ArticlePDF Available

# Study of structural, electronic and magnetic properties of CoFeIn and Co2FeIn Heusler alloys

Authors:

## Abstract and Figures

The structural, electronic and magnetic properties of half-Heusler CoFeIn and full-Heusler Co2FeIn 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 approximation (PBE-GGA) for the calculation of the structural properties, whereas the PBE-GGA+U approximation (where U is 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 calculated in the paramagnetic and ferromagnetic phases where we have found that both the CoFeIn and Co2FeIn 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 Co2FeIn alloy has a complete half-metallic nature. Through the obtained values of the total spin magnetic moment, we conclude that in general, the Co2FeIn alloy is half-metallic ferromagnet material whereas the CoFeIn alloy has a metallic nature.
Content may be subject to copyright.
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
,
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:
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 delectrons. 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.
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
rst 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 [47].
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 ne 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 conrmed 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 [1519].
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 rst-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
n
Correspondence to: LPQ3M-Laboratory, Faculty of Science and Technology,
Mascara University - 29000 Mascara, Algeria.
murtaza@icp.edu.pk (G. Murtaza), mabujafar@najah.edu (M.S. Abu-Jafar).
Journal of Magnetism and Magnetic Materials 394 (2015) 404409
(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 PerdewBurkeErnzerhof (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 mufn-tin sphere
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 mufn-tin (MT) and K
max
is the maximum modulus of the reciprocal vector K¼kþGin the
rst 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-Murnaghans 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
rst 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 tting
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 conrm 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 rst 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 eld.
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 rst 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 conrms 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 dened 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) 404409 405
fully spin-polarized, thus conrming the half-metallic character-
istics. The half-metallic gap (E
HM
)isdened 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 inuence 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 Bʹfor 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) 404409406
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. 47. 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 its 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 CoFe 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 SlaterPauling 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 SlaterPauling rule. Due to the strong hy-
bridization between the 3dCoCo and 3dCoFe 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) 404409 407
value of the SlaterPauling rule, whereas the metallic behavior of
the CoFeIn alloy generate a deviation of the total magnetic mo-
ment from the SlaterPauling 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
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 pd
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 conrm 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 SlaterPauling 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 inuences
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).
References
[1] H. Ohno, Science 281 (1998) 951.
[2] Q. Li, X. Gong, C. Wang, J. Wang, K. Ip, S. Hark, Adv. Mater. 16 (2004) 1436.
[3] R.A. de Groot, F.M. Mueller, P.G. van Engen, K.H.J. Buschow, Phys. Rev. Lett. 50
(1983) 2024.
[4] R.A. de Groot, Physica B 172 (1991) 45.
[5] R. Weht, W.E. Pickett, Phys. Rev. B 60 (1999) 13006.
[6] S.C. Lee, T.D. Lee, P. Blaha, K. Schwarz, J. Appl. Phys. 97 (2005) 10C307.
[7] B. Hulsen, M. Schefer, P. Kratzer, Phys. Rev. B 79 (2009) 094407.
[8] I. Zutic, J. Fabina, S. Das Sarma, Rev. Mod. Phys. 76 (2004) 323.
[9] K.A. Kilian, R.H. Victora, J. Appl. Phys. 87 (200 0) 7064.
[10] I. Zutic, S.D. Sarma, Rev. Mod. Phys. 76 (2004) 323340.
[11] F. Heusler, Verh. Dtsch. Phys. Ges. 5 (1903) 219.
[12] B. Balke, S. Wurmehl, G.H. Fecher, C. Felser, J. Kübler, Sci. Technol. Adv. Mater.
9 (2008) 014102.
[13] J. Hashemifar Rai, M. Jamal, M.P. Ghimire Lalmuanpuia, Sandeep D.T. Khathing,
P.K. Patra, B.I. Sharma Rosangliana, R.K. Thapa, Indian J. Phys 84 (2010) 593.
Fig. 7. Partial density of states (TDOS) for the Co
2
FeIn alloy for both Fe and Co states using the PBE-GGA þUapproximation.
Table 3
The calculated results of the total magnetic moment (M
tot
in m
B
) per unit cell and
the local magnetic moment of each site for the CoFeIn and Co
2
FeIn alloys obtained
using the PBE-GGA and PBE-GGAþUapproximations.
