Mavropoulos, P. (2003). Zinc-Blende Compounds of Transition

Elements with N, P, as, Sb, S, Se, and Te as Half-Metallic Systems. Physical

Review B, 67(10): 104417.

Galanakis, I, Mavropoulos, P and Dederichs, PH. (2006). Electronic Structure and

Slater–Pauling Behaviour in Half-Metallic Heusler Alloys Calculated from First

Principles. Journal of Physics D: Applied Physics, 39(5): 765.

Galanakis, I, Ostanin, S, Alouani, M, Dreyssé, H and Wills, J. (2000). Ab Initio

Ground State and L 2, 3 X-Ray Magnetic Circular Dichroism of Mn-Based

Heusler Alloys. Physical Review B, 61(6): 4093.

154

Galanakis, I, Özdoğan, K and Şaşıoğlu, E. (2008a). Ab Initio Electronic and Magnetic

Properties of Half-Metallic Nicrsi and Nimnsi Heusler Alloys: The Role of

Defects and Interfaces. Journal of Applied Physics, 104(8): 083916.

Galanakis, I, Şaşıoğlu, E and Özdoğan, K. (2008b). Magnetic Phase Transition in Half-

Metallic Comnsb and Nimnsb Semi-Heusler Alloys Upon Cu Doping: First-

Principles Calculations. Physical Review B, 77(21): 214417.

Gao, G, Yao, K, Şaşıoğlu, E, Sandratskii, L, Liu, Z and Jiang, J. (2007). Half-

Metallic Ferromagnetism in Zinc-Blende Cac, Src, and Bac from First Principles.


Gilleßen, M and Dronskowski, R. (2010). A Combinatorial Study of Inverse Heusler

Alloys by First‐Principles Computational Methods. Journal of computational

chemistry, 31(3): 612-619.

Gökoğlu, G. (2012). Ab Initio Electronic Structure of Nicocrga Half-Metallic Quaternary

Heusler Compound. Solid State Sciences, 14(9): 1273-1276.

Goll, G, Marz, M, Hamann, A, Tomanic, T, Grube, K, Yoshino, T and Takabatake,

T. (2008). Thermodynamic and Transport Properties of the Non-Centrosymmetric

Superconductor Labipt. Physica B: Condensed Matter, 403(5): 1065-1067.

Graf, T, Felser, C and Parkin, SS. (2011). Simple Rules for the Understanding of

Heusler Compounds. Progress in solid state chemistry, 39(1): 1-50.

Gruhn, T. (2010). Comparative Ab Initio Study of Half-Heusler Compounds for

Optoelectronic Applications. Physical Review B, 82(12): 125210.

Grünberg, P, Schreiber, R, Pang, Y, Brodsky, M and Sowers, H. (1986). Layered

Magnetic Structures: Evidence for Antiferromagnetic Coupling of Fe Layers

across Cr Interlayers. Physical Review Letters, 57(19): 2442.

Guo, S-D and Liu, B-G. (2011). Improved Half-Metallic Ferromagnetism of Transition-

Metal Pnictides and Chalcogenides Calculated with a Modified Becke-Johnson

Exchange Potential. EPL (Europhysics Letters), 93(4): 47006.

Gupta, DC and Bhat, IH. (2014). Full-Potential Study of Fe 2 Niz (Z= Al, Si, Ga, Ge).

Materials Chemistry and Physics, 146(3): 303-312.

Halilov, S and Kulatov, E. (1991). Electron and Magneto-Optical Properties of Half-

Metallic Ferromagnets and Uranium Monochalcogenide. Journal of Physics:

Condensed Matter, 3(33): 6363.

155

Hamidani, A, Bennecer, B and Boutarfa, B. (2009). Structural and Elastic Properties of

the Half-Heusler Compounds Irmnz (Z= Al, Sn and Sb). Materials Chemistry and

Physics, 114(2): 732-735.

Hanssen, K and Mijnarends, P. (1986). Positron-Annihilation Study of the Half-

Metallic Ferromagnet Nimnsb: Theory. Physical Review B, 34(8): 5009.

Hanssen, K, Mijnarends, P, Rabou, L and Buschow, K. (1990). Positron-Annihilation

Study of the Half-Metallic Ferromagnet Nimnsb: Experiment. Physical Review B,

42(3): 1533.

Hartjes, K and Jeitschko, W. (1995). Crystal Structures and Magnetic Properties of the

Lanthanoid Nickel Antimonides Lnnisb (Ln= La Nd, Sm, Gd Tm, Lu).

Journal of alloys and compounds, 226(1): 81-86.

Hatchard, T, Thorne, J, Farrell, S and Dunlap, R. (2008). Production of Ni100− X−

Ymnxgay Magnetic Shape Memory Alloys by Mechanical Alloying. Journal of

Physics: Condensed Matter, 20(44): 445205.

Helmholdt, R, De Groot, R, Mueller, F, Van Engen, P and Buschow, K. (1984).

Magnetic and Crystallographic Properties of Several C1 B Type Heusler

Compounds. Journal of Magnetism and Magnetic Materials, 43(3): 249-255.

Heusler, F. (1904). Über Manganbronze Und Über Die Synthese Magnetisierbarer

Legierungen Aus Unmagnetischen Metallen. Angewandte Chemie, 17(9): 260-

264.

Heusler, O. (1934). Kristallstruktur Und Ferromagnetismus Der Mangan‐Aluminium‐

Kupferlegierungen. Annalen der Physik, 411(2): 155-201.

Heyne, L, Igarashi, T, Kanomata, T, Neumann, K, Ouladdiaf, B and Ziebeck, K.

(2005). Atomic and Magnetic Order in the Weak Ferromagnet Covsb: Is It a Half-

Metallic Ferromagnet? Journal of Physics: Condensed Matter, 17(33): 4991.

Hirohata, A and Takanashi, K. (2014). Future Perspectives for Spintronic Devices.

Journal of Physics D: Applied Physics, 47(19): 193001.

Hongzhi, L, Zhiyong, Z, Li, M, Shifeng, X, Heyan, L, Jingping, Q, Yangxian, L and

Guangheng, W. (2007). Electronic Structure and Magnetic Properties of Fe2ysi

(Y= Cr, Mn, Fe, Co, Ni) Heusler Alloys: A Theoretical and Experimental Study.


Hordequin, C, Nozieres, J and Pierre, J. (1998). Half Metallic Nimnsb-Based Spin-

Valve Structures. Journal of magnetism and magnetic materials, 183(1-2): 225-

231.

156

Horne, M, Strange, P, Temmerman, W, Szotek, Z, Svane, A and Winter, H. (2004).

The Electronic Structure of Europium Chalcogenides and Pnictides. Journal of


Hu, S, Cazorla, C, Xiang, F, Ma, H, Wang, J, Wang, J, Wang, X, Ulrich, C, Chen, L

and Seidel, J. (2018). Strain Control of Giant Magnetic Anisotropy in Metallic

Perovskite Srcoo3-Δ Thin Films. ACS applied materials & interfaces.

Hu, Y and Zhang, J-M. (2017). Thermodynamic Stability, Magnetism and Half-

Metallicity of Various (100) Surfaces of Heusler Alloy Ti 2 Fesn. Materials

Chemistry and Physics, 192253-259.

Huang, H, Luo, S and Yao, K. (2012). First-Principles Study of Half-Metallic Properties

of the Heusler Alloy Ti 2 Coge. Journal of Magnetism and Magnetic Materials,

324(16): 2560-2564.

Huang, W, Wang, X, Chen, X, Lu, W, Damewood, L and Fong, C. (2014). Structural

and Electronic Properties of Half-Heusler Alloy Pdmnbi Calculated from First

Principles. Materials Chemistry and Physics, 148(1): 32-38.

Huang, W, Wang, X, Chen, X, Lu, W, Damewood, L and Fong, C. (2015). Structural

and Electronic Properties of Half-Heusler Alloys Ptxbi (with X= Mn, Fe, Co and

Ni) Calculated from First Principles. Journal of Magnetism and Magnetic

Materials, 377252-258.

Hussain, MK. (2018). Investigations of the Electronic and Magnetic Properties of Newly

(001) Surface Licrs and Licrse Half-Heusler Compounds. Applied Physics A,

124(4): 343.

Hybertsen, MS and Louie, SG. (1986). Electron Correlation in Semiconductors and

Insulators: Band Gaps and Quasiparticle Energies. Physical Review B, 34(8):

5390.

Hyeon, T. (2003). Chemical Synthesis of Magnetic Nanoparticles. Chemical

Communications(8): 927-934.

Inomata, K, Ikeda, N, Tezuka, N, Goto, R, Sugimoto, S, Wojcik, M and Jedryka, E.

(2016). Highly Spin-Polarized Materials and Devices for Spintronics∗. Science

and Technology of Advanced Materials.

Ishida, S, Akazawa, S, Kubo, Y and Ishida, J. (1982). Band Theory of Co2mnsn,

Co2tisn and Co2tial. Journal of Physics F: Metal Physics, 12(6): 1111.

157

Ishida, S, Fujii, S, Kashiwagi, S and Asano, S. (1995). Search for Half-Metallic

Compounds in Co2mnz (Z= Iiib, Ivb, Vb Element). Journal of the Physical

Society of Japan, 64(6): 2152-2157.

Ishida, S, Masaki, T, Fujii, S and Asano, S. (1997). Theoretical Predicts of Half-

Metallic Compounds with the C1 B Structure. Physica B: Condensed Matter,

239(1): 163-166.

Ishida, S, Masaki, T, Fujii, S and Asano, S. (1998). Theoretical Search for Half-

Metalliic Films of Co2mnz (Z Si, Ge). Physica B: Condensed Matter, 245(1):

1-8.

Ishikawa, M, Jorda, J and Junod, A. (1982). Superconductivity in D-and F-Band

Metals. Kernforschungszentrum Karlsruhe, Germany.

