47

Chapter 2

2.1 Introduction

The semi-Heusler alloys XYZ are ternary intermetallic involving two different

TMs X and Y, and Z is a sp valence element, and crystallized in the cubic the cubic

MgAgAs-type or C1b-type structure. This structure consists of three filled and one vacant

interpenetrating fcc sublattices. The third fcc structure is shifted by one-fourth of the unit

cell from the body diagonal of the rocksalt structure [1]. In principle, the semi-Heusler

alloys form a ternary stuffed variant of classical electron closed-shell semiconductors

which crystallize in a zincblende (ZnS-type) lattice, such as GaAs. The eight valence

electrons are distributed among three atoms instead of two. The third atom occupies the

octahedral vacancies in the ZnS-type lattice. This fact automatically leads to a formation of

a rocksalt-like sublattice characterized by ionic bonding interaction [2]. The relationship

between these different crystal lattices is displayed in fig. 2.1.

Fig. 2.1 A Schematic representation of Rock-salt, Zinc-blend and Semi-Heusler

type structure.

The relation between these three structures can be understood in the following way:

In the conventional stable structure, Y and Z atoms are located at 4a (0,0,0) and 4b

(½,½,½) positions, forming the rock-salt structure arrangement. The X atom is located in

the octahedral coordinated pocket, at one of the cube centre positions 4c (¼,¼,¼) leaving

the other position 4d (¾,¾,¾ ) empty. When the Z atomic positions are empty, the

Chapter 2

48

structure is analogous to the zinc-blende structure, which is common for a large number of

semiconductors [3].

The semi-Heusler alloys are structurally comparable to their parent alloys, the full-

Heusler alloys X2YZ, in a way that both structures can be considered as consisting of four

interpenetrating fcc lattices. But in full-Heusler alloys there are two sublattices occupied

by X atoms, and thus there is no vacant sublattice. It took almost 50 years, after the

discovery of Cu2MnAl full-Heusler [4] alloy, for scientists to realize that it possible to

leave one of these four sublattices unoccupied yielding XYZ alloys in Clb-type structure.

Castelliz [5] in 1952 found a single phase alloy at the composition CuMnSb which has a

crystal structure very similar to that of the Heusler alloys. Nowotny et al. [6] used X-ray

diffraction photographs to determine that the atomic arrangement in semi-Heusler alloy

was of the MgAgAs-type and the same as the full-Heusler structure except that one of the

four partial lattices was vacant. Forster et al. [7] in 1968 prepared the CuMnSb semi-

Heusler alloy and investigated its structure by X-ray and neutron diffraction techniques.

Their investigations revealed the alloy to have an ordered MgAgAs-type structure.

In a pioneering letter in 1983, de Groot et al. [8] showed that one of the semi-

Heusler compounds, NiMnSb, is a HMF i.e. a ferromagnetic metal for majority spin band

and semiconducting for the minority spin band leading to 100% spin polarization at EF.

Such HMFs can be considered hybrids between metals and semiconductors. Rapid

development of magneto-electronics intensified the interest in such materials since the

efficiency of any spin-dependent device scales with the spin polarization at EF. Adding the

spin degree of freedom to the conventional electronic devices has several advantages like

non-volatility, enhanced data processing speed, decreased power consumption and

increased integration densities [9].

The HMFs, like NiMnSb semi-Heusler alloys have interesting physical properties

and are attractive for research community due to their potential for technological

applications particularly in the field of spintronics i.e. tunnel junctions, spin valves etc.

[10-13]. It has relatively high Curie temperature (TC = 730 K), well above the room

temperature, HM character and structural similarity with semiconductors. The HM

ferromagnetism observed in NiMnSb has boosted the research activities in semi Heusler

alloys from both theoretical and experimental front. The semi-Heusler alloys NiMnZ (Z =

NiCrZ (Z = Si, P and Ge) semi-Heusler alloys

49

Si, P, Ge and As) were predicted as HMFs with high TC (715–1050 K) by Dinh et al. [14]

using Monte-Carlo simulation technique. Galanakis et al. [15] studied NiCrSi and NiMnSi

with the full-potential non-orthogonal local orbital minimum-basis band structure scheme

(FPLO) and the full-potential screened Korringa-Kohn-Rostoker (FSKKR) method within

the local spin density approximation (LSDA). They found that both the FPLO and FSKKR

methods yielded nearly the same DOS and minority-spin gap. Zhang et al. [16] predicted

NiCrM (M= P, As, Sb, S, Se and Te) as HMFs by FPLAPW method within LSDA

formalism. Luo et al. [17] predicted that NiCrAl, NiCrGa and NiCrIn are possible half-

metals with an energy gap in the minority spin band and with 100% spin polarization at the

EF.

