ELECTRONIC STRUCTURE, MAGNETIC ORDERING AND PHASE STABILITY OF LiFeX (X = P, As and Sb) UNDER...

December 9, 2013 15:38 WSPC/147-MPLB S0217984913502369 1–14

Modern Physics Letters BVol. 27, No. 32 (2013) 1350236 (14 pages)c© World Scientific Publishing Company

DOI: 10.1142/S0217984913502369

ELECTRONIC STRUCTURE, MAGNETIC ORDERING

AND PHASE STABILITY OF LiFeX (X = P,As and Sb)

UNDER PRESSURE

RAJENDRAN MAHESH

Department of Physics, Pondicherry Engineering College, Puducherry 605014, [email protected]

RAMASWAMY MURUGAN

Department of Physics, Pondicherry University, Puducherry 605014, [email protected]

BALAN PALANIVEL

Department of Physics, Pondicherry Engineering College, Puducherry 605014, Indiabp [email protected]

Received 22 July 2013Revised 22 October 2013Accepted 22 October 2013Published 6 December 2013

Electronic band structure calculations were performed on the nonmagnetc (NM) and an-tiferromagnetic (AFM) phases of LiFeX (X = P,As and Sb) compounds using ab initiomethod. The crystal structure of these compounds is well tetragonal P4/nmm structure(space group = 129). Self-consistent calculations were performed by planewave pseudo-potential, density functional based method using PWSCF-Quantum Espresso code. Tostudy the electronic structure and magnetic ordering, the total energies of these com-pounds have been computed as a function of reduced volumes and fitted with BrichMurnaghan equation. The estimated lattice parameters are in good agreement withavailable experimental data. The calculated Fe magnetic moment for LiFeSb is largerthan LiFeAs and LiFeP. The obtained electron–phonon coupling constant (λ) for theNM phase are very weak when compared to that of AFM phase of LiFeX compounds.Present calculations reveal that the electron–phonon coupling constant λ decreases as afunction of pressure.

Keywords: Electronic structure; magnetic ordering; structural phase stability.

1. Introduction

Recently discovered layered iron-based high temperature superconductors have re-

ceived a great deal of research interest. The new iron pnictide superconductors have

several interesting properties in the view point of the previously known class of

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http://dx.doi.org/10.1142/S0217984913502369

mailto:[email protected]




R. Mahesh, R. Murugan & B. Palanivel

unconventional superconductor such as heavy fermion materials and cuprates.1 Fe-

based superconductors have interesting properties like electron correlation effect,

collinear and noncollinear spin spiral structures and magnetic anisotropy, based

on their magnetic ordering and electronic structure. These materials also possess

various interesting physical properties, such as ferromagnetism (FM), antiferro-

magnetism (AFM), spin density waves (SDW), etc. Fe-based superconductors have

broad family of groups. The five main groups of AFeAs superconductors are known

as “1111”, “122”, “111”, “32225” and “42226”. The parent phases for these groups

of FeAs superconductors are ReFeAsO and BFeAsF for “1111”, BFe2As2 for “122”,

FeAs for “111”, Sr3Sc2Fe2As2O5 for “32225” and Sr4M2Fe2As2O6 for “42226”,

where Re, A, B and M are rare earth, alkaline, alkaline earth and transition metals,

respectively.2–4 All the above Fe based compounds have FeAs layer, which consist of

a square Fe lattice with As in the center of the square but being alternatively shifted

above and below the Fe plane. The FeAs layer is the conducting layer and dominates

near the Fermi level.5–7 The undoped materials of ReFeAsO,8 BaFe2As2,9 SrFe2As2

(Ref. 10) and SrFeAsF (Ref. 11), at normal conditions undergo a spin-density wave