Ito, K, Ito, W, Umetsu, RY, Nagasako, M, Kainuma, R, Fujita, A, Oikawa, K and

Ishida, K. (2008). Martensitic Transformation in Nicomnsn Metamagnetic Shape

Memory Alloy Powders. Materials transactions, 49(8): 1915-1918.

Izadi, S and Nourbakhsh, Z. (2011). Structural, Electronic and Magnetic Properties of

Nanolayer Andábulk of Mnco2si and Mnfecosi Compounds. Journal of

superconductivity and novel magnetism, 24(1-2): 825-831.

Jaiganesh, G, Eithiraj, R and Kalpana, G. (2010). Theoretical Study of Electronic,

Magnetic and Structural Properties of Mo and W Based Group V (N, P, as, Sb and

Bi) Compounds. Computational materials science, 49(1): 112-120.

Jedema, FJ, Filip, A and Van Wees, B. (2001). Electrical Spin Injection and

Accumulation at Room Temperature in an All-Metal Mesoscopic Spin Valve.

Nature, 410(6826): 345-348.

Jenkins, S and King, D. (2002). Formation of Interface States on a Half-Metal Surface.

Surface science, 501(3): L185-L190.

Jepson, O and Anderson, O. (1971). The Electronic Structure of Hcp Ytterbium. Solid

State Communications, 9(20): 1763-1767.

Jimbo, M, Kanda, T, Goto, S, Tsunashima, S and Uchiyama, S. (1993). Giant

Magnetoresistance in Soft Magnetic Nifeco/Cu Multilayers with Various Buffer

Layers. Journal of magnetism and magnetic materials, 126(1-3): 422-424.

Jonker, B, Park, Y, Bennett, B, Cheong, H, Kioseoglou, G and Petrou, A. (2000).

Robust Electrical Spin Injection into a Semiconductor Heterostructure. Physical

Review B, 62(12): 8180.

158

Julliere, M. (1975). Tunneling between Ferromagnetic Films. Physics Letters A, 54(3):

225-226.

Kabani, R, Terada, M, Roshko, A and Moodera, J. (1990). Magnetic Properties of

Nimnsb Films. Journal of Applied Physics, 67(9): 4898-4900.

Kainuma, R, Imano, Y, Ito, W, Sutou, Y, Morito, H, Okamoto, S, Kitakami, O,

Oikawa, K, Fujita, A and Kanomata, T. (2006). Magnetic-Field-Induced Shape

Recovery by Reverse Phase Transformation. Nature, 439(7079): 957-960.

Kainuma, R, Ito, W, Umetsu, R, Oikawa, K and Ishida, K. (2008). Magnetic Field-

Induced Reverse Transformation in B 2-Type Nicomnal Shape Memory Alloys.

Applied Physics Letters, 93(9): 091906.

Kandpal, HC, Fecher, GH and Felser, C. (2007). Calculated Electronic and Magnetic

Properties of the Half-Metallic, Transition Metal Based Heusler Compounds.


Kato, H, Okuda, T, Okimoto, Y, Tomioka, Y, Oikawa, K, Kamiyama, T and

Tokura, Y. (2002). Metal-Insulator Transition of Ferromagnetic Ordered Double

Perovskites:(Sr 1− Y Ca Y) 2 Fereo 6. Physical Review B, 65(14): 144404.

Kato, H, Okuda, T, Okimoto, Y, Tomioka, Y, Oikawa, K, Kamiyama, T and

Tokura, Y. (2004). Structural and Electronic Properties of the Ordered Double

Perovskites a 2 M Reo 6 (a= Sr, Ca; M= Mg, Sc, Cr, Mn, Fe, Co, Ni, Zn).


Kervan, N and Kervan, S. (2012). A First-Principle Study of Half-Metallic

Ferrimagnetism in the Ti 2 Coga Heusler Compound. Journal of Magnetism and

Magnetic Materials, 324(4): 645-648.

Kervan, S and Kervan, N. (2011). Spintronic Properties of the Ti 2 Cob Heusler

Compound by Density Functional Theory. Solid State Communications, 151(17):

1162-1164.

Kieven, D, Klenk, R, Naghavi, S, Felser, C and Gruhn, T. (2010). I-Ii-V Half-Heusler

Compounds for Optoelectronics: Ab Initio Calculations. Physical Review B,

81(7): 075208.

Kilian, K and Victora, R. (2000). Electronic Structure of Ni 2 Mnin for Use in Spin

Injection. Journal of Applied Physics, 87(9): 7064-7066.

Kimura, Y, Ueno, H and Mishima, Y. (2009). Thermoelectric Properties of

Directionally Solidified Half-Heusler (M0. 5a, M0. 5b) Nisn (Ma, Mb= Hf, Zr, Ti)

Alloys. Journal of electronic materials, 38(7): 934-939.

159

Kirillova, M, Makhnev, A, Shreder, E, Dyakina, V and Gorina, N. (1995). Interband

Optical Absorption and Plasma Effects in Half‐Metallic Xmny Ferromagnets.

physica status solidi (b), 187(1): 231-240.

Ko, V, Han, G and Feng, Y. (2010). Electronic Band Structure Matching for Half-and

Full-Heusler Alloys. Journal of Magnetism and Magnetic Materials, 322(20):

2989-2993.

Kodama, RH, Makhlouf, SA and Berkowitz, AE. (1997). Finite Size Effects in

Antiferromagnetic Nio Nanoparticles. Physical Review Letters, 79(7): 1393.

Kohn, W and Sham, LJ. (1965). Self-Consistent Equations Including Exchange and

Correlation Effects. Physical review, 140(4A): A1133.

Komesu, T, Borca, C, Jeong, H-K, Dowben, PA, Ristoiu, D, Nozières, J, Stadler, S

and Idzerda, Y. (2000). The Polarization of Sb Overlayers on Nimnsb (100).

Physics Letters A, 273(4): 245-251.

Kotani, T. (1995). Exact Exchange Potential Band-Structure Calculations by the Linear

Muffin-Tin Orbital–Atomic-Sphere Approximation Method for Si, Ge, C, and

Mno. Physical Review Letters, 74(15): 2989.

Kübler, J. (2000). Theory of Itinerant Electron Magnetism: Oxford University Press.

Kübler, J, William, A and Sommers, C. (1983). Formation and Coupling of Magnetic

Moments in Heusler Alloys. Physical Review B, 28(4): 1745.

Kulatov, E and Mazin, I. (1990). Extended Stoner Factor Calculations for the Half-

Metallic Ferromagnets Nimnsb and Cro2. Journal of Physics: Condensed Matter,

2(2): 343.

Lakdja, A, Rozale, H, Chahed, A and Benhelal, O. (2013). Ferromagnetism in the

Half-Heusler Xcsba Compounds from First-Principles Calculations (X= C, Si, and

Ge). Journal of alloys and compounds, 5648-12.

Larson, P, Mahanti, S and Kanatzidis, M. (2000). Structural Stability of Ni-Containing

Half-Heusler Compounds. Physical Review B, 62(19): 12754.

Lei, F, Tang, C, Wang, S and He, W. (2011). Half-Metallic Full-Heusler Compound Ti

2 Nial: A First-Principles Study. Journal of Alloys and Compounds, 509(17):

5187-5189.

Lewis, SP, Allen, PB and Sasaki, T. (1997). Band Structure and Transport Properties of

Cro 2. Physical Review B, 55(16): 10253.

160

Ležaić, M, Galanakis, I, Bihlmayer, G and Blügel, S. (2005). Structural and Magnetic

Properties of the (001) and (111) Surfaces of the Half-Metal Nimnsb. Journal of


Li, J, Li, Y, Dai, X and Xu, X. (2009). Band Structure Calculations for Heusler Phase

Co 2 Ybi and Half-Heusler Phase Coybi (Y= Mn, Cr). Journal of Magnetism and

Magnetic Materials, 321(5): 365-372.

Li, L, Yu, Y, Ye, GJ, Ge, Q, Ou, X, Wu, H, Feng, D, Chen, XH and Zhang, Y. (2014).

Black Phosphorus Field-Effect Transistors. Nature nanotechnology, 9(5): 372.

Lin, S-Y, Yang, X-B and Zhao, Y-J. (2014). First-Principle Prediction of Robust Half-

Metallic Te-Based Half-Heusler Alloys. Journal of magnetism and magnetic

materials, 350119-123.

Liu, B-G. (2003). Robust Half-Metallic Ferromagnetism in Zinc-Blende Crsb. Physical

Review B, 67(17): 172411.

Liu, G, Dai, X, Liu, H, Chen, J, Li, Y, Xiao, G and Wu, G. (2008). Mn 2 Co Z (Z= Al,

Ga, in, Si, Ge, Sn, Sb) Compounds: Structural, Electronic, and Magnetic

Properties. Physical Review B, 77(1): 014424.

Loss, D and DiVincenzo, DP. (1998). Quantum Computation with Quantum Dots.

Physical Review A, 57(1): 120.

Lou, X, Adelmann, C, Crooker, SA, Garlid, ES, Zhang, J, Reddy, KM, Flexner, SD,

Palmstrøm, CJ and Crowell, PA. (2007). Electrical Detection of Spin Transport

in Lateral Ferromagnet–Semiconductor Devices. Nature Physics, 3(3): 197-202.

Lu, H, Schaff, WJ, Hwang, J, Wu, H, Koley, G and Eastman, LF. (2001). Effect of an

Aln Buffer Layer on the Epitaxial Growth of Inn by Molecular-Beam Epitaxy.

Applied physics letters, 79(10): 1489-1491.

Luo, H, Liu, G, Meng, F, Wang, L, Liu, E, Wu, G, Zhu, X and Jiang, C. (2011).

Slater–Pauling Behavior and Half-Metallicity in Heusler Alloys Mn 2 Cuz (Z= Ge

and Sb). Computational materials science, 50(11): 3119-3122.

Luo, H, Meng, F, Feng, Z, Li, Y, Zhu, W, Wu, G, Zhu, X, Jiang, C and Xu, H.