Alloy Calculations Magnetic moment (l
B
)
Co Fe In Total
CoFeIn
PBE-GGA 1.0131 2.6355 0.0466 3.4371
PBE-GGAþU1.6030 3.2247 0.0520 4.5808
Co
2
FeIn
PBE-GGA 1.2102 2.8655 0.0378 5.0935
PBE-GGAþU1.5934 3.2286 0.0653 6.0556
Others Cal. 1.250
a
2.885
a
0.046
a
5.143
a
a
Ref. [33].
M. El Amine Monir et al. / Journal of Magnetism and Magnetic Materials 394 (2015) 404409408
[14] D.P. Rai, A. Sandeep, M.P. Ghimire, R.K. Thapa, Bull. Mater. Sci. 34 (2011) 1219.
[15] S.D. Li, Z.R. Yuan, L.Y. Lu, M.M. Liu, Z.G. Huang, F.M. Zhang, Y.W. Du, Mater. Sci.
Eng. A428 (2006) 332.
[16] A.T. Zayak, P. Entel, J. Magn. Magn. Mater. 874 (2005) 290291.
[17] J. Li, Y.X. Li, X.F. Dai, X.W. Xu, J. Magn. Magn. Mater. 321 (2009) 365.
[18] E. Valerio, C. Grigorescu, S.A. Manea, F. Guinneton, W.R. Branford, M. Autric,
Appl. Surf. Sci. 247 (2005) 151.
[19] M. Sargolzaei, M. Richter, K. Koepernik, I. Opahle, H. Eschrig, Phys. Rev. B74
(2006) 224410.
[20] K.M. Wong, S.M. Alay-e-Abbas, A. Shaukat, Y. Fang, Y. Lei, J. Appl. Phys. 113
(2013) 014304.
[21] K.M. Wong, S.M. Alay-e-Abbas, Y. Fang, A. Shaukat, Y. Lei, J. Appl. Phys. 114
(2013) 034901.
[22] P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864.
[23] P. Blaha, K. Schwarz, P. Sorantin, S.K. Trickey, Comput. Phys. Commun. 59
(1990) 339.
[24] J.P. Perdew, S. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.
[25] V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. Czyzyk, G.A. Sawatzky, Phys.
Rev. B 48 (1993) 16929.
[26] F.D. Murnaghan, Proc. Natl. Acad. Sci. USA 30 (1944) 5390.
[27] R.J. Soulen Jr., et al., Science 282 (1998) 85.
[28] K.L. Yao, G.Y. Gao, Z.L. Liu, L. Zhu, Solid State Commun. 133 (2005) 301.
[29] G.Y. Gao, K.L. Yao, E. Sasioglu, L.M. Sandratskii, Z.L. Liu, J.L. Jiang, Phys. Rev. B 75
(2007) 174442.
[30] I. Galanakis, P.H. Dederichs, N. Papanikolaou, Phys. Rev. B66 (2002) 134428.
[31] C.M. Fang, G.A. deWijs, R.A. deGroot, J. Appl. Phys. 91 (2002) 8340.
[32] I. Galanakis, P.H. Dederichs, N. Papanikolaou, Phys. Rev. B66 (2002) 174429.
[33] Huang Hung-Lung, Tung Jen-Chuan, Guo Guang-Yu, Phys. Rev. B91 (2015)
134409.
M. El Amine Monir et al. / Journal of Magnetism and Magnetic Materials 394 (2015) 404409 409
... Half-metallic ferromagnets (HMF) are of greatest interest for magnetooptical data recording among these alloys. Co 2 FeZ alloys characterized by high values of such important parameters as the magnetization and the Curie temperature [1][2][3][4][5][6] (see Table 1) are also classified among them. ...
... Their magnetic characteristics required for the analysis of galvanomagnetic properties were determined. According to the electron energy band calculations [1][2][3][4][5][6], all the studied alloys really belong to the HMF class in the case of atomic ordering in crystal structure L2 1 . ...
... The dependences of M 2 on H/M in the studied alloys Co 2 FeZ are plotted in Fig. 2. It can be = + χ Taking into account the results of processing the experimental data M(H) at H > 20 kOe by Eq. (1) (Fig. 2), we have calculated the spontaneous moments μ S ( Table 1). The same table contains the theoretical moments μ theor obtained by calculating the electron energy band structure of the alloys in the works [1][2][3][4][5][6]. It can be seen that μ S and μ theor are close to each other for the considered alloys except Co 2 FeIn. ...
