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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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