After the theoretical prediction of half-metallicity in NiMnSb, this characteristic

was also become well established in single crystals of NiMnSb with experiments such as

infrared absorption [18] and positron annihilation [19]. Although, these experiments

yielded 100% spin polarization at EF in single crystals of NiMnSb but were not able to

reproduce the HM character of bulk NiMnSb. The HM ferromagnetism was observed

experimentally for NiMnZ (Z = Pd, Pt, Sb) alloys with TC in the range 500–730 K [20].

Thin film of the HMF, NiMnSb on single crystal of the narrow gap semiconductor InSb by

Pulsed Laser Deposition (PLD) was grown by Androulakis et al. [21]. Gardelis et al. [22]

showed that both, bulk as well as thin film of NiMnSb exhibited the characteristics of a

HM system. Tanaka et al. [23] successfully performed the measurement of the conduction

electron spin polarization of epitaxial NiMnSb films, to test the prediction of half

metallicity in this material, by spin-dependent tunneling in planar tunnel junctions using

both a superconductor and a ferromagnet as spin detectors. Both types of junctions yielded

spin polarization in the range 25% - 28%. Ristoiu et al. [24] showed that during the growth

of the NiMnSb thin films, Sb and then Mn atoms segregate to the surface, which results in

degradation of spin polarization. But when they removed the excess of Sb by flash

annealing, they managed to get a nearly ordered stoichiometric thin film surface of

NiMnSb alloy and obtained the spin polarization of about 67 ± 9% at room temperature

[25].

Except the studied HM ferromagnetism in semi-Heusler alloys, these alloys have

also been subject to intense scrutiny due to their potential as a topological insulator (TI)

Chapter 2

50

with tunable electronic properties [26-28]. Recently, Xiao et al. [28] demonstrated, using

first-principles calculations, that LaPtBi semi-Heusler alloy becomes a strong TI upon the

application of a uniaxial strain along the [001] direction. This quantum nature and other

interesting physical properties of these materials, such as magnetism [29] and

superconductivity [30], characterize these materials as an exciting platform for novel

quantum phenomena. The electronic structure of the PtYSb and PtLaBi semi-Heusler

alloys was investigated using bulk sensitive HAXPES technique by Quardi et al. [31]. The

comparison of the experimental results to first-principles calculations gives a clear

evidence for the zero band gap state of these alloys.

Very recently, Damewood et al. [32] examined the bonding mechanism, magnetic

properties and the structure stability of three magnetic semi-Heusler alloys, namely LiMnZ

(Z = N, P and Si) and proposed a new ternary semi-Heusler alloy LiMnSi as HMF. Yao et

al. [33] investigated CoCrP and CoCrAs semi-Heusler alloys for their electronic structure

and magnetic properties using full potential method. They proposed that CoCrP and

CoCrAs are HMF with the same magnetic moment of 2.00 µB per formula unit. Both alloys

have large spin-flip (Esf) or HM gaps (up to 0.50 eV) and wide minority-spin gaps (Eg↓ >1

eV). The half-metallicity of CoCrP and CoCrAs can be retained even when their lattice

constants are changed by -4.8% to 6.6% and -7.7% to 4.5%, respectively.

In the present chapter, we investigated the electronic and magnetic properties of

some Ni-based general semi-Heusler alloys. After observing a lot of work on HM

ferromagnetism in NiMnZ series during last decade both from theoretical and experimental

fronts, we are highly motivated to search new semi-Heusler alloys with the composition

NiCrZ (Z = Si, Ge and P) showing HM ferromagnetism for future spintronic applications.