Article
The magnetization, Hall effect, and resistivity of Heusler alloys Co2FeZ (where Z = Al, Si, Ga, Ge, In, Sn, and Sb are s- and p-elements) have been studied at T = 4.2 K in magnetic fields H ≤ 100 kOe. In strong fields (H > 20 kOe), magnetization can be described by the Stoner model. The normal R0 and anomalous RS Hall effect coefficients have been determined. The coefficient RS is positive for almost all the studied alloys and represents a “linearly quadratic” resistivity function incorporating linear and quadratic terms. The constant R0 is negative for most alloys, and its absolute value is two or three orders of magnitude smaller than for RS. The magnetoresistivity of the studied alloys does not exceed several percent and may be both positive and negative for different specimens.
... Since Co2FeIn Heusler alloy was also predicted to exhibit a half-metallic nature [47], and it has also been earlier shown that the deposition of both Co-Fe and Co-In alloys from aqueous solutions is allowable [48,49], we have synthetized Heusler-based Co2FeIn alloy nanowires via templateassisted electrochemical deposition in the pores of AAO membranes. This easy and low-cost fabrication method opens up to the new possibility in the synthesis of novel Heusler nanomaterials suitable for spintronic applications. ...
... However, they tend to display the {220} planes nearly oriented perpendicular to the nanowire long axis exhibiting a pronounced {220} texture. The selected area electron diffraction, SAED, patterns (Figure 4 b) show spotted rings that can be indexed to the reflections of the (220), (400), (422), (440), (620), (444), (642), (660), (840) and (862) planes of aCo2FeIn Heusler phase with a lattice parameter of a = 5.72 ± 0.03 Å, which is lower than the calculated equilibrium lattice constant reported in reference[47]. All of such reflections satisfy the condition h + k + l = 4n (where n is an integer) with h, k and l all even. ...
Article
Full-text available
Cylindrical Co2FeIn Heusler alloy nanowires are synthesized via template-assisted electrochemical deposition into the hexagonally self-ordered nanopores of hard-anodic alumina membranes. The electroplated nanowires, with 180 ±20 nm in diameter and around 14.5 µm in length, exhibit a polycrystalline nature and they are homogeneous in composition. High-resolution transmission electron microscopy (HR-TEM), selected area electron diffraction (SAED) and X-ray diffraction (XRD) analysis confirmed a cubic A2 disordered phase of the ferromagnetic Heusler compound, with a lattice parameter of a = 5.764 ± 0.001 Å. In addition, these structural characterizations reveal that the Co2FeIn nanowires display a polycrystalline structure with a pronounced {220} texture. The temperature dependent magnetization behavior and anisotropy field distribution calculations display a dominant role of shape, magnetocrystalline and magnetoelastic terms on the effective magnetic anisotropy of Co2FeIn alloyed nanowire arrays. Magneto-optical Kerr effect measurements performed on single freestanding nanowires, after releasing from the hosting alumina templates, confirmed competing behavior between shape and magnetocrystalline anisotropy contributions, which lead to complex magnetization reversal process. This fabrication technique offers a promising and new forward-looking synthesis of novel Heusler nanomaterials for spintronics applications.
... Nonetheless, novel HAs are being studied theoretically due to fast computational facilities to predict their structural, electronic states, spin orientation, magnetic moment, bonding, mechanical, thermodynamic and thermoelectric properties. The recent first principles studies on some Co-based, [44][45][46][47][48][49] Fe-based, 36,38,[50][51][52][53] Zrbased [54][55][56] and Ti-based with new dimensions 57 HAs showed keen interest. As far as the research of Mn-based full HAs is concerned, Mn 2 VAl was found the first full HA investigated in theoretical [58][59][60] 68 have been investigated and half-metallic behaviour has been reported. ...
... The similar calculations are also performed to obtain total energy in the paramagnetic and FM phases and it is found that total energy is minimum in the FM phase like the other HAs. 44,45,52,62,67 The ground state properties like bulk modulus, B o and its first order pressure derivative, B o 0 are also calculated using Equation (1) and their values are presented in Table 1. Further, the stability of the Mn 2 PtCo is also checked in the Cu 2 MnAl-prototype structure by calculating the formation energy, ΔH Form : ...