(SDW) transition. By applying pressure or chemical doping, the spin density wave

is suppressed and exhibits superconductivity.12,13 In order to understand quantita-

tively the electrical, thermal and superconducting properties of materials, one needs

a proper description of an electron–lattice interaction.14 The undoped LiFeAs com-

pound shows superconducting phenomena at ambient condition but does not show

any SDW behavior which is reported by Tapp et al.15 and others.16–18 However,

the stoichiometric NaFeAs compound exhibits magnetic ordering is confirmed by

the experimental results.19

First-principles calculations20,21 of LaFeAsO, BaFe2As2 and SrFeAsF confirm

that the striped antiferromagnetic configuration (SAF) is the stable ground state for

these compounds, and also the same SAF order is stable in LiFeAs.22 The LiFeAs

compound has a Cu2Sb type tetragonal structure with space group P4/nmm and

it is confirmed by X-ray diffraction.16 It is well known that the stoner model can

explain the ground state properties of metals. Though LiFeAs has metallic nature,

the stoner model cannot explain temperature dependent behavior in this compound

as it neglects the instability in the directions of spin moments.17 Superconductiv-

ity in Fe based undoped iron pnictides induced by applying pressure was reported

in many high pressure experiments.23,24 However, doped iron pnictides show su-

perconductivity at ambient pressure. The critical transition temperature of doped

iron pnictides can be changed with the applied pressure.8,25 For LiFeAs, the crit-

ical transition temperature (Tc) of superconductivity decreases linearly with ap-

plied pressure at the rate of −1.5 K/GPa measured by various experimental tech-

nique.18,26,27 Recently, Wang et al. reported that the Tc decreases monotonously for

LiFeAs and LiFeP compounds with increasing pressure.28 The “111” type materials,

LiFeAs15,28 and LiFeP29,30 provide an exclusive way to study the effect of pressure

on Tc, since both the materials show superconducting and nonmagnetic properties.

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Electronic Structure, Magnetic Ordering and Phase Stability of LiFeX

Experimentally it is reported that the superconducting transition temperature of

LiFeP and LiFeAs are 6 K and 17 K, respectively. The pressure effect on transi-

tion temperature reveals that pressure suppresses Tc monotonously with a pressure

coefficient of −1.26 K/GPa and −1.38 K/GPa for LiFeP and LiFeAs, respectively.28

Zhang et al.31 report that the properties of LaFePO and LaFeAsO compounds

are closely related, suggesting a similar mechanism of superconductivity, and fur-

thermore when the compound dopes with heavier Pnictogen (As) exhibits higher

Tc. In LiFeSb compound the electronic structure, magnetic properties, Fermi sur-

face and SDW are closely related to Fe-As based superconductors. The properties of

Fe-Sb based superconductors when compared with LiFeAs will have a higher N(EF)

and a stronger SDW. In addition, this material is found to be dynamically stable,

evidenced by the absence of any unstable phonon modes reported in earlier calcula-

tions. The research in this type of materials includes many interesting observations

like coexistence of superconductivity and magnetic ordering. In the present work,

in order to understand the structural and magnetic ordering in LiFeX (X = P, As

and Sb) compounds, detailed electronic band structure calculations were performed

and the effect of pressure on magnetic moment and electron–phonon coupling con-

stant of LiFeX (X = P, As and Sb) compounds was reported using first-principles

method. Section 2 describes the method of calculation. Section 3 presents the crys-

tal structure details. The results and discussions are given in Sec. 4 and Sec. 5 is

devoted for conclusion.

2. Method of Calculation

Quantum Espresso32 is an integrated suite of computer codes for electronic-

structure calculations and materials modeling based on density-functional theory

(DFT). It uses plane waves basis sets and pseudo potentials (PPs) to represent

electron–ion interactions. Quantum Espresso code can thus be a very useful tool to

study the properties of metals and insulators having different crystal structures. The

atomic cores in this code are described by separable norm-conserving (NC) pseudo

potentials, ultra-soft (US) pseudo potentials, and projector-augmented wave (PAW)

sets.32 Another very important feature of this code is high performance nature both

in serial and parallel executions. The present calculations have been performed in a

plane-wave pseudo potential representation using the plane wave self-consistent field

(PWSCF) program within the generalized gradient approximation according to the

Perdew–Burke–Ernzerhof (GGA-PBE) exchange correlation potential function.33

In the present calculation of LiFeX (X = P, As and Sb) compounds, the valence

states for Li, Fe, P, As and Sb atoms are (2s, 2p), (3d, 4s, 4p), (3s, 3p), (4s, 4p) and

(5s, 5p), respectively. The magnetic and nonmagnetic calculations are carried out

with an energy cut-off of 40 Ryd for the wave functions and 400 Ryd for the charge

densities. For the electronic-structure calculations, the Brillouin-zone integrations

are performed by using the Gaussian smearing technique with a width of 0.04 Ryd.

