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Study of structural, electronic and magnetic properties of CoFeIn and

Co

2

FeIn Heusler alloys

M. El Amine Monir

a

, R. Khenata

a

, H. Baltache

a

, G. Murtaza

b,

n

, M.S. Abu-Jafar

c,d

,

A. Bouhemadou

e

, S. Bin Omran

f

, D. Rached

g

a

Laboratoire de Physique Quantique de la Matière et de la Modélisation Mathématique (LPQ3M), Faculté des Sciences, Université de Mascara, Mascara

29000, Algeria

b

Materials Modeling Lab, Department of Physics, Islamia College University, Peshawar, Pakistan

c

Dipartimento di Fisica Universita di Roma "La Sapienza", Roma, Italy

d

Department of Physics, An-Najah N. University, Nablus, Palestine

e

Laboratory for Developing New Materials and their Characterization, Department of Physics, Faculty of Science, University of Setif, 19000 Setif, Algeria

f

Department of Physics and Astronomy, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

g

Laboratoire des Matériaux Magnétiques, Faculté des Sciences, Université Djillali Liabès de Sidi Bel-Abbès, Sidi Bel-Abbès 22000, Algérie

article info

Article history:

Received 18 March 2015

Received in revised form

4 June 2015

Accepted 27 June 2015

Available online 2 July 2015

Keywords:

Heusler alloys

Electronic properties

Magnetic properties

FP-LAPW

PBE-GGAþU

abstract

The structural, electronic and magnetic properties of half-Heusler CoFeIn and full-Heusler Co

2

FeIn alloys

have been investigated by using the state of the art full-potential linearized augmented plane wave (FP-

LAPW) method. The exchange-correlation potential was treated with the generalized gradient approx-

imation (PBE-GGA) for the calculation of the structural properties, whereas the PBE-GGAþUapprox-

imation (where Uis the Hubbard Coulomb energy term) is applied for the computation of the electronic

and magnetic properties in order to treat the “d”electrons. The structural properties have been calcu-

lated in the paramagnetic and ferromagnetic phases where we have found that both the CoFeIn and

Co

2

FeIn alloys have a stable ferromagnetic phase. The obtained results of the spin-polarized band

structure and the density of states show that the CoFeIn alloy is a metal and the Co

2

FeIn alloy has a

complete half-metallic nature. Through the obtained values of the total spin magnetic moment, we

conclude that in general, the Co

2

FeIn alloy is half-metallic ferromagnet material whereas the CoFeIn alloy

has a metallic nature.

&2015 Elsevier B.V. All rights reserved.

1. Introduction

Half-metallic ferromagnetic materials have an exceptional

electronic structure, where one of the two spin bands has a me-

tallic character while the other band behaves in a semiconducting

or insulating nature around the Fermi level, which leads to 100%

spin-polarization. These types of materials have attracted atten-

tion due to their fundamental and potential engineering applica-

tion in spintronic [1] and photovoltaic devices [2]. Based on the

ﬁrst prediction of Groot et al. on the half-Heusler alloys, NiMnSb

and PtMnSb [3], many predictions of the half- and full-Heusler

alloys have been realized [4–7].

The Heusler alloys are attractive and have been gaining atten-

tion for magneto-electronic devices applications [8-9,1] and

spintronic applications [10] due to their high compatibility for

lattice matching with semiconductors and high Curie temperature

[11]. Many studies have been performed on the compounds Co

2

FeZ

(where Z¼Al, Si, Ga and Ge) such as the work of Balke et al. [12]

which employs the x-ray diffraction (XRD) and extended x-ray

absorption ﬁne structure (EXAFS) techniques. In addition, some

studies of the electronic and the magnetic properties of the

Co

2

MnAl and Co

2

CrSi alloys have conﬁrmed the half-metallicity of

these compounds [13,14]. Furthermore, many theoretical and ex-

perimental investigations of the half-Heusler CoYZ and full-

Heusler Co

2

YZ families have been realized [15–19].

The chemical stoichiometric formula of the half- and full-

Heusler alloy is XYZ and X

2

YZ, respectively, where X and Y are

transition metal and Z is the main group element. Full-Heusler

alloy crystallizes in the L2

1

cubic structure with space group

Fm

m

3

¯

and the half-Heusler alloy crystallizes in the Cl

b

structure with

space group

F

m

43

¯

.

In this present work, we have performed the ﬁrst-principles

DFT calculations on the structural, electronic, magnetic and ther-

mal properties of the CoFeIn and Co

2

FeIn Heusler alloys, using the

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/jmmm

Journal of Magnetism and Magnetic Materials

http://dx.doi.org/10.1016/j.jmmm.2015.06.077

0304-8853/&2015 Elsevier B.V. All rights reserved.

n

Correspondence to: LPQ3M-Laboratory, Faculty of Science and Technology,

Mascara University - 29000 Mascara, Algeria.