Article
The structural, electronic, magnetic, mechanical and thermodynamic properties of the Mn2PtCo Heusler alloy have been investigated in the frame work of density functional theory (DFT). The cohesive energies confirm the Cu2MnAl‐prototype structure of Mn2PtCo with the ferromagnetic phase. The spin polarized electronic band profile of the Mn2PtCo exhibits its metallic character by considering the generalized gradient approximation (GGA) and modified Becke‐Johnson (GGA‐mBJ) approximation in the calculations. The magnetic moment is calculated to ~9 μB and it is in accordance with the Slater‐Pauling rule. From the analysis of mechanical properties the brittle nature is anticipated. Further to seek the applications of Mn2PtCo in device fabrication, the thermodynamic properties like entropy, heat capacity at constant volume, Debye temperature, Gruneisen parameter and thermal expansion coefficient within the temperature and pressure range of 0 to 1000 K and 0 to 24 GPa, respectively have also been estimated. For the first time, d‐group elements constitute full Heusler alloy, Mn2PtCo and its ground state structure found to be Cu2MnAl prototype. The alloy is ferromagnetic (FM) with high magnetic moment value of 9 μB. Heusler alloys are best candidates for device fabrication; therefore, Mn2PtCo is investigated to calculate various thermodynamic parameters like entropy, heat capacity at constant volume, Debye temperature, Gruneisen constant and thermal expansion coefficient under temperature and pressure. The alloy is found mechanically stable and elastically anisotropic, hard and brittle.
... In order to demonstrate their usage as multipurpose materials in various applications, many theoretical and experimental studies on Heusler alloys have been conducted [13][14][15][16][17][18][19][20][21][22][23][24][25][26]. However, there are few experimental and theoretical studies about Ir-based Heusler alloys [27][28][29][30][31][32][33][34]. ...
Article
The magnetic, electronic, elastic and vibrational properties of Ir2MnAl Heusler alloy are investigated with generalised gradient approximation (GGA) within the frame of Density Functional Theory (DFT). The ferromagnetic (FM) and non-magnetic (NM) states of Ir2MnAl Heusler alloy in Cu2MnAl and Hg2CuTi crystal structures have been compared. It is found that the ferromagnetic state in the Cu2MnAl structure is energetically more stable than other states. The obtained structural parameters are consistent with the current experimental and theoretical results. The spin-polarised electronic band structures of the material exhibit half-metallic behaviour with band gap in spin minority state from 0.382 eV at the Γ-X symmetry points, making it useful for spintronics applications. The calculated total magnetic moment of Ir2MnAl Heusler alloy is 4 μB which comply with the Slater- Pauling rule. Furthermore, the uniform strain has also been implemented to examine the magnetoelectronic and half-metallic properties of this alloy. As a result, the half-metallicity is preserved in lattice constants between 5.872 Åand 6.187 Å. The obtained negative formation energy indicates both energetic and thermodynamic stability of this alloy. Moreover, the computed elastic constants state that this material is mechanically stable since it fulfills the Born stability criteria. The calculated B/G ratio and Cauchy pressure imply that Ir2MnAl is a ductile material in nature. Additionally, the vibrational properties are studied and it is found that this material is dynamically stable since there is no negative frequency value in phonon dispersion curves.
Article
The Heusler compounds have been recognized not only for their applications in spintronic and memory devices but also for thermoelectric devices. In this paper, the electronic and thermoelectric properties of Mn2PtCo full-Heusler compound have been investigated by using the full-potential linearized augmented planewave method and the Boltzmann semi-classical Boltzmann transport theory, respectively. The Mn2PtCo was found stable in Cu2MnAl-prototype structure with ferromagnetic phase. The Mn2PtCo showed metallic character in both the spin channels using generalized gradient approximation. Further, thermoelectric properties like Seebeck coefficient, electrical conductivity, electronic thermal conductivity and power factor have been obtained within the specified temperature range (0–1000 K). The value of power factor was calculated to be 5.90 × 1011 WK−2m−1s−1 at 1000 K.