The energy convergences are checked with respect to the cut-off energy and k-point

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sampling. For k-point sampling a grid of 16×16×12 is used for nonmagnetic (NM),

ferromagnetic (FM) and antiferromagnetic (AFM) ordering of LiFeX (X = P, As

and Sb) compounds in P4/nmm structure. Within the frame work of the linear

response theory, the electron–phonon interaction coefficients are calculated.

3. Crystal Structure

At ambient conditions LiFeX (X = P, As and Sb) crystallize in a tetragonal unit

cell with space group P4/nmm. These compounds have a layered structure of Fe-

X (X = P, As and Sb), which consist of a square Fe lattice with X in the center

of the square but being alternatively shifted above and below the Fe plane. The

unit cell of the LiFeX (X = P, As and Sb) has two Li, two Fe and two X atoms.

The atomic positions for Li is (0.25, 0.25, zLi), 2c site, Fe atom at (0.75, 0.25, 0.5)

2b site and X (P or As or Sb) at (0.25, 0.25, zx) 2c site. The experimental lattice

parameters15,34 are used to calculate Vexp in the present calculations. The c/a ratio

for tetragonal phase of LiFeX compounds are optimized by total energy minimiza-

tion The optimized internal coordinates are also estimated for LiFeX compounds

at equilibrium volume using the Broyden–Fletcher–Goldfarb–Shanno algorithm.35

The calculated values of lattice parameters and internal coordinates are listed in

Table 1 along with experimental values and since LiFeSb is a hypothetical com-

pound, earlier reported values are given for comparison. The calculated lattice pa-

rameters (a and c) for tetragonal phase are increased by replacing X = P to As and

As to Sb. This is mainly due to increase in atomic radius of Pnictogen atoms: RAT

(P) = 2.06 A < RAT (As) = 2.14 A < RAT (Sb) = 2.35 A. However, P → As and

As → Sb replacement shows the anisotropic deformation of the crystal structure.

In fact, as going from P → As, the a and c parameter increase to 1.025 and 1.058

times respectively whereas going from As → Sb, they increase to 1.059 and 1.011

times, respectively. This type of anisotropic deformation of crystal structure due to

atomic substitutions was also reported for a set of layered phases.3,36,37

Table 1. The evaluated lattice parameters, c/a ratio and Z parameters of the LiFeXcompounds.

Compound a (A) c (A) c/a ZLi ZX

LiFeP 3.6995 6.006 1.633 0.8583 0.2956

(3.6955)∗ (6.0411)∗ (1.6347)∗ (0.856)∗ (0.2803)∗

LiFeAs 3.7936 6.3562 1.675 0.8626 0.2686

(3.791)∗∗ (6.3639)∗∗ (1.678)∗∗ (0.8459)∗∗ (0.2635)∗∗

LiFeSb 4.0182 6.4245 1.5988 0.7064 0.2439

(4.0351)∗∗∗ (6.3712)∗∗∗ (1.5789)∗∗∗ (0.697)∗∗∗ (0.228)∗∗∗

Expt: ∗Ref. 34, ∗∗Ref. 15, Reported: ∗∗∗Ref. 31.

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Table 2. Total DOS at EF, electronic heat capacity (γ) and Pauli paramag-netic susceptibility (χ) for LiFeX (X = P, As and Sb) compounds.