(2009). Ferromagnetism in the Mn-Based Heusler Alloy Mn 2 Nisb. Journal of

Applied Physics, 105(10): 103903.

Luo, H, Zhang, H, Zhu, Z, Ma, L, Xu, S, Wu, G, Zhu, X, Jiang, C and Xu, H.

(2008a). Half-Metallic Properties for the Mn 2 Fe Z (Z= Al, Ga, Si, Ge, Sb)

Heusler Alloys: A First-Principles Study. Journal of Applied Physics, 103(8):

083908.

161

Luo, H, Zhu, Z, Liu, G, Xu, S, Wu, G, Liu, H, Qu, J and Li, Y. (2008b). Ab-Initio

Investigation of Electronic Properties and Magnetism of Half-Heusler Alloys

Xcral (X= Fe, Co, Ni) and Nicrz (Z= Al, Ga, in). Physica B: Condensed Matter,

403(1): 200-206.

Lv, S, Li, H, Han, D, Wu, Z, Liu, X and Meng, J. (2011). A Better Ferrimagnetic Half-

Metal Lucu3mn4o12: Predicted from First-Principles Investigation. Journal of

magnetism and magnetic materials, 323(5): 416-421.

Madsen, GK and Singh, DJ. (2006). Boltztrap. A Code for Calculating Band-Structure

Dependent Quantities. Computer Physics Communications, 175(1): 67-71.

Maekawa, S and Gafvert, U. (1982). Electron Tunneling between Ferromagnetic Films.

IEEE Transactions on magnetics, 18(2): 707-708.

Mancoff, F, Clemens, B, Singley, E and Basov, D. (1999). Infrared Probe of the

Electronic Structure and Carrier Scattering in Nimnsb Thin Films. Physical

Review B, 60(18): R12565.

Mañosa, L, Planes, A, Acet, M, Duman, E and Wassermann, E. (2004). Magnetic

Shape Memory in Ni–Mn–Ga and Ni–Mn–Al. Journal of Magnetism and


Mastronardi, K, Young, D, Wang, C-C, Khalifah, P, Cava, R and Ramirez, A.

(1999). Antimonides with the Half-Heusler Structure: New Thermoelectric

Materials. Applied Physics Letters, 74(10): 1415-1417.

Mavropoulos, P, Galanakis, I and Dederichs, P. (2004). Multilayers of Zinc-Blende

Half-Metals with Semiconductors. Journal of Physics: Condensed Matter,

16(24): 4261.

Mikami, M, Ozaki, K, Takazawa, H, Yamamoto, A, Terazawa, Y and Takeuchi, T.

(2013). Effect of Ti Substitution on Thermoelectric Properties of W-Doped

Heusler Fe^ Sub 2^ Val Alloy. Journal of electronic materials, 42(7): 1801.

Mikhailov, GM and Rai, D. (2018). Electronic, Elastic and X-Ray Spectroscopic

Properties of Direct and Inverse Full Heusler Compounds: Dft+ U Study. arXiv

preprint arXiv:1805.02618.

Miura, Y, Nagao, K and Shirai, M. (2004a). Atomic Disorder Effects on Half-

Metallicity of the Full-Heusler Alloys Co 2 (Cr 1− X Fe X) Al: A First-Principles

Study. Physical Review B, 69(14): 144413.

Miura, Y, Shirai, M and Nagao, K. (2004b). First-Principles Study on Half-Metallicity

of Disordered Co2 (Cr1-Xfex) Al. Journal of applied physics, 957225-7227.

162

Miyazaki, T, Kumagai, S and Yaoi, T. (1997). Spin Tunneling in Ni-Fe/Al2o3/Co

Junction Devices. Journal of applied physics, 813753-3757.

Miyazaki, T and Tezuka, N. (1995). Giant Magnetic Tunneling Effect in Fe/Al 2 O 3/Fe

Junction. Journal of Magnetism and Magnetic Materials, 139(3): L231-L234.

Mizuguchi, M, Akinaga, H, Manago, T, Ono, K, Oshima, M, Shirai, M, Yuri, M,

Lin, H, Hsieh, H and Chen, C. (2002). Epitaxial Growth of Zinc-Blende

Cras/Gaas Multilayer. Journal of Applied Physics, 91(10): 7917-7919.

Mohankumar, R, Ramasubramanian, S, Rajagopalan, M, Raja, MM, Kamat, S and

Kumar, J. (2015). Effect of Fe Substitution on the Electronic Structure, Magnetic

and Thermoelectric Properties of Co 2 Fesi Full Heusler Alloy: A First Principle

Study. Computational Materials Science, 10934-40.

Monir, MEA, Khenata, R, Baltache, H, Murtaza, G, Abu-Jafar, M, Bouhemadou, A,

Omran, SB and Rached, D. (2015). Study of Structural, Electronic and Magnetic

Properties of Cofein and Co 2 Fein Heusler Alloys. Journal of Magnetism and


Moodera, JS, Kinder, LR, Wong, TM and Meservey, R. (1995). Large

Magnetoresistance at Room Temperature in Ferromagnetic Thin Film Tunnel

Junctions. Physical Review Letters, 74(16): 3273.

Moodera, JS, Nassar, J and Mathon, G. (1999). Spin-Tunneling in Ferromagnetic

Junctions. Annual Review of Materials Science, 29(1): 381-432.

Murnaghan, F. (1944a). The Compressibility of Media under Extreme Pressures.

Proceedings of the national academy of sciences of the United States of

America, 30(9): 244.

Murnaghan, F. (1944b). The Compressibility of Media under Extreme Pressures.

Proceedings of the National Academy of Sciences, 30(9): 244-247.

Murnaghan, FD. (1937). Finite Deformations of an Elastic Solid. American Journal of

Mathematics235-260.

Nagao, K, Shirai, M and Miura, Y. (2004). Ab Initio Calculations of Zinc-Blende

Cras/Gaas Superlattices. Journal of Applied Physics, 95(11): 6518-6520.

Nanda, B and Dasgupta, I. (2003). Electronic Structure and Magnetism in Half-Heusler

Compounds. Journal of Physics: Condensed Matter, 15(43): 7307.

Nishino, Y, Kato, M, Asano, S, Soda, K, Hayasaki, M and Mizutani, U. (1997).

Semiconductorlike Behavior of Electrical Resistivity in Heusler-Type Fe 2 Val

Compound. Physical Review Letters, 79(10): 1909.

163

Ogawa, T, Shirai, M, Suzuki, N and Kitagawa, I. (1999). First-Principles Calculations

of Electronic Structures of Diluted Magnetic Semiconductors (Ga, Mn) As.

Journal of Magnetism and Magnetic Materials, 196428-429.

Ohno, H. (1998). Making Nonmagnetic Semiconductors Ferromagnetic. science,

281(5379): 951-956.

Ono, K, Okabayashi, J, Mizuguchi, M, Oshima, M, Fujimori, A and Akinaga, H.

(2002). Fabrication, Magnetic Properties, and Electronic Structures of Nanoscale

Zinc-Blende Mnas Dots. Journal of applied physics, 91(10): 8088-8092.

Orgassa, D, Fujiwara, H, Schulthess, T and Butler, W. (1999). First-Principles

Calculation of the Effect of Atomic Disorder on the Electronic Structure of the

Half-Metallic Ferromagnet Nimnsb. Physical Review B, 60(19): 13237.

Ouardi, S, Fecher, GH, Felser, C and Kübler, J. (2013). Realization of Spin Gapless

Semiconductors: The Heusler Compound Mn 2 Coal. Physical Review Letters,

110(10): 100401.

Özdog, K and Galanakis, I. (2009). First-Principles Electronic and Magnetic Properties

of the Half-Metallic Antiferromagnet Cr2mnsb. Journal of Magnetism and

Magnetic Materials, 321(15): L34-L36.

Özdogan, K, Galanakis, I, Şaşioglu, E and Aktaş, B. (2006). Search for Half-Metallic

Ferrimagnetism in V-Based Heusler Alloys Mn2vz (Z= Al, Ga, in, Si, Ge, Sn).


Özdoğan, K, Şaşıoğlu, E and Galanakis, I. (2009). Tuning the Magnetic Properties of

Half-Metallic Semi-Heusler Alloys by Sp-Electron Substitution: The Case of

Aumnsn1− Xsbx Quaternary Alloys. Journal of Physics D: Applied Physics,

42(8): 085003.

Pask, J, Yang, L, Fong, C, Pickett, W and Dag, S. (2003). Six Low-Strain Zinc-Blende

Half Metals: An Ab Initio Investigation. Physical Review B, 67(22): 224420.

Pauling, L. (1938). The Nature of the Interatomic Forces in Metals. Physical Review,

54(11): 899.

Perdew, JP, Burke, K and Ernzerhof, M. (1996a). Generalized Gradient

Approximation Made Simple. Physical Review Letters, 77(18): 3865.

Perdew, JP, Burke, K and Wang, Y. (1996b). Generalized Gradient Approximation for

the Exchange-Correlation Hole of a Many-Electron System. Physical Review B,

54(23): 16533.

164

Peruman, KV, Mahendran, M, Seenithurai, S, Chokkalingam, R, Singh, R and

Chandrasekaran, V. (2010). Internal Stress Dependent Structural Transition in

Ferromagnetic Ni–Mn–Ga Nanoparticles Prepared by Ball Milling. Journal of

Physics and Chemistry of Solids, 71(11): 1540-1544.

Picozzi, S, Continenza, A and Freeman, A. (2002). Co 2 Mn X (X= Si, Ge, Sn) Heusler

Compounds: An Ab Initio Study of Their Structural, Electronic, and Magnetic

Properties at Zero and Elevated Pressure. Physical Review B, 66(9): 094421.

Picozzi, S, Continenza, A and Freeman, A. (2004). Role of Structural Defects on the

Half-Metallic Character of Co 2 Mnge and Co 2 Mnsi Heusler Alloys. Physical

Review B, 69(9): 094423.