Article
Full-text available
The aim of this work was to study by means of the full potential linear muffin-tin orbital (FP-LMTO) method within GGA and GGA+U approach the various physical properties of the NbCoSn and NbFeSb half-Heusler (HH) compounds. The equilibrium ground states properties were calculated and compared with available experimental and theoretical data. The elastic constants have been calculated, and revealed that our compounds are mechanically stable. The obtained elastic modulus divulged that our compounds are elastically anisotropic and categorizing them as brittle compounds. The GGA approach showed a semi-conductor nature. However, the GGA+U approach showed a significant improvement over other theoretical work. We remarked from the band structures that the two materials showed a p-type semiconductor, with relatively high power factors. Furthermore, the optical quantities are calculated and discussed in detail. Hence, by our findings, the studied compounds could be used for thermoelectric and optoelectronic applications.
Article
To meet energy demand, half-Heuslers (HH) are proved to be a cost-effective and energy-efficient choice for advanced spintronic and energy storage applications. The structural, electronic, magnetic, vibrational, elastic, thermodynamic and thermoelectric properties of the innovative HH CrVZ (where Z = S, Se, & Te) alloys are studied by using density functional theory (DFT). All materials are found to be magnetically active with 100% spin polarization where partially filled 3d-orbitals of Cr confirm the major contribution to the magnetic moment. The ferromagnetic (FM) state is observed to be the most energetically stable state among the non-magnetic (NM) and antiferromagnetic (AFM) states for all the HH CrVZ alloys with their optimized lattice parameters ranging from 5.47 Å to 6.00 Å. The HH CrVSe alloy is found to have the lowest direct bandgap (EBG) of 1.07 eV with a comparatively highest half-metallic gap (EHM) of 0.44 eV, due to the d-d hybridization. Our calculated cohesive (EC) and formation (Ef) energies indicate the chemical and thermodynamic stability of the studied HH CrVZ alloys. The phonon dispersion curves for the HH CrVSe and CrVTe alloys show that they are vibrationally stable while HH CrVS alloy shows soft modes with imaginary frequency due to the small ionic size of the S-ion. The calculated Cauchy pressure, Pugh and Poisson ratio prove that all studied compounds are hard, elastically brittle, anisotropic, and mechanically stable. The temperature fluctuation for specific heat (CV), Entropy (S) and Free Energy (F) follows the Quasi-harmonic Debye model with expected Dulong-petit limit 75 J/mol/K. The thermoelectric investigations although shows the lower values of the Seebeck coefficient and power factor. Our investigated half-metallic HH CrVZ alloys can be the potential contenders for the spintronic applications.
Article
Full-text available
Previous calculations indicate that the CoVTe half-Heusler alloy appears half-metallic (HM) with spin polarization equal to 100%. We predict the spin polarisation and related alloy properties for the CoVTe (001), (111), and (110) surfaces and interface with a BeTe semiconductor. All the calculations were based on the generalized gradient approximation (GGA) with the Clb structure, using a first-principles investigation. We find a weak relaxation with (001) terminations, meaning the two terminations are stable and have stronger relaxations with the V (111) surface. The (001) V–Te surface has half-metallicity (HM) preserved with the HM energy gap of 0.22 eV and full spin polarisation, so the surface is useful for applications in the field of spintronics when using thin films, while other surfaces showed a high spin polarisation with values of 85–96%. For The CoVTe/BeTe interface demonstrates a weak relaxation for both structures. For VTe–Te*, the HM is destroyed and the minority spin is close to the Fermi level, with a higher spin polarization equal to 93%. The VTe–Be configuration retains HM, suggesting it is a good candidate for spintronic applications. The values of the magnetic moment for the surface and interface are calculated because these values may change when used as a thin film.
Article
The electrical resistivity ρ(T) of the band ferromagnets Co2FeZ (where Z = Al, Si, Ga, Ge, In, Sn, and Sb are s- and p-elements of Mendeleev’s Periodic Table) has been investigated in the temperature range 4.2 K < T < 1100 K. It has been shown that the dependences ρ(T) of these alloys in a magnetically ordered state at temperatures T < TC are predominantly determined by the specific features of the electronic spectrum in the vicinity of the Fermi level. The processes of charge carrier scattering affect the behavior of the electrical resistivity ρ(T) only in the vicinity of the Curie temperature TC and above, as well as in the low-temperature range (at T ≪ TC).