Total DOS at EF γ χ

Compound (states/eV) (mJ K−2 mol−1) (10−4 emu/mol)

LiFeP 3.33(3.349)∗ 7.854(7.894)∗ 1.077(1.078)∗

LiFeAs 3.35(3.823)∗ 7.900(9.011)∗ 1.080(1.231)∗

LiFeSb 3.59 8.46 1.160

Reported: ∗Ref. 42.

4. Results and Discussion

In general, the calculated band structure and total density of states (DOS) for

LiFeX compounds have similar profiles and are in good agreement with earlier

observations.21,38–41 In the case of Fe-X covalent bonds, the bonding–antibonding

splitting is very sensitive to the distance between iron-pnictogen atoms. Thus, the

reduction in distance between iron and pnictogen atoms leads to an increase in

bonding–antibonding splitting for LiFeX compounds and to moving of Fe-3d states

away from the Fermi level. The calculated N(EF) for LiFeSb is equal to 3.59 eV

per unit cell which is slightly more than that of LiFeAs.

The Sommerfeld constant namely electronic heat capacity (γ) and the Pauli

paramagnetic susceptibility (χ) were calculated for NM phase of LiFeX (X = P,

As and Sb) compounds under the assumption of free electron model. The Sommer-

feld constant was estimated using the relation γ = (π2/3) N(EF)k2B where N(EF)

is DOS at the Fermi level and kB is the Boltzmann constant. The Pauli paramag-

netic susceptibility can be determined by the relation χ = μ2BN(EF) where μB is the

Bohr magneton. The Sommerfeld constant obtained from the present calculation are

listed in Table 2 along with earlier reported values42 for comparison. The estimated

Sommerfeld constants are in the sequence of γ (LiFeP) <γ (LiFeAs) <γ (LiFeSb)

and this may be due to increasing trend in calculated DOS at EF. Available ex-

perimental Sommerfeld constants as obtained from specific-heat measurements18,29

also demonstrate an increase in the sequence of γ (LiFeP) <γ (LiFeAs) which is in

good agreement with our estimations.

4.1. Structural stability and magnetic order

To study the structural stability of these compounds the calculated total ener-

gies are computed for all three compounds by varying the molecular volume from

1.10 V0 to 0.80 V0, where V0 = Vexp. The calculated total energies of different

magnetic ordering namely, nonmagnetic (NM), ferromagnetic (FM) and antifer-

romagnetic (AFM) are fitted with Birch–Murnaghan equation of state43 for the

P4/nmm structure. The equilibrium lattice parameters and the bulk modulus (B)

are estimated from the fitted total energies. The obtained bulk modulus for LiFeX

(X = P, As and Sb) in the NM and AFM ordering are 103, 121.6, 94.2 GPa and

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Table 3. Fe magnetic moment (μB) for FMand AFM ordering in P4/nmm structure ofLiFeX compounds.

MFe (μB)

System FM AFM

LiFeP 0.18 0.83

LiFeAs 0.45(0.38)∗ 2.165(2.54)∗

LiFeSb 0.49 2.46(2.92)∗∗

Reported: ∗Ref. 49, ∗∗Ref. 50.

86.5, 73.3, 68.9 GPa, respectively. From the above data, it is very clear that the

bulk modulus of LiFeX compound in NM state is more than that of AFM state.

The smaller bulk modulus in AFM ordering is due to weaker interactions between

atoms and smaller force constants which in turn decrease the phonon frequency of

these compounds.44 The fitted total energies of these compounds reveal that AFM

ordering is stable when compared to NM or FM ordering. The variation of the total

energy versus the relative molecular volumes for LiFeX (X = P, As and Sb) are

given in Figs. 1(a)–1(c).

Tapp et al.15 reported that LiFeAs does not show any spin-density wave behav-

ior but exhibits superconductivity at ambient pressure without chemical doping.