This type of selection of alloys is made to observe the change in HM ferromagnetism and

magnitude of Eg↓ by substituting the sp-element (Si) in reference compound, NiCrSi, with

next element along its group/period i.e. the transition from NiCrSi to NiCrGe/NiCrP.

2.2 Details of the calculations

The first-principles solid state calculations of the electronic structure of NiCrZ (Z =

Si, Ge and P) semi-Heusler alloys have been performed using the relativistic all electron

full potential linearized augmented plane wave (FPLAPW) method as implemented in the

NiCrZ (Z = Si, P and Ge) semi-Heusler alloys

51

WIEN2k code [34]. The calculations are based on the density functional theory (DFT)

[35]. The generalized gradient approximation (GGA) within Perdew-Burke-Ernzerhof

parameterization [36] has been used to construct exchange and correlation (XC) potentials

in the calculations. The k-space integration has been done by the modified tetrahedron

method [37]. For these calculations, the radii of the muffin-tin spheres representing all the

atoms are chosen as: NiMTR = Cr

MTR = 2.1 a.u., Si PMT MTR R= = 2.3 a.u. and Ge

MTR = 2.4 a.u. The

maximum value lmax for the orbital quantum number for the waves inside the atomic

spheres is 10. The wave function in the interstitial region is expanded in plane waves with

a cut-off decided by MT maxR k = 7, while the charge density is expanded using Fourier

expansion up to maxG = 12 a.u.-1. The convergence of the calculated eigen values have

been checked with respect to the number of augmented plane waves and also with respect

to the number of k-points used. We have used 287 k-points in the irreducible Brillouin

zone (IBZ) to obtain the self-consistency. The energy convergence criterion was set to 10-4

Ry/cell and the charge convergence was also monitored along with it. The NiCrZ Heusler

alloys crystallize in C1b-type structure such that the unit cell contains three atoms as basis

with Ni atom at (0,0,0), Cr at (¼,¼,¼) and Z at (¾,¾,¾ ) and with a void at (½,½,½ ) in

Wyckoff coordinates as shown in Fig. 2.2.

Fig. 2.2 C1b-type structure of NiCrSi Heusler alloy in primitive-cell mode (left) and

corresponding Brillouin Zone (BZ) and its IBZ (in red color) on right.

Chapter 2

52

2.3 Results and discussion

Here we have described important results of various ground state properties

separately of studied semi-Heusler alloys and discussed the important outcome of the study

as follows.

2.3.1 Structural properties

As the alloys under study have not been grown experimentally till date, therefore,

we have determined their equilibrium lattice parameters by optimization process in the

neighborhood of lattice parameters calculated by other authors. These calculations have

already predicted ferromagnetic (FM) nature of the present alloys. In Fig. 2.3, structural

optimization in FM configuration performed by minimizing the total energy with respect to

lattice parameters for NiCrZ (Z = Si, Ge and P) alloys is presented and the equilibrium

values of lattice parameters (a) are summarized in Table 2.1. In all cases, the optimized

lattice parameters are in close agreement with the previously calculated values [13-15].

Rest of the calculations has been performed at these optimized values.

Fig. 2.3 Total energy versus lattice parameter of NiCrZ (Z = Si, Ge and P) Heusler

alloys. The solid lines show a polynomial fit for determining the

equilibrium lattice constants.

NiCrZ (Z = Si, P and Ge) semi-Heusler alloys

53

Table 2.1 Optimized lattice parameters, calculated DOS for majority and minority spin

(i.e. ρ↑(EF) and ρ↓ (EF) in states/eV) and spin polarization (‘P’) at EF. The calculated VB

maximum (Emax (C)), CB minimum (Emin (X)) and minority-spin gap (Eg↓) energy of

NiCrZ (Z = Si, Ge and P) Heusler alloy with EF fixed at 0 eV are also presented.

Alloys (NV)

a (Å) Emax(C) (eV)

Emin(X) (eV)

Eg↓ (eV)

ρ↑ ρ↓ ‘P’

NiCrSi(20) NiCrGe(20) NiCrP(21)

This work Others [15] This work Others [14] This work Others [16]

5.453 5.527 5.585 5.643 5.451 5.59

-0.44 - -0.22 - -0.47 -

0.47 - 0.53 - 0.33 -

0.91 1.07 0.75 - 0.80 0.70

0.92 0.59 - 2.13 -

0 - 0 - 0 -

1 - 1 - 1 -

2.3.2 Density of state (DOS)

First of all, we report calculated DOS for present systems using FPLAPW method

in Fig. 2.4.