Article
Full-text available
Investigation of the structural, electronic and magnetic properties of full-Heusler Co2VIn as well as half-Heusler CoVIn Cobalt based Heusler compounds using density functional theory (DFT) leads to the general conclusion that Co2VIn and CoVIn are half-metallic materials with a gap at the Fermi level in the minority states and majority states respectively. A Hubbard-like Coulomb correlation term U has been included in the DFT (DFT+U) for the computation of the electronic and magnetic properties of the compounds. The structural properties have been calculated for the paramagnetic and ferromagnetic phases, and both Co2VIn and CoVIn are found to be stable in the ferromagnetic phase. The calculated magnetic moments are 2 μB and 0.9 μB per formula unit for Co2VIn and CoVIn respectively.
Article
Full-text available
In this paper, we perform a systematic {\it ab initio} study of two principal spin-related phenomena, namely, anomalous Hall effect and current spin polarization, in Co$_2$Fe-based Heusler compounds Co$_2$FeX (X = Al, Ga, In, Si, Ge, Sn) within the generalized gradient approximation (GGA). The accurate full-potential linearized augmented plane-wave method is used. We find that the spin-polarization of the longitudinal current ($P^L$) in Co$_2$FeX (X = Al, Ga, In, Al$_{0.5}$Si$_{0.5}$ and Sn) is $\sim$100 \% even though that of the electronic states at the Fermi level ($P^D$) is not. Further, the other compounds also have a high current spin polarization with $P^L > 85$ \%. This indicates that all the Co$_2$FeX compounds considered are promising for spin-transport devices. Interestingly, $P^D$ is negative in Co$_2$FeX (X = Si, Ge and Sn), differing in sign from the $P^L$ as well as that from the transport experiments. Secondly, the calculated anomalous Hall conductivities (AHCs) are moderate, being within 200 S/cm, and agree well with the available experiments on highly L2$_1$ ordered Co$_2$FeSi specimen although they differ significantly from the reported experiments on other compounds where the B2 antisite disorders were present. Surprisingly, the AHC in Co$_2$FeSi decreases and then changes sign when Si is replaced by Ge and finally by Sn. Third, the calculated total magnetic moments agree well with the corresponding experimental ones in all the studied compounds except Co$_2$FeSi where a difference of 0.3 $\mu_B$/f.u. exists. We also perform the GGA plus on-site Coulomb interaction $U$ calculations in the GGA+$U$ scheme. We find that including the $U$ affects the calculated total magnetic moment, spin polarization and AHC significantly, and in most cases, results in a disagreement with the available experimental results.
Article
Full-text available
Using the full-potential screened Korringa-Kohn-Rostoker method we study the full-Heusler alloys based on Co, Fe, Rh, and Ru. We show that many of these compounds show a half-metallic behavior; however, in contrast to the half-Heusler alloys the energy gap in the minority band is extremely small due to states localized only at the Co (Fe, Rh, or Ru) sites which are not present in the half-Heusler compounds. The full-Heusler alloys show a Slater-Pauling behavior and the total spin magnetic moment per unit cell (Mt) scales with the total number of valence electrons (Zt) following the rule Mt=Zt-24. We explain why the spin-down band contains exactly 12 electrons using arguments based on group theory and show that this rule holds also for compounds with less than 24 valence electrons. Finally we discuss the deviations from this rule and the differences compared to the half-Heusler alloys.
Article
Full-text available
The electronic and magnetic properties of Co2CrSi is calculated by using full-potential linearized augmented plane wave (FP–LAPW) method based on density functional theory (DFT). Density of states (DOS), magnetic moment and band structures of the system are presented. For the exchange and correlation energy, local spin density approximation (LSDA+U) with the inclusion of Hubbard potential U is used. Our calculation shows indirect bandgap of 0·91 eV in the minority channel of DOS. This is supported by band structures and hence favoured the half metallic ferromagnetic (HMF) nature of the system. The effective magnetic moment of 4·006 μB also supported our conclusion with a near integral value. The DOS of Co and Cr were found to hybridize and was also responsible for the ferromagnetic nature of the system.