Zhang et al.27 observed a gradual decrease in the spin moment and the loss of

coherence of spin coupling as the temperature is lowered below Tc. However, the

observation of magnetic transition at about 160–165 K in LiFeAs single crystal

which leads to the situation that magnetic ordering can universally exist in the

iron arsenide superconductors is reported by Wang et al.45 There are already many

reports21,46–48 on the calculations of the magnetic states of iron arsenide super-

conductors by density-functional theory (DFT). A general agreement is that these

systems possess low localized moments suggesting that spin fluctuations may play

an important role on the superconductivity. In order to understand the magnetic

properties of LiFeX compounds, the local Fe magnetic moment in LiFeX com-

pounds have been computed for FM as well as for AFM ordering. The calculated

magnetic moments of Fe atom are tabulated in Table 3. The calculated Fe magnetic

moments, at normal pressure, are comparable with previously reported values.49,50

The calculated local Fe magnetic moment is more in AFM state than in the FM

state. In general, larger Fe magnetic moment in iron antimonides than in arsenides

or phosphides can explain the enhanced stability of AFM with respect to the NM

phase. The larger local Fe magnetic moment for antimonides is also due to their

larger lattice constants. Besides, very small local Fe moment for phosphates may be

due to smaller intra-atomic exchange coupling as well as relatively smaller lattice

constants. In order to ensure the validity of the above result, similar calculations

were done by replacing Li atom by alkali metals like Na and K. The calculated

Fe magnetic moments of these AFeX (A = Na, K) compounds in AFM ordering

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0.8 0.9 1.0 1.1-0.74

-0.72

-0.70

-0.68

-0.66

-0.64

-0.62

To

t-E

ner

gy(

-138

+)R

yd

v/v0

LiFeP NM FM AFM

(a)

0.8 0.9 1.0 1.1

-1.00

-0.98

-0.96

-0.94

-0.92

-0.90

-0.88

To

t-E

ner

gy(

-582

+)R

yd

v/v0

LiFeAs NM FM AFM

(b)

0.8 0.9 1.0 1.1-0.84

-0.82

-0.80

-0.78

-0.76

-0.74

-0.72

-0.70

To

t-E

ner

gy(

-928

+)R

yd

v/v0

LiFeSb NM FM AFM

(c)

Fig. 1. (Color online) Represents the calculated total energies versus molecular volume ofLiFeX (X = P, As and Sb) compounds.

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Table 4. Fe magnetic mo-ments (μB) of other iron pnic-tides AFeX (A = Na and K)compounds in AFM ordering.

Compound MFe (μB)

NaFeP 0.76

NaFeAs 1.66(2.0)∗

NaFeSb 2.09

KFeP 0.045

KFeSb 1.93

KFeAs 1.63(1.96)∗

Reported: ∗Ref. 51.

Fig. 2. Valance charge density contour in (110) plane for LiFeSb compound.

are listed along with the reported values51 in Table 4. The Fe magnetic moment of

AFeX compounds show the similar trend as observed in LiFeX (X = P, As and

Sb) compounds.

However, the reported data on Fe spin magnetic moment for iron pnictides

obtained from various experimental techniques are inconsistent. For example,

X-ray absorption experiment in LiFeAs52 indicated a large Fe spin magnetic mo-

ment, whereas observations made from spin-specific probes suggest a much smaller

local spin moment. The presence of smaller spin magnetic moment is also confirmed

by ESR experiment27 and SQUID measurements.15 Spin measurements made from

ESR and SQUID are contrast to the reported value of Fe spin moment by X-ray

absorption experiment.

For transition metals and narrow-band compounds, the modified tight-binding

approximation (MTBA) approach seems to be yielding more accurate results,

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especially in predicting anisotropic properties.14 The physical property and struc-

ture of any compound is due to the nature of bonding. The bonding picture of LiFeX

(X = P, As and Sb) is very similar to other Fe-based superconductors and can be

classified as a high-anisotropic mixture of ionic, covalent and metallic contribu-

tions.42 In LiFeSb compound, the valance charge density of 110 planes is shown in

Fig. 2. The calculated DOS shows the delocalized Fe 3d states near-Fermi energy

which indicates the metallic-like Fe–Fe bonds inside [Fe-X ] blocks. The oxidation

numbers of atoms are: Li1+, Fe2+ and (P, As, Sb)3−. Thus, the charge states are

(1+) for single atomic Li sheets and (2−)− for blocks [Fe-X ], i.e. the charge transfer

occurs from Li1+ sheets to [Fe2 P2(As2) (Sb2)]2− blocks. In addition, inside [Fe2

P2 (As2) (Sb2)] blocks, ionic bonding takes place between Fe-X atoms.