E-mail addresses: khenata_rabah@yahoo.fr (R. Khenata),

murtaza@icp.edu.pk (G. Murtaza), mabujafar@najah.edu (M.S. Abu-Jafar).

Journal of Magnetism and Magnetic Materials 394 (2015) 404–409

generalized gradient approximation scheme (PBE-GGAþU)

(where Uis the Hubbard Coulomb energy).

2. Computational detail

The results of the structural, electronic and magnetic properties

of the CoFeIn and Co

2

FeIn Heusler alloys are obtained by em-

ploying the full-potential linearized augmented plane wave plus

local orbital (FP-LAPWþlo) method [20,21 ] which is based on the

density functional theory (DFT) [22] and is implemented in the

WIEN2k code [23]. In this approach, the generalized gradient ap-

proximation in the scheme of the Perdew–Burke–Ernzerhof (PBE-

GGA) [24] has been used to treat the structural properties,

whereas we have also adopted the PBE-GGAþU[25] method

(where U¼3.26 eV) in order to simulate the electronic and mag-

netic properties of both the Heusler alloys. The mufﬁn-tin sphere

radii R

MT

were chosen as equal to 2.3, 2.4 and 2.6 a.u for the Co, Fe

and In atoms, respectively. The plane wave cut-off parameter is

taken as R

MT

K

max

¼8, where R

MT

is the mufﬁn-tin (MT) and K

max

is the maximum modulus of the reciprocal vector K¼kþGin the

ﬁrst Brillouin zone. Integrations of the Brillouin zone are per-

formed on the mesh of 9 99 with 35 k-point. In the following

calculations, the Co (4s

2

3d

7

), Fe (4s

2

3d

6

) and In (5s

2

5p

1

4d

10

) states

are treated as valence electrons. The SCF iterations stop when the

change in the absolute value of the total energy is less than

1*10

4

Ry.

The full-Heusler alloys (X

2

YZ) has the L2

1

cubic structure with

the space group

Fm

m

3

¯

, where the X atoms occupies the sites (1/4,

1/4, 1/4) and (3/4, 3/4, 3/4) whereas the Y and Z atoms occupies

the positions (1/2, 1/2, 1/2) and (0, 0, 0), respectively. In the case of

the half-Heusler alloys (XYZ) which crystallize in the Cl

b

structure

with

F

m

43

¯

as the space group, X, Y and Z atoms are localized at (1/

4, 1/4, 1/4), (1/2, 0, 1/2) and (0, 0, 0), respectively.

3. Results and discussion

3.1. Structural properties

The empirical Birch-Murnaghan’s equation of states (EOS) [26]

is used to optimize the volume of the unit cell by the energy

minimization procedure, where the parameters obtained at the

static equilibrium are: lattice constant (a

0

), bulk modulus (B

0

), its

ﬁrst pressure derivative (Bʹ) and minimum total energy (E

0

). The

EOS is given by the following expression:

⎡

⎣

⎢

⎢

⎛

⎝

⎜⎞

⎠

⎟⎛

⎝

⎜⎞

⎠

⎟

⎤

⎦

⎥

⎥

EV EV BV

BB

BV

V

V

V1

11

Tot

B

0

000

()= ()+ ′( ′ − ) −+ −

′

where Vis the volume and V

0

,B

0

and Bʹare the ﬁtting

parameters.

The structural properties of the CoFeIn and Co

2

FeIn Heusler

alloys are calculated in both the paramagnetic (PM) and ferro-

magnetic (FM) states by using the PBE-GGA parameterization.

Fig. 1 of the CoFeIn and Co

2

FeIn alloys shows that the total en-

ergies optimized in the ferromagnetic state are lower than the

ones in the paramagnetic state, which conﬁrm that the CoFeIn and

Co

2

FeIn alloys are stable in the ferromagnetic phase. In Table 1,we

have depicted the equilibrium structural parameters such as the

lattice constant (a

0

), bulk modulus (B

0

) and its ﬁrst pressure de-

rivative (Bʹ) under the both the paramagnetic and ferromagnetic

phases. However, there are no other experimental or theoretical

results for comparison with the present calculations. Hence, these

structural results can serve as the reference data for further works

in the ﬁeld.