Pierre, J, Skolozdra, R, Tobola, J, Kaprzyk, S, Hordequin, C, Kouacou, M, Karla, I,

Currat, R and Lelievre-Berna, E. (1997). Properties on Request in Semi-

Heusler Phases. Journal of alloys and compounds, 262101-107.

Prinz, GA. (1998). Magnetoelectronics. science, 282(5394): 1660-1663.

Prinz, GA. (1999). Magnetoelectronics Applications. Journal of magnetism and

magnetic materials, 200(1-3): 57-68.

Puselj, M and Ban, Z. (1969). Crystal Structure of Ticuhg2. CROATICA CHEMICA

ACTA, 41(2): 79-&.

Qi, S, Shen, J and Zhang, C-H. (2015). First-Principles Study on the Structural,

Electronic and Magnetic Properties of the Ti 2 Vz (Z= Si, Ge, Sn) Full-Heusler

Compounds. Materials Chemistry and Physics, 164177-182.

Raj, K and Moskowitz, R. (1990). Commercial Applications of Ferrofluids. Journal of

Magnetism and Magnetic Materials, 85(1-3): 233-245.

Rasool, MN, Hussain, A, Javed, A, Khan, MA and Iqbal, F. (2016). Structural

Stability, Electronic and Magnetic Behaviour of Spin-Polarized Ycovz (Z= Si,

Ge) and Ycotiz (Z= Si, Ge) Heusler Alloys. Materials Chemistry and Physics,

183524-533.

Rauf, S, Arif, S, Haneef, M and Amin, B. (2015). The First Principle Study of Magnetic

Properties of Mn 2 Wsn, Fe 2 Ysn (Y= Ti, V), Co 2 Ysn (Y= Ti, Zr, Hf, V, Mn)

and Ni 2 Ysn (Y= Ti, Zr, Hf, V, Mn) Heusler Alloys. Journal of Physics and

Chemistry of Solids, 76153-169.

Ristoiu, D, Nozieres, J, Borca, C, Borca, B and Dowben, PA. (2000a). Manganese

Surface Segregation in Nimnsb. Applied Physics Letters, 76(17): 2349-2351.

165

Ristoiu, D, Nozieres, J, Borca, C, Komesu, T, Jeong, H-K and Dowben, PA. (2000b).

The Surface Composition and Spin Polarization of Nimnsb Epitaxial Thin Films.

EPL (Europhysics Letters), 49(5): 624.

Ritchie, L, Xiao, G, Ji, Y, Chen, T, Chien, C, Zhang, M, Chen, J, Liu, Z, Wu, G and

Zhang, X. (2003). Magnetic, Structural, and Transport Properties of the Heusler

Alloys Co 2 Mnsi and Nimnsb. Physical Review B, 68(10): 104430.

Roy, A, Bennett, JW, Rabe, KM and Vanderbilt, D. (2012). Half-Heusler

Semiconductors as Piezoelectrics. Physical Review Letters, 109(3): 037602.

Rozale, H, Amar, A, Lakdja, A, Moukadem, A and Chahed, A. (2013). Half-

Metallicity in the Half-Heusler Rbsrc, Rbsrsi and Rbsrge Compounds. Journal of

magnetism and magnetic materials, 33683-87.

Sadouki, H, Belkadi, A, Zaoui, Y, Amari, S, Obodo, K, Beldi, L and Bouhafs, B.

(2018a). Prediction of Half-Metallicity in the Nas, Nase and Nate Alkali-Metal

Chalcogenides Using First Principles. International Journal of Computational

Materials Science and Engineering1850015.

Sadouki, H, Belkadi, A, Zaoui, Y, Beldi, L, Bouhafs, B, Méçabih, S and Abbar, B.

(2018b). Ab-Initio Prediction of Half-Metallicity in Lithium Chalcogenides

Compounds Lix (X= S, Se and Te) in Zinc-Blende and Wurtzite Structures.

Computational Condensed Matter, 16.

Saeed, Y, Nazir, S, Shaukat, A and Reshak, AH. (2010). Ab-Initio Calculations of Co-

Based Diluted Magnetic Semiconductors Cd1− Xcoxx (X= S, Se, Te). Journal of


Sakurada, S and Shutoh, N. (2005). Effect of Ti Substitution on the Thermoelectric

Properties of (Zr, Hf) Nisn Half-Heusler Compounds. Applied Physics Letters,

86(8): 082105.

Sanvito, S and Hill, NA. (2000). Ground State of Half-Metallic Zinc-Blende Mnas.


Sanyal, B, Bergqvist, L and Eriksson, O. (2003). Ferromagnetic Materials in the Zinc-

Blende Structure. Physical Review B, 68(5): 054417.

Şaşıoğlu, E, Sandratskii, L and Bruno, P. (2004). First-Principles Calculation of the

Intersublattice Exchange Interactions and Curie Temperatures of the Full Heusler

Alloys Ni 2 Mn X (X= Ga, in, Sn, Sb). Physical Review B, 70(2): 024427.

Sattar, MA, Rashid, M, Hashmi, MR, Ahmad, S, Imran, M and Hussain, F. (2016a).

Theoretical Investigations of Half-Metallic Ferromagnetism in New Half–Heusler

166

Ycrsb and Ymnsb Alloys Using First-Principle Calculations. Chinese Physics B,

25(10): 107402.

Sattar, MA, Rashid, M, Hashmi, MR, Rasool, MN, Mahmood, A and Ahmad, S.

(2016b). Spin-Polarized Calculations of Structural, Electronic and Magnetic

Properties of Half Heusler Alloys FeVZ (Z= Si, Ge, Sn) Using Ab-Initio Method.

Materials Science in Semiconductor Processing, 5148-54.

Schladt, TD, Schneider, K, Shukoor, MI, Natalio, F, Bauer, H, Tahir, MN, Weber, S,

Schreiber, LM, Schröder, HC and Müller, WE. (2010). Highly Soluble

Multifunctional Mno Nanoparticles for Simultaneous Optical and Mri Imaging

and Cancer Treatment Using Photodynamic Therapy. Journal of Materials

Chemistry, 20(38): 8297-8304.

Schliemann, J, Egues, JC and Loss, D. (2003). Nonballistic Spin-Field-Effect

Transistor. Physical Review Letters, 90(14): 146801.

Schmalhorst, J, Kämmerer, S, Sacher, M, Reiss, G, Hütten, A and Scholl, A. (2004).

Interface Structure and Magnetism of Magnetic Tunnel Junctions with a Co 2 Mn

Si Electrode. Physical Review B, 70(2): 024426.

Schwall, M and Balke, B. (2011). Niobium Substitution in Zr 0.5 Hf 0.5 Nisn Based

Heusler Compounds for High Power Factors. Applied Physics Letters, 98(4):

042106.

Schwarz, K, Blaha, P and Madsen, G. (2002). Electronic Structure Calculations of

Solids Using the Wien2k Package for Material Sciences. Computer Physics

Communications, 147(1): 71-76.

Sham, L and Kohn, W. (1966). One-Particle Properties of an Inhomogeneous

Interacting Electron Gas. Physical Review, 145(2): 561.

Shan, R, Sukegawa, H, Wang, W, Kodzuka, M, Furubayashi, T, Ohkubo, T, Mitani,

S, Inomata, K and Hono, K. (2009). Demonstration of Half-Metallicity in

Fermi-Level-Tuned Heusler Alloy Co 2 Feal 0.5 Si 0.5 at Room Temperature.

Physical Review Letters, 102(24): 246601.

Sharma, S, Dewhurst, J and Ambrosch-Draxl, C. (2005). All-Electron Exact Exchange

Treatment of Semiconductors: Effect of Core-Valence Interaction on Band-Gap

and D-Band Position. Physical Review Letters, 95(13): 136402.

Sharma, V, Solanki, A and Kashyap, A. (2010a). Electronic, Magnetic and Transport

Properties of Co2tiz (Z= Si, Ge and Sn): A First-Principle Study. Journal of


167

Sharma, V, Solanki, A and Kashyap, A. (2010b). Electronic, Magnetic and Transport

Properties of Co 2 Tiz (Z= Si, Ge and Sn): A First-Principle Study. Journal of

Magnetism and Magnetic Materials, 322(19): 2922-2928.

Shirai, M. (2001). Electronic and Magnetic Properties of 3d Transition-Metal-Doped

Gaas. Physica E: Low-dimensional Systems and Nanostructures, 10(1-3): 143-

147.

Shishidou, T, Freeman, A and Asahi, R. (2001). Effect of Gga on the Half-Metallicity

of the Itinerant Ferromagnet Cos 2. Physical Review B, 64(18): 180401.

Sholl, D and Steckel, JA. (2011). Density Functional Theory: A Practical Introduction:

John Wiley & Sons.

Skovsen, I, Bjerg, L, Christensen, M, Nishibori, E, Balke, B, Felser, C and Iversen,

BB. (2010). Multi-Temperature Synchrotron Pxrd and Physical Properties Study

of Half-Heusler Ticosb. Dalton Transactions, 39(42): 10154-10159.

Slater, JC. (1936). The Ferromagnetism of Nickel. Physical Review, 49(7): 537.

Ślebarski, A, Maple, M, Wrona, A and Winiarska, A. (2001). Kondo-Type Behavior

in Fe 2− X M X Tisn (M= Co, Ni). Physical Review B, 63(21): 214416.

Snyder, GJ and Toberer, ES. (2008). Complex Thermoelectric Materials. Nature

materials, 7(2): 105-114.

Soeya, S, Hayakawa, J, Takahashi, H, Ito, K, Yamamoto, C, Kida, A, Asano, H and

Matsui, M. (2002). Development of Half-Metallic Ultrathin Fe3o4 Films for

Spin-Transport Devices. Applied physics letters, 80(5): 823-825.

Son, Y-W, Cohen, ML and Louie, SG. (2006). Half-Metallic Graphene Nanoribbons.

Nature, 444(7117): 347-349.