Fig. 2.4 Calculated total DOS of NiCrZ (Z = Si, Ge and P) Heusler alloys. Here EF is

shifted to E = 0 eV.

Chapter 2

54

The splitting of minority DOS in vicinity of EF is clearly visible which governs the

100% spin polarization (‘P’ = 1, as also listed in Table 2.1) for this spin channel.

Therefore, these alloys have fully spin polarized current and are useful for spin injection

with high efficiency. In this way, these are responsible for maximizing the efficiency of

spintronic devices.

In all present systems, majority DOS is very small in conduction band (CB). The

Cr atom has four majority electrons in d orbital and therefore many unfilled states are

available mainly for minority electrons which results in the crowded minority DOS for

each in CB.

Fig. 2.5 Calculated Partial DOS of NiCrSi Heusler alloy.

NiCrZ (Z = Si, P and Ge) semi-Heusler alloys

55

The partial spin-resolved DOS for all studied alloys are also analyzed in order to

find out the contributions of various electrons in total DOS. It is expected that partial spin-

resolved DOS is almost similar for these alloys. Therefore, as a representative, we have

presented the partial spin-resolved DOS of NiCrSi only in Fig. 2.5. The detailed

investigation of this alloy reveals that while almost all Ni-3d states are concentrated at

lower energies in VB and occupied but the Cr-3d states are distributed both in the region of

lower and higher energies and strongly localized.

The 3d-majority/minority spin states of Cr are dominant in VB/CB. The

contribution of sp-element (Si) towards the total DOS is quite small. The Si-p states have a

low intensity of DOS (i.e. ~ -0.3–0.3 states/eV) whereas Si-s states have almost negligible

contribution in DOS throughout the measured energy range.

Considering NiCrSi as a reference compound, we have substituted sp-element (Si)

by next element along its group/period and studied its effect on HM ferromagnetism and

Eg↓. Along the group, this transition leads to NiCrGe. We have observed that the majority

DOS in the vicinity of EF are almost similar whereas the minority DOS shifts towards

higher energy in resultant alloy (NiCrGe). The half metallicity remains energetically

favorable and no qualitative changes in DOS occur on this substitution. The nearest

neighbor (nn) distance increases to 2.42 Å in NiCrGe as compared to 2.36 Å in NiCrSi.

Thus, there exists poorer p-d hybridization which leads to formation of longer and weaker

bonds. As a result, the minority DOS in valence band (VB) are pushed closer to EF which

slightly closes the band gap in this channel and reduces the Eg↓ from 0.91 eV to 0.75 eV.

On the other hand, substitution of Si in NiCrSi by next sp-element along its period

yields NiCrP. In resultant compound, the number of valence electrons of sp-element (P) in

same shell increases by unity which plays an important role for the distribution of d-

electrons in eg and t2g states at Ni and Cr sites due to p-d hybridization. Here we have

found that the total DOS in both spin channels shift downwards in energy in the measured

energy range. This shifting is due to increased effective nuclear charge on P atom as

compared to Si. The nn distance in NiCrP and NiCrSi remains same (i.e. 2.36 eV). Thus, it

is expected to have a very small change in Eg↓ from this transition. The calculated value of

Eg↓ decreases to 0.80 eV on this transition. The little change is probably due to an

Chapter 2

56

additional electron which is responsible for increased electron–electron correlation and

results in more delocalization of electrons.

The calculated band gap along with VB maximum and CB minimum in minority

spin channel for all Heusler alloys is also listed in Table 1. Among present alloys, NiCrSi

has highest gap of 0.91 eV. We predict a smaller value of gap for this compound than the

corresponding value (1.07 eV) calculated by Galanakis et al. [15] using FPLO and FSKKR

methods. In case of NiCrP, our calculated gap (0.80 eV) is larger than as calculated (0.70

eV) by Zhang et al. [16] using LSDA as XC potentials. This might be due to the reason

that LSDA underestimate the gap of a half metal. Our results are expected to be quite

accurate as we have adopted GGA formalism which is known to work better than LSDA

for Heusler alloys [38] and for TMs, in general [39].