4.2. Pressure effect on magnetic moment and Tc

Applied pressure has an advantage of introducing less disorder when compared to

chemical substitution. The AFM order is strong as well as stable in the studied pres-

sure range. In general, the electronic and magnetic structures are strongly affected

by the pressure effect. The lattice structure of Fe-X layers is stable under compres-

sion, which indicates that the distance between the neighboring Fe-X and Li layers

is reduced by pressure. Hence, the calculated magnetic moment of Fe atom decreases

under pressure. This may strengthen the coupling between the neighboring Fe-X

layers and stabilize the antiferromagnetic ordering in the Fe-X layers. The pressure

dependence of Fe magnetic moments for LiFeX (X = P, As and Sb) compounds in

the AFM ordering is shown in Fig. 3. From Fig. 3, it is clear that the Fe magnetic

moment in the AFM ordering decreases linearly with varying pressure in LiFeX

(X = P, As and Sb) compounds similar to the other Fe-based superconductors.53

-0.5 0.0 0.5 1.0 1.5 2.0 2.50.4

0.6

0.8

2.0

2.2

2.4

Fe

Mag

net

icm

om

ent(

μμ μμΒΒ ΒΒ)

Pressure(GPa)

Fe-Magnetic moment LiFeP LiFeAs LiFeSb

Fig. 3. (Color online) Calculated Fe magnetic moment (μB) for LiFeX (X = P, As and Sb)compounds under pressures.

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Table 5. Variation of λ (electron–phonon coupling constant) and densityof the states at the Fermi level N(EF) (states/eV) in LiFeX (X = P, Asand Sb) compounds in NM phase under pressures (GPa).

Pressure Electron–phonon coupling Density of statesCompounds (GPa) constant (λ) N(EF) (states/eV)

0 0.221 3.33LiFeP 1 0.188 3.20

2 0.033 2.91

0 0.259 3.35LiFeAs 1 0.077 3.20

2 0.033 3.15

0 0.057 3.59LiFeSb 1 0.053 3.43

2 0.051 3.37

For LiFeP and LiFeAs, the experimental measurements show that the super-

conductivity Tc decreases linearly with pressure at a rate of −1.26 K/GPa, and

−1.38 K/GPa experimentally.28 In the present calculation, the pressure effect on

superconductivity Tc in the NM phase of LiFeX (X = P, As and Sb) compounds are

investigated using the optimized internal coordinates estimated by the Broyden–

Fletcher–Goldfarb–Shanno algorithm. In general, a compression of the lattice by

applying pressure causes an increase in bandwidth, which in turn results in a de-

crease in the average density of states. From Table 5, it is evident that a slight

change in the average density of states N(EF) occurs at Fermi level due to pres-

sure. Even though, the calculated value of N(EF) for LiFeSb is comparable with

that of other LiFeX compounds, the low value of electron–phonon coupling con-

stant may be due to increase in bond angle of Sb–Fe–Sb and Fe–Sb distances.

The present results show that, with increasing pressure, N(EF) decreases and the

phonon frequencies increases, resulting with decrease in electron–phonon coupling

constant λ. All these factors will lead to a lower Tc and hence negative pressure

coefficient of Tc for these compounds.

This change in electron–phonon coupling constant due to pressure certainly

affects transition temperature Tc, since Tc is very much dependent on λ as given by

the Allen Dynes modified McMillan formula54 for calculation of superconductivity

Tc as mentioned below.