Song, W, Wang, J and Wu, Z. (2009a). Half Metallic Properties of Sr 2 Cuoso 6.

Chemical Physics Letters, 482(4): 246-248.

Song, W, Zhao, E, Meng, J and Wu, Z. (2009b). Near Compensated Half-Metal in

Sr2nioso6. Journal of Chemical Physics, 130(11): 114707.

Sootsman, JR, Chung, DY and Kanatzidis, MG. (2009). New and Old Concepts in

Thermoelectric Materials. Angewandte Chemie International Edition, 48(46):

8616-8639.

Soulen, R, Byers, J, Osofsky, M, Nadgorny, B, Ambrose, T, Cheng, S, Broussard,

PR, Tanaka, C, Nowak, J and Moodera, J. (1998). Measuring the Spin

Polarization of a Metal with a Superconducting Point Contact. science, 282(5386):

85-88.

168

Städele, M, Majewski, J, Vogl, P and Görling, A. (1997). Exact Kohn-Sham Exchange

Potential in Semiconductors. Physical Review Letters, 79(11): 2089.

Stroppa, A, Picozzi, S, Continenza, A and Freeman, A. (2003). Electronic Structure

and Ferromagnetism of Mn-Doped Group-Iv Semiconductors. Physical Review B,

68(15): 155203.

Suits, JC. (1976). New Magnetic Compounds with Heusler and Heusler-Related

Structures. Physical Review B, 14(9): 4131.

Sun, S. (2006). Recent Advances in Chemical Synthesis, Self‐Assembly, and

Applications of Fept Nanoparticles. Advanced Materials, 18(4): 393-403.

Szotek, Z, Temmerman, W, Svane, A, Petit, L, Stocks, G and Winter, H. (2004).

Half-Metallic Transition Metal Oxides. Journal of magnetism and magnetic

materials, 2721816-1817.

Tan, J-J, Ji, G-F, Chen, X-R and Gou, Q-Q. (2010). Condensed Matter: Structural,

Mechanical, and Thermal Properties: Phase Transition and Phonon Spectrum of

Zinc-Blende Structure Znx (X= S, Se, Te). Communications in Theoretical

Physics, 531160-1166.

Tanaka, C, Nowak, J and Moodera, J. (1997). Magnetoresistance in Ferromagnet-

Insulator-Ferromagnet Tunnel Junctions with Half-Metallic Ferromagnet Nimnsb

Compound. Journal of Applied Physics, 81(8): 5515-5517.

Tanaka, CT, Nowak, J and Moodera, JS. (1999). Spin-Polarized Tunneling in a Half-

Metallic Ferromagnet. Journal of Applied Physics, 86(11): 6239-6242.

Tanveer, W, Faridi, M, Noor, N, Mahmood, A and Amin, B. (2015). First-Principles

Investigation of Structural, Elastic, Electronic and Magnetic Properties of Be 0.75

Co 0.25 Y (Y S, Se and Te) Compounds. Current Applied Physics, 15(11): 1324-

1331.

Tedrow, P and Meservey, R. (1973). Spin Polarization of Electrons Tunneling from

Films of Fe, Co, Ni, and Gd. Physical Review B, 7(1): 318.

Toboła, J, Kaprzyk, S and Pecheur, P. (2003). Theoretical Search for Magnetic Half‐

Heusler Semiconductors. physica status solidi (b), 236(2): 531-535.

Tobola, J, Pierre, J, Kaprzyk, S, Skolozdra, R and Kouacou, M. (1998). Crossover

from Semiconductor to Magnetic Metal in Semi-Heusler Phases as a Function of

Valence Electron Concentration. Journal of Physics: Condensed Matter, 10(5):

1013.

169

Tran, F and Blaha, P. (2009). Accurate Band Gaps of Semiconductors and Insulators

with a Semilocal Exchange-Correlation Potential. Physical Review Letters,

102(22): 226401.

Tran, F, Blaha, P and Schwarz, K. (2007). Band Gap Calculations with Becke–Johnson

Exchange Potential. Journal of Physics: Condensed Matter, 19(19): 196208.

Uher, C, Yang, J, Hu, S, Morelli, D and Meisner, G. (1999). Transport Properties of

Pure and Doped Mnisn (M= Zr, Hf). Physical Review B, 59(13): 8615.

Ullakko, K, Huang, J, Kantner, C, O’handley, R and Kokorin, V. (1996). Large

Magnetic‐Field‐Induced Strains in Ni2mnga Single Crystals. Applied Physics

Letters, 69(13): 1966-1968.

Umamaheswari, R, Yogeswari, M and Kalpana, G. (2013). Electronic Properties and

Structural Phase Transition in a 4 [M 4 O 4](a= Li, Na, K and Rb; M= Ag and

Cu): A First Principles Study. Solid State Communications, 15562-68.

Umamaheswari, R, Yogeswari, M and Kalpana, G. (2014). Ab-Initio Investigation of

Half-Metallic Ferromagnetism in Half-Heusler Compounds Xyz (X= Li, Na, K

and Rb; Y= Mg, Ca, Sr and Ba; Z= B, Al and Ga). Journal of magnetism and

magnetic materials, 350167-173.

Van Dinh, A, Sato, K and Katayama-Yoshida, H. (2009). Structural and Magnetic

Properties of Room Temperature Ferromagnets Nicrz. Journal of Computational

and Theoretical Nanoscience, 6(12): 2589-2596.

Van Roy, W, De Boeck, J, Brijs, B and Borghs, G. (2000). Epitaxial Nimnsb Films on

Gaas (001). Applied Physics Letters, 77(25): 4190-4192.

Vivas, RC, Pedro, S, Cruz, C, Tedesco, J, Coelho, A, Carvalho, AMG, Rocco, D and

Reis, M. (2016). Experimental Evidences of Enhanced Magnetocaloric Properties

at Room Temperature and Half-Metallicity on Fe 2 Mnsi-Based Heusler Alloys.

Materials Chemistry and Physics, 17423-27.

Wang, C, Guo, Y, Casper, F, Balke, B, Fecher, G, Felser, C and Hwu, Y. (2010). Size

Correlated Long and Short Range Order of Ternary Co 2 Fega Heusler

Nanoparticles. Applied Physics Letters, 97(10): 103106.

Wang, H, Wang, B, Li, Q, Zhu, Z, Wang, R and Woo, C. (2007). First-Principles

Study of the Cubic Perovskites Bi M O 3 (M= Al, Ga, in, and Sc). Physical

Review B, 75(24): 245209.

170

Wang, X, Antropov, V and Harmon, B. (1994). First Principles Study of Magneto-

Optical Properties of Half Metallic Heusler Alloys: Nimnsb and Ptmnsb. IEEE

Transactions on Magnetics, 30(6): 4458-4460.

Wang, X, Cheng, Z, Guo, R, Wang, J, Rozale, H, Wang, L, Yu, Z and Liu, G.

(2017a). First-Principles Study of New Quaternary Heusler Compounds without

3d Transition Metal Elements: Zrrhhfz (Z= Al, Ga, in). Materials Chemistry and

Physics, 19399-108.

Wang, X, Cheng, Z and Liu, G. (2017b). Largest Magnetic Moments in the Half-

Heusler Alloys Xcrz (X= Li, K, Rb, Cs; Z= S, Se, Te): A First-Principles Study.

Materials, 10(9): 1078.

Watanabe, K. (1976). K. Watanabe, Trans. Jpn. Inst. Met. 17, 220 (1976). Trans. Jpn.

Inst. Met., 17220.

Webster, P. (1971). Magnetic and Chemical Order in Heusler Alloys Containing Cobalt

and Manganese. Journal of Physics and Chemistry of Solids, 32(6): 1221-1231.

Webster, P and Ziebeck, K. (1988a). Alloys and Compounds of D-Elements with Main

Group Elements. Part, 275-184.

Webster, P and Ziebeck, K. (1988b). Landolt-Börnstein—Group Iii Condensed Matter

Vol 19c: Heidelberg: Springer) p.

Webster, P, Ziebeck, K, Town, S and Peak, M. (1984). Magnetic Order and Phase

Transformation in Ni2mnga. Philosophical Magazine B, 49(3): 295-310.

Webster, PJ. (1969). Heusler Alloys. Contemporary Physics, 10(6): 559-577.

Winterlik, J, Fecher, GH, Felser, C, Jourdan, M, Grube, K, Hardy, F, von

Löhneysen, H, Holman, K and Cava, R. (2008). Ni-Based Superconductor:

Heusler Compound Zrni 2 Ga. Physical Review B, 78(18): 184506.

Wolf, S, Awschalom, D, Buhrman, R, Daughton, J, Von Molnar, S, Roukes, M,

Chtchelkanova, AY and Treger, D. (2001). Spintronics: A Spin-Based

Electronics Vision for the Future. science, 294(5546): 1488-1495.

Wooten, F. (1972). Optical Properties of Solids.

Wurmehl, S, Fecher, GH, Kandpal, HC, Ksenofontov, V, Felser, C, Lin, H-J and

Morais, J. (2005). Geometric, Electronic, and Magnetic Structure of Co 2 Fesi:

Curie Temperature and Magnetic Moment Measurements and Calculations.


Wurmehl, S, Fecher, GH, Kroth, K, Kronast, F, Dürr, HA, Takeda, Y, Saitoh, Y,

Kobayashi, K, Lin, H-J and Schönhense, G. (2006). Electronic Structure and

171

Spectroscopy of the Quaternary Heusler Alloy Co2cr1− Xfexal. Journal of

Physics D: Applied Physics, 39(5): 803.

Xiao, D, Yao, Y, Feng, W, Wen, J, Zhu, W, Chen, X, Stocks, GM and Zhang, Z.

(2010). Half-Heusler Compounds as a New Class of Three-Dimensional

Topological Insulators. arXiv preprint arXiv:1008.0057.