2.3.3 Magnetic properties

The total spin magnetic moment per unit cell (Mtot) and atom resolved spin

magnetic moments calculated at optimized lattice parameters for present alloys are listed in

Table 2.2. In Fig. 2.6, the calculated moments for semi-Heusler alloys as a function of the

total number of valence electrons have been depicted. The corresponding theoretical data

from previous calculations [14-16] is also listed for exhaustive comparison.

Table 2.2 Total and atom resolved magnetic moments of NiCrZ (Z = Si, Ge and P)

Heusler alloys; Nv denotes the total number of accumulated electrons in the alloy.

Alloys (NV)

MNi

(µB) MCr

(µB) MZ

(µB) Mtot

(µB) NiCrSi(20) NiCrGe(20) NiCrP(21)

This work Others [15] This work Others [16] This work Others [14]

0.11 0.17 0.05 - 0.15 0.12

1.96 1.89 2.01 - 2.74 2.99

-0.09 -0.09 -0.11 - -0.10 -0.12

2.00 1.96 2.00 - 3.00 2.98

NiCrZ (Z = Si, P and Ge) semi-Heusler alloys

57

Fig. 2.6 Schematic representation of the calculated total spin magnetic moments (m)

for NiCrZ (Z = Si, Ge and P) Heusler alloys (dark circles).The dotted line

represents the Slater-Pauling behavior.

The dotted line represents the SP rule for these alloys. The calculated integer

magnetic moment justifies that the present alloys obey SP rule according to which total

spin magnetic moment scales accurately with the number of valence electrons and is

expressed as, Vm 18n= − . Thus, these alloys exist in the stable HM configuration. In

Table 2.2, we summarize the total and atom resolved spin magnetic moment calculated at

optimized lattice parameters for present Heusler alloys.

The large exchange splitting of Cr-3d states leads to the localized spin magnetic

moment at Cr site. Our calculation predicts larger spin moment at Cr site than at Ni site i.e.

the spin moment is mainly carried by the low valent transition metal atom Cr. The local

magnetic moments of Cr atom are very close to each other in NiCrSi and NiCrGe (~2.00

µB) structures indicating similar electronic environments whereas in NiCrP, due to increase

in one electron on P atom, the exchange splitting of Cr-3d states enhances the magnetic

Chapter 2

58

moment on Cr atom to 2.74 µB. Ni carries a small spin moment of ~0.05–0.15 µB due to the

hybridization with the Cr-3d states in each alloy. The sp-atom shows a negligibly small

spin magnetic moment which is antiparellel to the moment of TM atoms.

2.3.4 Bandstructures

The band structures of studied systems for minority spin channel are presented in

Fig. 2.7. Due to similar electronic configuration, NiCrSi and NiCrGe have qualitatively

same bandstructure with similar type of bands both in VB and CB. But in NiCrP, the

energy bands in VB lie deeper in energy as compared to rest of two alloys, resulting due to

an extra electron in the same valence shell. The common feature of all three systems is an

indirect band gap along Γ–X direction i.e. in ∆-direction, perpendicular to (100) plane due

to hybridization of TM-d states. In all these systems, the Ni-3d and Cr-3d states are

hybridized to form bonding and antibonding states separated by a gap. The actual

magnitude of Eg↓ depends on how sp-p states finally hybridized with TM-d states. Insight

study of these systems shows that sp-elements decide the degree of occupation of p-d

orbitals, leading to different minority band gap.

Fig. 2.7 Calculated bandstructures of NiCrZ (Z = Si, Ge and P) in minority spin

channel.