Tc =ωln

1.2exp

[− 1.04(1 + λ)

λ− μ∗(1 + 0.62λ)

], (1)

where ωln is the logarithmic average phonon frequency, μ∗ is the Coulomb pseudo

potential and λ is the electron–phonon coupling constant given by

λ = 2

∫ ∞

o

α2F (ω)

ωdω (2)

ωln = exp

[2

λ

∫ ∞

0

α2F (ω) lnω

ωdω

]. (3)

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0.0 0.5 1.0 1.5 2.00.00

0.05

0.10

0.15

0.20

0.25

0.30

Ele

ctro

n P

ho

non

co

up

ling

con

stan

t(La

mbd

a)

Pressure(GPa)

LiFeP LiFeAs LiFeSb

Fig. 4. (Color online) Electron–phonon coupling constant in LiFeX (X = P, As and Sb) com-pounds under pressures.

The electron–phonon coupling constant λ and the logarithmically averaged fre-

quency ωln are directly obtained by evaluating in Eqs. (2) and (3) where the

electron–phonon spectral function α2F (ω) can be determined self-consistency by

the linear response theory.

The superconducting transition temperature (Tc) for LiFeP compound has been

calculated at normal pressure using Allen Dynes modified McMillan formula.54 It

is found that the calculated superconducting transition temperature is much less

than 1 K, however experimental value of Tc is about 6 K. Similarly, the calculated

values of Tc for other LiFeX compounds are very small when compared with experi-

mental values. This kind of discrepancy between calculated and measured Tc is also

reported in earlier works.44,55 These observations may suggest that Fe based super-

conductors are not of the conventional type, where the attractive electron–electron

interaction is mediated by phonons. The calculated Tc values may be improved by

lowering the Coulomb potential which is not straightforward. Based on the lim-

itations of McMillan formula and its modifications, it is a fair assumption that

pressure effect on electronic band structure will reflect on the calculated values of

electron–phonon coupling constant (λ). The pressure effect on transition tempera-

ture reveals that pressure suppresses Tc monotonously with a pressure coefficient of

−1.26 K/GPa and −1.38 K/GPa for LiFeP and LiFeAs, respectively.28 The calcu-

lated values of electron–phonon coupling constant (λ) at normal pressure are very

low. However, calculated λ values at different pressures show the negative pressure

coefficients of λ for all LiFeX compounds. The variation of electron–phonon cou-

pling constant (λ) of LiFeX (X = P, As and Sb) compounds with applied pressure

is shown in Fig. 4.

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5. Conclusion

In summary, structural, electronic and magnetic properties of LiFeX (X = P, As

and Sb) compounds have been studied using the Quantum Espresso method. The

calculated lattice parameters (a and c) for tetragonal phase increases by replacing

X = P to As and As to Sb. This is mainly due to increase in atomic radius of

Pnictogen atoms. The total energies of these compounds at different volumes re-

veal that antiferromagnetic ordering is more stable when compared to nonmagnetic

or ferromagnetic ordering. The Fe magnetic moment for FM and AFM magnetic

ordering were calculated and compared with available data. The Fe magnetic mo-

ment for LiFeSb is larger than LiFeP or LiFeAs, indicating that LiFeSb has more

stable spin density waves. The lattice structure of Fe-X layers, including the angle

between Fe and X atoms and the bond length is hardly changed by pressure. It

indicates that the distance between the neighboring Fe-X and Li layers is reduced

by pressure. Hence, the calculated magnetic moment of iron atom decreases under

pressure. From the charge density map it is found that the valance charge density

distributed mainly around the Fe-X (X = P, As and Sb) layers. The calculated

values of electron–phonon coupling constant (λ) at normal pressure are very low,

however, the calculated λ values at different pressures show the negative pressure

coefficients of λ for all LiFeX compounds. The present results show that with in-

creasing pressure, N(EF) decreases and the phonon frequencies increase, resulting

with decrease in electron phonon coupling constant λ.

Acknowledgments

The authors are thankful to Professors S. Baroni, S. de Gironcoli, A. Dal Corso and

P. Giannozzi, CNR-INFM Democritos National Simulation Center, 34100 Trieste,

Italy, for providing Quantum Espresso code.

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ELECTRONIC STRUCTURE, MAGNETIC ORDERING AND PHASE STABILITY OF LiFeX (X = P, As and Sb) UNDER...

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