Xie, W-H, Xu, Y-Q, Liu, B-G and Pettifor, D. (2003). Half-Metallic Ferromagnetism

and Structural Stability of Zincblende Phases of the Transition-Metal

Chalcogenides. Physical Review Letters, 91(3): 037204.

Xie, W, Jin, Q and Tang, X. (2008). The Preparation and Thermoelectric Properties of

Ti 0.5 Zr 0.25 Hf 0.25 Co 1− X Ni X Sb Half-Heusler Compounds. Journal of

applied physics, 103(4): 043711.

Xu, B, Wang, Y, Zhao, W and Yan, Y. (2011). Thermoelectric Properties of Heusler-

Type Compound Fe2v1− Xnbxal. Journal of Applied Physics, 110(1): 013530.

Xu, G, Liu, E, Du, Y, Li, G, Liu, G, Wang, W and Wu, G. (2013). A New Spin

Gapless Semiconductors Family: Quaternary Heusler Compounds. EPL

(Europhysics Letters), 102(1): 17007.

Xu, N, Raulot, J-M, Li, Z, Bai, J, Zhang, Y, Zhao, X, Zuo, L and Esling, C. (2012).

Oscillation of the Magnetic Moment in Modulated Martensites in Ni2mnga

Studied by Ab Initio Calculations. Applied Physics Letters, 100(8): 084106.

Xu, Y-Q, Liu, B-G and Pettifor, D. (2003). Half-Metallic Ferromagnetism of Mnbi in

Zincblende Phase. Physica B: Condensed Matter, 3291117-1118.

Yadav, MK and Sanyal, B. (2015). First Principles Study of Thermoelectric Properties

of Li-Based Half-Heusler Alloys. Journal of alloys and compounds, 622388-393.

Yakushiji, K, Saito, K, Mitani, S, Takanashi, K, Takahashi, Y and Hono, K. (2006).

Current-Perpendicular-to-Plane Magnetoresistance in Epitaxial Co 2 Mn Si∕ Cr∕

Co 2 Mn Si Trilayers. Applied Physics Letters, 88(22): 222504.

Yan, B and de Visser, A. (2014). Half-Heusler Topological Insulators. MRS Bulletin,

39(10): 859-866.

Yao, K, Gao, G, Liu, Z and Zhu, L. (2005a). Half-Metallic Ferromagnetism of Zinc-

Blende Crs and Crp: A First-Principles Pseudopotential Study. Solid state

communications, 133(5): 301-304.

Yao, K, Gao, G, Liu, Z, Zhu, L and Li, Y. (2005b). Half-Metallic Ferromagnetic

Semiconductors of V-and Cr-Doped Cdte Studied from First-Principles

Pseudopotential Calculations. Physica B: Condensed Matter, 366(1): 62-66.

172

Yokoyama, M, Yamaguchi, H, Ogawa, T and Tanaka, M. (2005). Zinc-Blende-Type

Mnas Nanoclusters Embedded in Gaas. Journal of applied physics, 97(10):

10D317.

Yousuf, S and Gupta, DC. (2017). Investigation of Electronic, Magnetic and

Thermoelectric Properties of Zr 2 Niz (Z= Al, Ga) Ferromagnets. Materials

Chemistry and Physics, 19233-40.

Zeier, WG, Schmitt, J, Hautier, G, Aydemir, U, Gibbs, ZM, Felser, C and Snyder,

GJ. (2016). Engineering Half-Heusler Thermoelectric Materials Using Zintl

Chemistry. Nature Reviews Materials, 1(6): 16032.

Zenasni, H, Faraoun, H and Esling, C. (2013). First-Principle Prediction of Half-

Metallic Ferrimagnetism in Mn-Based Full-Heusler Alloys with Highly Ordered

Structure. Journal of magnetism and magnetic materials, 333162-168.

Zhang, L, Brück, E, Tegus, O, Buschow, K and De Boer, F. (2003a). The

Crystallization of Amorphous Fe 2 Mnge Powder Prepared by Ball Milling.

Journal of alloys and compounds, 352(1): 99-102.

Zhang, M, Dai, X, Hu, H, Liu, G, Cui, Y, Liu, Z, Chen, J, Wang, J and Wu, G.

(2003b). Search for New Half-Metallic Ferromagnets in Semi-Heusler Alloys

Nicrm (M= P, as, Sb, S, Se and Te). Journal of Physics: Condensed Matter,

15(46): 7891.

Zhang, M, Hu, H, Liu, G, Cui, Y, Liu, Z, Wang, J, Wu, G, Zhang, X, Yan, L and

Liu, H. (2003c). Half-Metallic Ferromagnetism in Zinc-Blende Crbi and the

Stability of the Half-Metallicity of Zinc-Blende Crm (M= P, as, Sb, Bi). Journal

of Physics: Condensed Matter, 15(29): 5017.

Zhang, M, Liu, Z-H, Hu, H-N, Liu, G-D, Cui, Y-T, Wu, G-H, Brück, E, de Boer, FR

and Li, Y-X. (2004). Half-Metallic Ferromagnetism in Hypothetical Semi-

Heusler Alloys Niv M (M= P, as, Sb, S, Se, and Te). Journal of Applied Physics,

95(11): 7219-7221.

Zhang, Y, Liu, W and Niu, H. (2008). Half-Metallic Ferromagnetism in Cr-Doped

Alp—Density Functional Calculations. Solid state communications, 145(11-12):

590-593.

Zhao, J, Matsukura, F, Takamura, K, Chiba, D, Ohno, Y, Ohtani, K and Ohno, H.

(2003). Zincblende Crsb/Gaas Multilayer Structures with Room-Temperature

Ferromagnetism. Materials Science in Semiconductor Processing, 6(5-6): 507-

509.

173

Zhu, W, Liu, E, Feng, L, Tang, X, Chen, J, Wu, G, Liu, H, Meng, F and Luo, H.

(2009). Magnetic-Field-Induced Transformation in Femnga Alloys. Applied

Physics Letters, 95(22): 222512.

Zhu, W, Sinkovic, B, Vescovo, E, Tanaka, C and Moodera, J. (2001). Spin-Resolved

Density of States at the Surface of Nimnsb. Physical Review B, 64(6): 060403.

Ziebeck, K and Neumann, K. (2001). Magnetic Properties of Metals. Landolt-B€

ornstein, New Series, Group III, 3264-414.

Ziebeck, K and Webster, P. (1974). A Neutron Diffraction and Magnetization Study of

Heusler Alloys Containing Co and Zr, Hf, V or Nb. Journal of Physics and

Chemistry of Solids, 35(1): 1-7.

Žutić, I, Fabian, J and Sarma, SD. (2004). Spintronics: Fundamentals and Applications.

Reviews of modern physics, 76(2): 323.

174

Appendix-I

The lattice constant, electronic properties, magnetic moment, EBG and EHM represents

energy band gap, HM gap of all the 90 HH XYZ materials at the three types. Magnetic

ground state (NM, FM, AFM) and their energy EFM & EAFM, vibrational stability at the γ-

point (f/i shows the imaginary phonon frequency) with preferred type are also illustrated

for all the DFT investigated 90 HH XYZ materials.

LiVZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Mag-

netic

State

Stable

(at

γ-

point)

EFM

(eV)

EAFM

(eV)

LiVSi T1 5.85 SC 2.00 1.43 ---- T1 FM Yes -63.25

-62.72

T2 5.58 Metallic 1.99 ---- ----

T3 5.79 HM 2.00 0.94 0.38

LiVGe T1 5.93 SC 2.00 1.06 ---- T1 FM Yes -60.22

-59.61

T2 5.68 Metallic 2.03 ---- ----

T3 5.97 HM 2.00 1.10 0.47

LiVSn T1 6.37 HM 2.00 0.89 0.47 T1 FM Yes -54.94

-54.65

T2 6.05 Metallic 2.16 ---- ----

T3 6.38 HM 2.00 0.77 0.36

LiVS T1 5.55 Metallic 1.47 ---- ---- T1 AFM f/i

1.72

THz

-65.29

-65.57

T2 5.71 Metallic 3.99 ---- ----

T3 5.87 HM 4.00 5.30 0.49

LiVSe T1 5.94 Metallic 2.64 ---- ---- T1 AFM Yes -60.73

-61.11

T2 5.95 Nearly

HM

3.99 4.05 0.07

T3 6.14 HM 4.00 4.66 0.51

LiVTe T1 6.46 Metallic 3.82 ---- ---- T1 AFM Yes -56.8

-56.95

T2 6.26 Metallic 3.99 ---- ----

T3 6.47 HM 4.00 3.58 0.78

175

NaVZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Mag-

netic

State

Stable

(at

γ-

point)

EFM

(eV)

EAFM

(eV)

NaVSi T1 6.25 HM 2.00 1.11 0.52 T1 FM Yes -55.55

-55.15

T2 6.23 Metallic 2.17 ---- ----

T3 6.20 HM 2.00 1.29 0.62

NaVGe T1 6.32 HM 2.00 1.16 0.50 T1 FM Yes -53.12

-52.80

T2 6.33 Metallic 2.26 ---- ----

T3 6.28 HM 2.00 1.37 0.60

NaVSn T1 6.73 HM 2.00 1.05 0.47 T1 AFM Yes

-49.25

-49.46

T2 6.66 Metallic 2.50 ---- ----

T3 6.66 HM 2.00 0.98 0.29

NaVS T1 6.19 HM 4.00 5.63 0.67 T1 AFM f/i

3.3

THz

-58.31

-58.83

T2 6.28 HM 4.00 4.47 0.39

T3 6.21 HM 4.00 5.55 0.91

NaVSe T1 6.46 HM 4.00 4.91 0.54 T1 AFM f/i

1.1

THz

-55.52

-55.67

T2 6.49 HM 4.00 3.73 0.19

T3 6.44 HM 4.00 4.75 0.69

NaVTe T1 6.84 HM 4.00 4.18 0.54 T1 FM Yes -52.54

-52.38

T2 6.79 HM 4.00 3.41 0.58

T3 6.75 HM 4.00 3.88 0.54

KVZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Mag-

netic

State

Stable

(at

γ-

point)