NiCrZ (Z = Si, P and Ge) semi-Heusler alloys

59

In last, we present the spin resolved band structure of reference alloy, NiCrSi in

Fig. 2.8, focusing on some important regions. In both spin channels of NiCrSi, a low lying

band (not shown in figure), ranging from ~ -11.0 to ~ -7.7 eV arises due to s electrons of

sp-element (Si) which remains isolated from rest of the bands. In minority spin channel,

the next triple-degenerated band at U point is due to the sp-p states. It follows by the

double-degenerated (eg) and triple-degenerated (t2g) bands formed by Ni and Cr bonding

admixture. The antibonding hybrids are separated from bonding hybrids by an indirect gap

along Γ–X direction. In this way, we have exactly nine occupied minority bands. In

majority state of this system, there is a series of bands from ~ - 6.0 to 0 eV where Ni-3d

states contribute significantly with a small contribution from Cr-3d and Si-3p states. In

contrast to minority state, we have 11 electrons in majority bands. The two remaining

electrons are found in antibonding (eg) states.

Fig. 2.8 Bandstructure and DOS of NiCrSi for majority (left) and minority (right)

states.

Chapter 2

60

2.4 Conclusions

In conclusion, we have investigated, in details, the effect of substitution of Si atom

in NiCrSi semi-Heusler alloy by Ge and P on its electronic and magnetic properties in

order to analyze the effect of changing the sp-element on half-metallicity and magnetism.

We predict, using the FPLAPW method, that the all three semi Heusler alloys are HMFs

with EF lying in the semiconducting gap of the minority spin channel. The NiCrSi alloy has

highest value (0.91 eV) of Eg↓,. We predict a smaller value of gap for this alloy than the

corresponding value (1.07 eV) as calculated by Galanakis et al. [15] The substitution of sp-

element (Si) by next element along its group/period results in NiCrGe Heusler alloy. This

substitution increases the nn distance from 2.36 Å in NiCrSi to 2.42 Å in NiCrGe. This

makes the p-d hybridization poorer which henceforth leads to formation of longer and

weaker bonds. This slightly closes band gap in minority spin channel and reduces the Eg↓

from 0.91 eV to 0.75 eV. On the other hand, substitution of Si in NiCrSi by next sp-

element along its period yields NiCrP. In resultant alloy, the number of valence electrons

of sp-element (P) in same shell increases by unity which increased effective nuclear charge

on P atom as compared to Si and results in shifting of DOS, in both spin channel, towards

lower energy in the measured energy range. This transition of sp-element reduces the value

of Eg↓ to 0.80 eV.

The magnetic moment is mainly localized on Cr atom due to large exchange

splitting of Cr-3d states and the total spin magnetic moments of all the studied Heusler

alloys are in well agreement with the Slater-Pauling rule ( Vm 18n= − ) which emphasizes

the stable HM configuration for these systems. The substitution of sp-element, Si to Ge/P

in NiCrSi has strong influence on the position of EF and governs a decrease in Eg↓, but it is

not responsible for the origin of gap. A close structural similarity between Zinc-Blend

semiconductors and semi Heusler alloys makes the latter compatible in conventional

semiconductors technology for industrial applications which clearly shows the importance

of the present study.

NiCrZ (Z = Si, P and Ge) semi-Heusler alloys

61

References

1. Poon S. J., in Recent Trends in Thermoelectric Materials Research I, edited by

Tritt T. M., Semiconductors and Semimetals Vol. 70, Chap. 2, pp. 37–76

(Academic, New York), 2001.

2. Casper F., Graf T., Chadov S., Balke B., and Felser C., Half-Heusler compounds:

novel materials for energy and spintronic applications, Semicond. Sci. Technol.

27, 063001 (2012).

3. Nanda B. R. K., and Dasgupta I., Electronic structure and magnetism in doped

semiconducting half-Heusler compounds, J. Phys.: Condens. Matter 17, 5037

(2007)

4. Heusler Fr. Verh. Deutsch. Phys. Ges 5, 219 (1903).

5. Castelliz L., Mh. Chem. 82, 1314 (1952).

6. Nowotny H., and Glatzl B., Mh. Chem. 83, 237 (1952).

7. Forster R. H., and Johnston G. B., Studies on the Heusler alloys-III. The antiferro-

magnetic phase in the Cu-Mn-Sb system, J. Phys. Chem. Solids 29, 855 (1968).

8. de Groot R. A., Mueller F. M., van Engen P. G., and Buschow K. H. J., New class

of materials: half-metallic ferromagnets, Phys. Rev. Lett. 50, 2024 (1983).