3.2. Electronic properties

3.2.1. Electronic structure

The spin-polarized electronic structures of the CoFeIn and

Co

2

FeIn Heusler alloys have been studied at their equilibrium

lattice parameters by employing the PBE-GGAþUscheme. The

PBE-GGAþUcalculated spin-polarized band structures along the

high symmetry directions in the ﬁrst Brillouin zone are illustrated

as shown in Figs. 2 and 3, respectively. Our obtained results using

the PBE-GGAþUscheme depict that the majority-spin band

structures (spin-up case) for the two alloys have a metallic beha-

vior, where the energy bands cross the Fermi level. On the other

hand, the minority-spin band structures (spin-down case) for the

Co

2

FeIn alloy exhibit a semiconducting nature which conﬁrms the

half-metallicity property. The calculated PBE-GGAþUband struc-

ture shows that the Co

2

FeIn alloy is a complete half-metal and the

CoFeIn alloy is metal because some band energies cross the Fermi

level in its minority-spin band structure. According to the PBE-

GGAþUcalculations, the Co

2

FeIn alloy presents typical half-me-

tallic properties while the CoFeIn alloy does not have this property.

The electron spin-polarization at the Fermi level is deﬁned by

the following expression [27].

PEE

EE

FF

FF

ρρ

ρρ

=↑( )− ↓( )

↑( )+ ↓( )

where

ρ

↑(E

F

) and

ρ

↓(E

F

) are the spin dependent densities of

states at E

F

for the majority and minority-spin cases, respectively.

In our results, the Co

2

FeIn alloy calculated with the PBE-GGA þU

scheme has P(%)¼100%, hence the electrons at the Fermi level are

Fig. 1. Calculated total energy optimization variation versus volumes for both

paramagnetic (PM) and ferromagnetic (FM) phases for the (a) CoFeIn and

(b) Co

2

FeIn alloys.

M. El Amine Monir et al. / Journal of Magnetism and Magnetic Materials 394 (2015) 404–409 405

fully spin-polarized, thus conﬁrming the half-metallic character-

istics. The half-metallic gap (E

HM

)isdeﬁned as the minimum be-

tween the lowest energy of the majority-spin and minority-spin

conduction bands with respect to the Fermi level and the absolute

values of the highest energy of the majority-spin and minority-

spin valence bands [28,29]. The obtained values of E

HM

,

ρ

↑(E

F

),

ρ

↓

(E

F

) and P(%) are listed in Table 2, where the results given by the

PBE-GGAþUscheme are improved as compared to the values

calculated by the PBE-GGA scheme. This is due to the inﬂuence of

the U-Hubbard Coulomb energy correlation on the positions of the

electronic states.

Table 1

The calculated equilibrium lattice constant a

0

, bulk modulus Band its pressure derivative B’ʹfor the CoFeIn and Co

2

FeIn Heusler alloys in both the paramagnetic and

ferromagnetic phases using the PBE-GGA approximation.

Alloy Lattice parameter a

0

(Å) Bulk modulus B(GPa) B'

Paramagnetic state Ferromagnetic state Paramagnetic state Ferromagnetic state Paramagnetic state Ferromagnetic state

CoFeIn 5.7334 5.8326 140.1188 112.6025 4.7027 4.2278

Co

2

FeIn 5.9114 5.9819 188.1621 165.6474 5.2856 4.9547

Fig. 2. Spin polarized electronic band structure of the CoFeIn alloy at the equilibrium lattice parameter using the PBE-GGAþUapproximation.

Fig. 3. Spin polarized electronic band structure of the Co

2

FeIn alloy at the equilibrium lattice parameter using the PBE-GGA þUapproximation.

Table 2

The calculated results of the half-metallic E

HM

(eV), band gaps and spin-minority

band gaps E

g

(eV) and the spin-polarization at the Fermi level (E

F

) of the CoFeIn and

Co

2

FeIn alloys obtained using the PBE-GGA and PBE-GGA þUapproximations.

Alloy E

HM

(eV) E

g

(Γ-X) (eV) ρ↑(E

F

)ρ↓(E

F

)P(%)