EFM

(eV)

EAFM

(eV)

KVSi T1 6.80 Nearly

HM

2.00 1.29 0.04 T3 FM Yes

-48.80

-48.26

T2 6.98 HM 2.00 1.37 0.31

T3 6.55 HM 2.00 1.49 0.21

KVGe T1 6.87 Nearly

HM

2.00 1.33 0.02 T3 FM Yes -46.74

-46.40

T2 7.08 HM 1.99 1.31 0.21

T3 6.64 HM 2.00 1.59 0.15

KVSn T1 7.27 Nearly

HM

1.99 1.31 0.03 T3 AFM f/i

1.09

THz

-45.09

-45.26

T2 7.43 Metallic 3.22 ---- ----

T3 7.01 Nearly

HM

1.99

1.39 0.04

KVS T1 6.69 HM 4.00 5.40 1.32 T1 FM f/i

3.7

THz

-49.49

-48.82

T2 6.87 HM 4.00 3.94 0.76

T3 6.54 HM 4.00 5.29 1.19

KVSe T1 6.92 HM 4.00 4.75 0.99 T1 FM f/i

3.7

THz

-51.67

-51.43

T2 7.08 HM 4.00 3.42 0.60

T3 6.77 HM 4.00 4.83 1.18

KVTe T1 7.30 HM 4.00 4.38 1.08 T3 FM f/i

1.1

THz

-49.49

-48.82

T2 7.42 HM 4.00 3.10 0.71

T3 7.08 HM 4.00 3.99 0.94

176

RbVZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Mag-

netic

State

Stable

(at

γ-

point)

EFM

(eV)

EAFM

(eV)

RbVSi T1 7.04 Nearly

HM

2.00 1.38 0.01 T3 FM

f/i

1.9

THz

-46.69

-46.18

T2 7.27 HM 1.99 1.25 0.23

T3 6.72 Nearly

HM

2.00 1.16 0.004

RbVGe T1 7.12 Nearly

HM

2.00 1.36 0.03 T3 FM

f/i

1.7

THz

-44.78

-44.46

T2 7.37 HM 1.99 1.20 0.18

T3 6.80 Nearly

HM

2.00 1.25 0.04

RbVSn T1 7.51 Nearly

HM

2.00 1.33 0.06 T3 AFM

f/i

1.75

THz

-43.47

-43.52

T2 7.71 Metallic 3.84 ---- ----

T3 7.18 Nearly

HM

1.99 1.13 0.20

RbVS T1 6.95 HM 4.00 4.80 1.19 T1 FM f/i

4.04

THz

-51.29

-51.09

T2 7.18 HM 4.00 3.41 0.78

T3 6.74 HM 4.00 4.81 1.05

RbVSe T1 7.18 HM 4.00 4.26 0.91 T1 FM f/i

3.1

THz

-49.44

-49.16

T2 7.39 HM 4.00 2.96 0.65

T3 6.95 HM 4.00 4.43 1.04

RbVTe T1 7.56 HM 4.00 3.97 0.96 T3 FM Yes -48.01

-47.34

T2 7.74 HM 4.00 2.73 0.73

T3 7.27 HM 4.00 3.73 0.83

CsVZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Mag-

netic

State

Stable

(at

γ-

point)

EFM

(eV)

EAFM

(eV)

CsVSi T1 7.25 Nearly

HM

1.99 1.32 0.12 T3 FM

f/i

1.6

THz

-45.99

-45.44

T2 7.37 Metallic 2.25 ---- ----

T3 6.85 Nearly

HM

2.00 0.58 0.10

CsVGe T1 7.37

Nearly

HM

2.00 1.31 0.14 T3 FM f/i

1.2

THz

-44.18

-43.76

T2 7.49 HM 1.99 1.31 0.21

T3 6.94 HM 2.00 1.59 0.15

CsVSn T1 7.76

Nearly

HM

2.00 1.30 0.18 T3 FM Yes -42.90

-42.57

T2 7.89 HM 1.99 1.31 0.21

T3 7.32 Nearly

HM

1.99 0.66 0.15

CsVS T1 7.25 HM 4.00 4.16 1.13 T3 FM Yes -49.97

-49.46

T2 7.44 HM 4.00 3.21 0.97

T3 6.93 HM 4.00 3.92 0.68

CsVSe T1 7.50 HM 4.00 3.69 0.87 T3 FM Yes -48.62

-48.03

T2 7.69 HM 4.00 2.76 0.86

T3 7.13 HM 4.00 3.66 0.66

CsVTe T1 7.89 HM 4.00 3.54 0.94 T3 FM f/i

2.1

THz

-47.30

-46.69

T2 6.26 HM 4.00 2.44 0.92

T3 7.45 HM 4.00 3.18 0.54

177

LiNbZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Mag-

netic

State

Stable

(at

γ-

point)

EFM

(eV)

EAFM

(eV)

LiNbSi T1 5.92 Metallic 0.00 ---- ---- T1 NM Yes -68.78

-68.78

T2 5.62 Metallic 0.00 ---- ----

T3 6.01 Metallic 0.00 ---- ----

LiNbGe T1 6.01 Metallic 0.01 ---- ---- T1

NM

Yes

-64.79 -64.79

T2 5.72 Metallic 0.00 ---- ----

T3 6.11 Metallic 0.00 ---- ----

LiNbSn T1 6.44 Metallic 1.48 ---- ---- T2 NM Yes -58.29 -58.28

T2 6.06 Metallic 0.02 ---- ----

T3 6.51 Metallic 0.39 ---- ----

LiNbS T1 5.92 Metallic 1.15 ---- ---- T1 FM Yes -68.21

-68.16

T2 5.54 Metallic 1.73 ---- ----

T3 5.82 Metallic 1.15 ---- ----

LiNbSe T1 6.02 Metallic 1.27 ---- ---- T1 FM Yes -63.31

-63.16

T2 5.98 Metallic 2.71 ---- ----

T3 6.13 Metallic 1.36 ---- ----

LiNbTe T1 6.44 Metallic 1.36 ---- ---- T1 FM Yes -58.98

-58.79

T2 6.27 Metallic 2.97 ---- ----

T3 6.50 Metallic 1.48 ---- ----

NaNbZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Mag-

netic

State

Stable

(at

γ-

point)

EFM

(eV)

EAFM

(eV)

NaNbSi T1 6.25 Metallic 0.96 ---- ---- T1 AFM Yes -60.27

-60.31

T2 6.24 Metallic 1.88 ---- ----

T3 6.29 Metallic 1.30 ---- ----

NaNbGe T1 6.33 Metallic 1.51 ---- ---- T1 FM Yes -57.19

-57.08

T2 6.33 Metallic 1.99 ---- ----

T3 6.38 HM 2.00 1.03 0.13

NaNbSn T1 6.81 HM 2.00 1.05 0.36 T1 NM Yes -52.96

-52.96

T2 6.63 Metallic 2.03 ---- ----

T3 6.80 HM 2.00 0.84 0.28

NaNbS T1 6.07 Metallic 1.52 ---- ---- T1 FM Yes -60.52

-60.48

T2 6.44 HM 4.00 4.38 0.62

T3 6.10 Metallic 1.42 ---- ----

NaNbSe T1 6.47 Metallic 1.54 ---- ---- T1 AFM f/i

1.43

THz

-56.87

-56.94

T2 6.62 HM 4.00 3.89 0.59

T3 6.50 Metallic 2.60 ---- ----

NaNbTe T1 6.71 Metallic 1.51 ---- ---- T1 AFM f/i

0.9

THz

-53.49

-53.69

T2 6.88 HM 4.00 3.11 0.32

T3 6.79 Metallic 2.65 ---- ----

178

KNbZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Magnetic

State

Stable

(at

γ-

point)

EFM

(eV)

EAFM

(eV)

KNbSi T1 6.79 HM 2.00 1.13 0.54 T1 FM Yes -52.38

-52.03

T2 6.84 HM 2.00 0.57 0.19

T3 6.64 HM 2.00 1.39 0.65

KNbGe T1 6.86 HM 2.00 1.15 0.46 T1 FM Yes -50.14

-49.78

T2 6.95 HM 2.00 0.74 0.08

T3 6.72 HM 2.00 1.49 0.60

KNbSn T1 7.25 HM 2.00 1.10 0.34 T1 FM Yes -47.53

-47.24

T2 7.27 Metallic 2.22 ---- ----

T3 7.07 HM 2.00 1.32 0.42

KNbS T1 6.55 Metallic 1.85 ---- ---- T1 AFM f/i

3.4

THz

-53.72

-54.44

T2 6.94 HM 4.00 4.23 1.24

T3 6.78 HM 4.00 5.18 1.24

KNbSe T1 7.01 HM 4.00 4.98 1.22 T1 AFM f/i

2.3

THz

-51.77

-52.12

T2 7.13 HM 4.00 3.75 1.04

T3 6.97 HM 4.00 4.81 1.13

KNbTe T1 7.36 HM 4.00 4.37 1.05 T1 AFM f/i

0.5

THz

-49.63

-49.72

T2 7.42 HM 4.00 3.47 1.09

T3 7.26 HM 4.00 4.46 0.87

179

RbNbZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Magnetic

State

Stable

(at

γ-

point)

EFM

(eV)

EAFM

(eV)