9. Wolf S. A., Awschalom D. D., Buhrman R. A., Daughton J. M., von Molnár S.,

Roukes M. L., Chtchelkanova A. Y., and Treger D. M., Spintronics: A spin based

electronics vision for the future, Science 294, 1488 (2001).

10. Datta S., and Das B., Electronic analog of the electro-optic modulator, Appl.

Phys. Lett. 56, 665 (1999).

11. Kilian K. A., and Victora R. H., Electronic structure of Ni2MnIn for use in spin

injection, J. Appl. Phys. 87, 7064 (2000).

12. Tanaka C. T., Nowak J., and Moodera J. S., Spin-polarized tunneling in a half-

metallic ferromagnet, J. Appl. Phys. 86, 6239 (1999).

13. Caballero J. A., Park Y. D., Childress J.R., Bass J., Chiang W.-C., Reilly A.C.,

Pratt W.P. Jr., and Petroff F., J. Vac. Sci. Technol. A 16, 1801 (1998); Hordequin

C., Nozières J. P., and Pierre J., Half metallic NiMnSb-based spin-valve

structures, J. Magn. Magn. Mater. 183, 225 (1998).

14. Dinh V. A., Sato K., and Katayama-Yoshida H., New high-Tc half-Heusler

Chapter 2

62

ferromagnets NiMnZ(Z =Si,P,Ge,As), J. Phys. Soc. Jpn. 77, 014705 (2008).

15. Galanakis I., Özdoğan K., and Şaşioglu E., Ab initio electronic and magnetic

properties of half-metallic NiCrSi and NiMnSi Heusler alloys: The role of defects

and interfaces, J. Appl. Phys. 104, 083916 (2008).

16. Zhang M., Dai X., Hu H., Liu G., Cui Y., Liu Z., Chen J., Wang J., and Wu G.,

Search for new half-metallic ferromagnets in semi-Heusler alloys NiCrM (M = P,

As, Sb, S, Se and Te), J.Phys. Condens. Matter 15, 7891 (2003).

17. Luo H., Zhu Z., Liu G., Xu S., Wu G.,Liu H., Qu J., and Li Y., 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 403, 200 (2008).

18. Kirillova M. N., Makhnev A. A., Shreder E. I., Dyakina V. P., and Gorina N. B.,

Interband Optical Absorption and Plasma Effects in Half-Metallic XMnY

Ferromagnets, Phys. Status Solidi B 187, 231 (1995).

19. Hanssen K. E. H. M., and Mijnarends P. E., Positron-annihilation study of the

half-metallic ferromagnet NiMnSb: Theory, Phys. Rev. B 34, 5009 (1990);

Hanssen K. E. H. M., and Mijnarends P. E., Rabou L. P. L. M., and Buschow

K.H.J., Positron-annihilation study of the half-metallic ferromagnet NiMnSb:

Experiment, ibid. 42, 1533 (1990).

20. Webster P. J., and Ziebeck K. R. A., Alloys and compounds of d-elements with

main group elements, Part 2, ed.: Wijn H.R.J., vol. 19, pp. 75-184, Landolt-

Börnstein, New Series, Group III, (Springer, Berlin), 1986.

21. Androulakis J., Gardelis S., Buckle P. D., and Giapintzakis J., Magnetic

properties of the half-metallic ferromagnet NiMnSb grown on InSb by pulsed

laser deposition, Appl. Phys. A 79, 1211 (2004).

22. Gardelis S., Androulakis J., Monnereau O., Buckle P. D., and Giapintzakis J.,

Possible use of the half-Hausler alloy NiMnSb in spintronics: synthesis and

physical properties of arc melted NiMnSb and of NiMnSb thin films grown on

InSb by pulsed laser deposition, J. Phys. Conf. Ser. 10, 167 (2005).

23. Tanaka C. T., Nowak J., and Moodera J. S., Spin-polarized tunneling in a half-

metallic ferromagnet, J. Appl. Phys. 86, 6239 (1999).