CoFeIn

PBE-GGA –– 0.8009 0.0039 –

PBE-GGAþU–– 0.5829 4.0625 –

Co

2

FeIn

PBE-GGA –– 0.8195 0.0002 –

PBE-GGAþU 0.8148 0.8148 0.6077 0.0000 100

M. El Amine Monir et al. / Journal of Magnetism and Magnetic Materials 394 (2015) 404–409406

3.2.2. Density of states

The total (TDOS) and partial (PDOS) densities of states of the

CoFeIn and Co

2

FeIn Heusler alloys at their equilibrium lattice

parameters as calculated by using the PBE-GGAþUpara-

meterization are depicted in Figs. 4–7. The PDOS of the CoFeIn and

Co

2

FeIn alloys are mainly occupied with the 3d-Co and 3d-Fe

electrons and we can clearly see that for both alloys, there exists a

large exchange splitting between the majority-spin and minority-

spin of the 3d-Co and 3d-Fe states. The 3d-Co and 3d-Fe states are

divided into the e

g

states at the low energy and the t

2g

states at the

high energy. From Figs. 4 and 6of the TDOS plots, we remark that

the Co

2

FeIn alloy is completely half-metallic, whereas the CoFeIn

alloy is metallic because it’s TDOS of the minority-spin presents a

peak at the Fermi level. In the CoFeIn and Co

2

FeIn alloys

(Figs. 5 and 7), the e

g

and t

2g

states of the Co and Fe sites dom-

inates the part of the plots where E

F

ZEin both spin channels. In

the CoFeIn alloy, the e

g

and t

2g

states of the Co and Fe atoms are

totally occupied in the majority-spin case as well as the e

g

state of

the Co and Fe atoms in the minority-spin case. Conversely, for the

Co

2

FeIn alloy, only the t

2g

state of the Fe atom for the minority-

spin is partially occupied and the other states are all occupied. The

hybridization exists between Co–Fe in the 3d orbital and also

between the second adjoining 3d-Co and 3d-Co orbital. The

domination of the 3d-Fe electrons around the Fermi level in the

case of minority-spin for the CoFeIn alloy is the explanation of the

suspension of the gap in this region.

3.3. Magnetic properties

The total magnetic moment in the full-Heusler and half-

Heusler alloys is submissive to the Slater–Pauling rule. For the full-

Heusler alloy, it will be equal to M

T

¼Z

T

–24 [30,31] and for the

half-Heusler alloy, it will be M

T

¼Z

T

–18 [32], where M

T

is the total

magnetic moment per unit cell and Z

T

is the total number of va-

lence electrons. The obtained values of the total magnetic moment

of the CoFeIn and Co

2

FeIn alloys by utilizing the PBE-GGAþU

approximation are agglomerated in Table 3. The CoFeIn and

Co

2

FeIn alloys have 21 and 30 valence electrons, respectively,

which generate total magnetic moment of 3 m

B

and 6 m

B

, respec-

tively, according to the Slater–Pauling rule. Due to the strong hy-

bridization between the 3dCo–Co and 3dCo–Fe states, the total

magnetic moment of the Co

2

FeIn alloy obtained by the PBE-

GGAþUscheme is 6

μ

B

which is in excellent agreement with the

Fig. 4. Total density of states (TDOS) for the CoFeIn alloy using the PBE-GGA þU

approximation.

Fig. 5. Partial density of states (TDOS) for the CoFeIn alloy for both Fe and Co states using the PBE-GGA þUapproximation.

Fig. 6. Total density of states (TDOS) for the Co

2

FeIn alloy using the PBE-GGAþU

approximation.

M. El Amine Monir et al. / Journal of Magnetism and Magnetic Materials 394 (2015) 404–409 407

value of the Slater–Pauling rule, whereas the metallic behavior of

the CoFeIn alloy generate a deviation of the total magnetic mo-

ment from the Slater–Pauling value. In addition, we noted that the

total magnetic moment of the two alloys is mainly contributed by

the Co and Fe sites, where these contributions are due to the large

exchange splitting in the Co and Fe atoms for the majority-spin

and minority-spin channels. The local magnetic moments of each

site are also listed in Table 3, where the In atoms have a negligible

local magnetic moment with opposite sign in comparison with the

Fe and Co elements. This indicates that the magnetic moment of

the Co and Fe sites interact in anti-parallel behavior with those of

the In atoms, where the anti-parallel interaction is due to both p–d

hybridizations of the 5p-In states to the 3d-Co and 3d-Fe orbital of

the transition elements, respectively.

4. Conclusions

In this study, we have investigated the structural, electronic

and magnetic properties of the CoFeIn half-Heusler and Co

2

FeIn

full-Heusler alloys within the FP-LAPW method and both the PBE-

GGA and PBE-GGAþUschemes have been chosen as the ex-

change-correlation potential. The study of the structural

properties reveals that the total energy in the two compounds is

lower in the ferromagnetic phase then the paramagnetic phase

which conﬁrm that both alloys are stable in the ferromagnetic

phase. From the electronic structure, there is a large exchange

splitting between the majority and minority spins, where the PBE-

GGAþUelectronic band structures show that the CoFeIn alloy is a

metal whereas the Co

2

FeIn alloy has a complete half-metallicity

property with a half-metal gap of 0.81 eV. The origin of the

magnetism comes from the exchange splitting of the 3d-Co and

3d-Fe states, where its obtained values are in agreement according

to the Slater–Pauling rule. In comparison to the results obtained

with the PBE-GGA scheme, the electronic and magnetic results are

much improved with the PBE-GGAþUapproximation. This is due

to the U-Hubbard Coulomb energy which extensively inﬂuences

the 3d-Co and 3d-Fe states.

Acknowledgments

For Authors (R. Khenata and S. Bin-Omran) this work was

funded by the National Plan for Science, Technology and Innova-

tion (MAARIFAH) from the King Abdul-Aziz City for Science and

Technology, Kingdom of Saudi Arabia (award # 11-NAN1465-02).

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