RbNbSi T1 6.97 HM 2.00 1.18 0.28 T3 FM Yes -49.37

-48.68

T2 7.05 Nearly

HM 2.00 0.46 0.01

T3 6.77 HM 2.00 1.24 0.57

RbNbGe T1 7.07 HM 2.00 1.19 0.19 T3 FM Yes -47.19

-46.50

T2 7.18 HM 2.00 1.33 0.51

T3 6.85 Metallic 2.15 ---- ----

RbNbSn T1 7.45 HM 2.00 1.12 0.11 T3 FM Yes -45.83

-45.14

T2 7.54 Metallic 2.15 ---- ----

T3 7.19 HM 2.00 1.19 0.33

RbNbS T1 7.00 HM 4.00 5.08 1.46 T1 AFM f/i

3.5

THz

-51.31

-51.59

T2 7.22 HM 4.00 3.79 1.30

T3 6.93 HM 4.00 4.74 0.99

RbNbSe T1 7.23 HM 4.00 4.71 1.39 T1 AFM f/i

2.9

THz

-49.61

-49.62

T2 7.41 HM 4.00 3.38 1.11

T3 7.06 HM 4.00 4.37 0.85

RbNbTe T1 7.60 HM 4.00 4.24 1.27 T3 FM Yes -47.59

-46.89

T2 7.71 HM 4.00 3.11 1.11

T3 7.41 HM 4.00 3.82 0.75

180

CsNbZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Magnetic

State

Stable

(at

γ-point)

EFM

(eV)

EAFM

(eV)

CsNbSi T1 7.21 HM 2.00 1.03 0.04 T3 FM Yes -49.22

-48.64

T2 7.23 TI 2.00 ---- ----

T3 6.87 HM 2.00 0.47 0.11

CsNbGe T1 7.21 HM 2.00 1.05 0.19 T3 FM Yes -47.12

-46.52

T2 7.23 Metallic 2.10 ---- ----

T3 6.96 HM 2.00 0.62 0.14

CsNbSn T1 7.68 HM 2.00 1.07 0.14 T3 FM Yes -45.72

-45.09

T2 7.68 Metallic 2.39 ---- ----

T3 7.28 HM 2.00 0.69 0.16

CsNbS T1 7.27 HM 4.00 4.33 1.33 T3 NM Yes -49.52

-49.52

T2 7.43 HM 4.00 3.37 1.33

T3 6.56 SC 0.00 0.93 ----

CsNbSe T1 7.50 HM 4.00 4.23 1.42 T3 NM Yes -47.22

-47.65

T2 7.64 HM 4.00 3.09 1.25

T3 6.74 SC 0.00 0.89 ----

CsNbTe T1 7.87 HM 4.00 3.86 1.36 T3 FM Yes -47.16

-46.45

T2 8.01 HM 4.00 2.84 1.26

T3 7.55 HM 4.00 3.23 0.39

181

LiTaZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Magnetic

State

Stable

(at

γ-point)

EFM

(eV)

EAFM

(eV)

LiTaSi T1 5.91 Metallic 0.00 ---- ---- T1

NM

Yes -74.05

-74.05

T2 5.61 Metallic -0.00 ---- ----

T3 6.01 Metallic 0.00 ---- ----

LiTaGe T1 6.00 Metallic 0.01 ---- ---- T1 NM Yes -69.68

-69.68

T2 5.71 Metallic 0.00 ---- ----

T3 6.11 Metallic -0.00 ---- ----

LiTaSn T1 6.43 Metallic 0.03 ---- ---- T2 NM Yes -62.44

-62.44

T2 6.05 Metallic 0.00 ---- ----

T3 6.51 Metallic 0.01 ---- ----

LiTaS T1 5.68 Metallic 0.58 ---- ---- T1 NM YES -71.99

-71.99

T2 5.60 Metallic 1.62 ---- ----

T3 5.81 Metallic 0.59 ---- ----

LiTaSe T1 6.00 Metallic 1.48 ---- ---- T1 FM YES -66.63

-66.55

T2 5.90 Metallic 2.34 ---- ----

T3 6.09 Metallic 1.17 ---- ----

LiTaTe T1 6.42 Metallic 1.53 ---- ---- T1 FM YES -62.32

-62.13

T2 6.18 Metallic 2.30 ---- ----

T3 6.49 Metallic 1.66 ---- ----

182

NaTaZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Magnetic

State

Stable

(at

γ-point)

EFM

(eV) EAFM

(eV)

NaTaSi T1 6.22 Metallic -0.02 ---- ---- T1 NM Yes -65.34

-65.34

T2 6.16 Metallic 0.20 ---- ----

T3 6.30 Metallic -0.04 ---- ----

NaTaGe T1 6.30 Metallic -0.00 ---- ---- T1 NM Yes -57.52

-57.52

T2 6.35 Metallic 1.86 ---- ----

T3 6.40 Metallic 1.15 ---- ----

NaTaSn T1 6.71 HM 2.00 1.18 0.17 T1 FM Yes -56.87

-56.68

T2 6.55 Metallic 0.40 ---- ----

T3 6.77 Metallic 1.93 ---- ----

NaTaS T1 6.05 Metallic 1.86 ---- ---- T1 FM Yes -63.46

-63.41

T2 6.48 Metallic 3.99 ---- ----

T3 6.11 Metallic 1.72 ---- ----

NaTaSe T1 6.32 Metallic 1.90 ---- ---- T1 FM Yes -59.83

-59.70

T2 6.63 Metallic 3.99 ---- ----

T3 6.46 Metallic 2.00 ---- ----

NaTaTe T1 6.69 Metallic 1.71 ---- ---- T1 FM Yes -56.64

-56.48

T2 6.84 HM 4.00 ---- ----

T3 6.74 Metallic 2.02 ---- ----

183

KTaZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Magnetic

State

Stable

(at

γ-

point)

EFM

(eV) EAFM

(eV)

KTaSi T1 6.70 HM 2.00 1.34 0.50 T1 FM Yes -56.60

-56.42

T2 6.84 HM 2.00 0.31 0.02

T3 6.61 HM 2.00 1.05 0.04

KTaGe T1 6.80 HM 2.00 1.41 0.69 T1 FM Yes -54.07

-53.81

T2 6.95 HM 2.00 0.37 0.18

T3 6.71 HM 2.00 1.18 0.28

KTaSn T1 7.17 HM 2.00 1.31 0.54 T1 FM Yes -51.29

-50.90

T2 7.23 Metallic 2.01 ---- ----

T3 7.06 HM 2.00 1.05 0.35

KTaS T1 6.48 HM 2.00 0.221 0.10 T1 AFM f/i

2.97

THz

-55.97

-56.22

T2 7.02 HM 4.00 3.17 0.43

T3 6.30 Metallic 0.25 ---- ----

KTaSe T1 6.75 Metallic 2.00 ---- ---- T1 AFM f/i

2.05

THz

-53.64

-53.99

T2 7.17 HM 4.00 2.75 0.14

T3 6.99 HM 3.99 4.45 0.47

KTaTe T1 7.08 Metallic 2.01 ---- ---- T1 AFM f/i

1.08

THz

-51.34

-51.72

T2 7.42 HM 4.00 2.60 0.25

T3 7.03 Metallic 2.71 ---- ----

184

RbTaZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Magn

etic

State

Stable

(at

γ-

point)

EFM

(eV) EAFM

(eV)

RbTaSi T1 6.89 HM 2.00 1.36 0.63 T1 FM Yes -53.13

-52.71

T2 7.05 HM 2.00 0.16 0.03

T3 6.72 Metallic 1.99 ---- ----

RbTaGe T1 6.99 HM 2.00 1.39 0.55 T1 FM Yes -50.81

-50.32

T2 7.17 HM 2.00 0.22 0.04

T3 7.17 HM 2.00 0.25 0.06

RbTaSn T1 7.36 HM 2.00 1.23 0.31 T3 FM Yes -

49.087

-48.55

T2 7.38 HM 0.21 ---- ----

T3 7.16 HM 2.00 1.05 0.35

RbTaS T1 6.79 Metallic 2.00 ---- ---- T1 AFM f/i

4.2

THz

-52.38

-52.95

T2 7.32 HM 4.00 2.63 0.50

T3 6.91 HM 4.00 4.82 0.65

RbTaSe T1 7.19 Metallic 0.02 ---- ---- T1 AFM f/i

2.43

THz

-50.89

-51.17

T2 7.32 HM 4.00 2.17 0.24

T3 7.15 HM 4.00 4.20 0.47

RbTaTe T1 7.53 Metallic 2.18 ---- ---- T3 FM Yes -48.90

-48.37

T2 7.72 HM 4.00 2.17 0.24

T3 7.37 HM 4.00 3.70 0.24

185

CsTaZ (where Z=Si, Ge, Sn, S, Se, Te)

XYZ Types a

(Å)

Electronic

Behaviour

µtot

(µB)

EBG

(eV)

EHM

(eV)

Preferred

type

Magnetic

State

Stable

(at

γ-

point)

EFM

(eV) EAFM

(eV)

CsTaSi T1 7.01 HM 2.00 0.91 0.32 T3 FM Yes -53.19

-52.87

T2 7.05 Metallic 1.99 ---- ----

T3 6.82 Metallic 1.96 ---- ----

CsTaGe T1 7.15 HM 2.00 1.14 0.24 T3 FM Yes -50.84

-50.46

T2 7.20 Metallic 2.00 ---- ----

T3 6.91 Metallic 1.98 ---- ----

CsTaSn T1 7.55 Nearly HM 2.00 1.17 0.01 T3 FM Yes -49.37

-48.93

T2 7.55 Metallic 2.06 ---- ----

T3 7.23 Metallic 1.99 ---- ----

CsTaS T1 7.26 HM 4.00 3.82 0.64 T3 NM Yes -52.05

-52.05

T2 7.19 HM 4.00 2.85 0.82

T3 6.51 SC 0 0.53 ----

CsTaSe T1 7.48 Metallic 3.91 ---- ---- T3 NM Yes -52.02

-52.02

T2 7.70 HM 3.99 2.07 ----

T3 6.68 SC 0 0.53 ---

CsTaTe T1 7.81 Metallic -2.52 ---- ---- T3 NM Yes -49.01

-49.01

T2 8.03 HM 4.0 1.83 0.42

T3 6.98 SC 0 0.44 ----

Investigation of Structural, Electronic and Magnetic...

Documents

Transcript of Investigation of Structural, Electronic and Magnetic...