NiCrZ (Z = Si, P and Ge) semi-Heusler alloys

63

24. Caruso A. N., Borca C. N., Ristoiu D., Nozières J. P., and Dowben P. A., A

comparison of surface segregation for two semi-Heusler alloys: TiCoSb and

NiMnSb, Surf. Sci. 525, L109 (2003); Ristoiu D., Nozières J. P., Borca C. N.,

Komesu T., Jeong H.-K., and Dowben P. A., The surface composition and spin

polarization of NiMnSb epitaxial thin films, Europhys. Lett. 49, 624 (2000);

Ristoiu D., Nozières J. P., Borca C. N., Borca B., and Dowben P. A., Manganese

surface segregation in NiMnSb, Appl. Phys. Lett. 76, 2349 (2000); Komesu T.,

Borca C. N., Jeong H. –K., Dowben P. A., Ristoiu D., Nozières J. P., Stadler S.,

and Idzerda Y. U., The polarization of Sb overlayers on NiMnSb(100), Phys. Lett.

A 273, 245 (2000).

25. Galanakis I., and Dederichs P.H., Half-metallic Heusler alloys: Fundamentals

and applications, Lecture Notes in Physics, vol. 676, ed.: Dederichs P. H. (Berlin;

Springer), 2005.

26. Chadov S., Qi X., Kubler J., Fecher G. H., Felser C., and Zhang S. C., Tunable

multifunctional topological insulators in ternary Heusler compounds, Nat. Mater.

9, 541 (2010).

27. Li C., Lian J. S., and Jiang Q., Antiferromagnet topological insulators with AB2C

Heusler structure, Phys. Rev B 83, 235125 (2011).

28. Xiao D., Yao Y., Feng W., Wen J., Zhu W., Chen X. –Q., G. M. Stocks, and Z.

Zhang, Half-Heusler compounds as a new class of three-dimensional Topological

Insulators, Phys. Rev. Lett. 105, 096404 (2010).

29. Canfield P. C., Thompson J. D. , Beyermann W. P., Lacerda A. , Hundley M. F.,

Peterson E., Fisk Z., and Ott H. R., Magnetism and heavy fermion‐like

behavior in the RBiPt series, J. Appl. Phys. 70, 5800 (1991).

30. Goll G., Marz M., Hamann A., Tomanic T., Grube K., Yoshino T., and Takabatake

T., Thermodynamic and transport properties of the non-centrosymmetric

superconductor LaBiPt, Physica B 403, 1065 (2008).

31. Ouardi S., Shekhar C., Fecher G. H., Kozina X., Stryganyuk G., Felser C., Ueda

S., and Kobayashi K., Electronic structure of Pt based topological Heusler

compounds with C1b structure and “zero band gap”, Appl. Phys. Lett. 98,

211901 (2011).

Chapter 2

64

32. Damewood L., Busemeyer B., Shaughnessy M., Fong C. Y., Yang L. H., and

Felser C., Bonding, magnetic properties and stability of the half-Heusler alloys

LiMnZ (Z=N, P, Si), arXiv:1301.6367v2 (2013).

33. Yao Z., Zhang Y. S., and Yao K. L., Large half-metallic gap in ferromagnetic

semi-Heusler alloys CoCrP and CoCrAs, Appl. Phys. Lett. 101, 062402 (2012).

34. Blaha P., Schwarz K., Madsen G. K. H., Kvasnicka D., and Luitz J., WIEN2k, An

augmented plane wave + Local Orbitals Program for calculating Crystal

Properties (Schwarz K., Techn. Universitat Wien, Wien, Austria), 2001, ISBN 3-

9501031-1-2.

35. Singh D. J., Plane waves, pseudopotentials and the LAPW method, (Kluwer

Academic Publishers, Boston, Dortrecht, London), 1994.

36. Perdew J. P., Burke K., and Ernzerhof M., Generalized gradient approximation

made simple, Phys. Rev. Lett. 77, 3865 (1996).

37. Blöch P. E., Jepsen O., and Anderson O. K., Improved tetrahedron method for

Brillouin-zone integrations, Phys Rev B 49, 16223 (1994).

38. Kumar M., Nautiyal T., and Auluck S., Full potential results on the magneto-

optical properties of the Heusler compounds Co2FeX (X = Al, Ga, Si and Ge), J.

Phys.: Condens. Mater. 21, 196003 (2009).

39. Ozolins V., and Korling M., Full-potential calculations using the generalized

gradient approximation: Structural properties of transition metals, Phys. Rev. B

48, 18304 (1993).