Article
Full-text available
A qualitative approach using room-temperature confocal microscopy is employed to investigate the spatial distribution of shallow and deep oxygen vacancy (Vo) concentrations on the polar (0001) and non-polar (10ī0) surfaces of zinc oxide (ZnO) nanowires (NWs). Using the spectral intensity variation of the confocal photoluminescence of the green emission at different spatial locations on the surface, the Vo concentrations of an individual ZnO NW can be obtained. The green emission at different spatial locations on the ZnO NW polar (0001) and non-polar (10ī0) surfaces is found to have maximum intensity near the NW edges, decreasing to a minimum near the NW center. First-principles calculations using simple supercell-slab (SS) models are employed to approximate/model the defects on the ZnO NW (10ī0) and (0001) surfaces. These calculations give increased insight into the physical mechanism behind the green emission spectral intensity and the characteristics of an individual ZnO NW. The highly accurate density functional theory (DFT)-based full-potential linearized augmented plane-wave plus local orbitals (FP-LAPW + lo) method is used to compute the defect formation energy (DFE) of the SSs. Previously, using these SS models, it was demonstrated through the FP-LAPW + lo method that in the presence of oxygen vacancies at the (0001) surface, the phase transformation of the SSs in the graphite-like structure to the wurtzite lattice structure will occur even if the thickness of the graphite-like SSs are equal to or less than 4 atomic graphite-like layers [Wong et al., J. Appl. Phys. 113, 014304 (2013)]. The spatial profile of the neutral Vo DFEs from the DFT calculations along the ZnO [0001] and [10ī0] directions is found to reasonably explain the spatial profile of the measured confocal luminescence intensity on these surfaces, leading to the conclusion that the green emission spectra of the NWs likely originate from neutral oxygen vacancies. Another significant result is that the variation in the calculated DFE along the ZnO [0001] and [10ī0] directions shows different behaviors owing to the non-polar and polar nature of these SSs. These results are important for tuning and understanding the variations in the optical response of ZnO NW-based devices in different geometric configurations.
Article
Full-text available
We present the study of half metallacity of Co2MnAl as half-Heusler alloy in L21 structure which consists of four inter-penetrating fcc sub-lattices. Density functional theory based electronic structure calculations will be performed by using the full-potential linear augmented plane wave (FP-LAPW). We will use the general gradient approximation method (GGA) and local density approximation method called LDA+U. Density of states and band structure results will be presented in this paper.
Article
A superconducting point contact is used to determine the spin polarization at the Fermi energy of several metals. Because the process of supercurrent conversion at a superconductor-metal interface (Andreev reflection) is limited by the minority spin population near the Fermi surface, the differential conductance of the point contact can reveal the spin polarization of the metal. This technique has been applied to a variety of metals where the spin polarization ranges from 35 to 90 percent: Ni0.8Fe0.2, Ni, Co, Fe, NiMnSb, La0.7Sr0.3MnO3, and CrO2.
Article
We have studied the electron structure and magnetic properties of Heusler phase Co2YBi and half-Heusler phase CoYBi (Y=Mn, Cr) by using the full-potential linearized-augmented plane-wave (FLAPW) method. Co2MnBi and Co2CrBi are predicted to be half-metallic magnetism with a total magnetic moment of 6 and 5 μB, respectively, well consistent with the Slater–Pauling rule. We also predict CoMnBi to be half-metallic magnetism with a slight compression. The gap origin for Co2MnBi and Co2CrBi is due to the 3d electron splitting of Mn (Cr) and Co atoms, and the gap width depends on Co electron splitting. The atom coordination surroundings have a great influence on the electron structure, and consequently the Y site in the X2YZ structure has a more remarkable electron splitting than the X site due to the more symmetric surroundings. The investigation regarding the lattice constant dependence of magnetic moment shows that the Co magnetic moment exhibits an opposite behavior with the change of the lattice constant for Heusler and half-Heusler alloys, consequently leading to the different variation trends for total magnetic moment. The variation of total and atom magnetic moment versus lattice constant can be explained by the extent of 3d electron splitting and localization of Mn (Cr) and Co atoms for both the series of alloys.
Article
This paper deals with the ground state of an interacting electron gas in an external potential v(r). It is proved that there exists a universal functional of the density, Fn(r), independent of v(r), such that the expression Ev(r)n(r)dr+Fn(r) has as its minimum value the correct ground-state energy associated with v(r). The functional Fn(r) is then discussed for two situations: (1) n(r)=n0+n(r), n/n01, and (2) n(r)= (r/r0) with arbitrary and r0. In both cases F can be expressed entirely in terms of the correlation energy and linear and higher order electronic polarizabilities of a uniform electron gas. This approach also sheds some light on generalized Thomas-Fermi methods and their limitations. Some new extensions of these methods are presented.
Article
Effect of annealing on the magnetocaloric effect (MCE) of half-Heusler CoMnSb alloy has been investigated in a low magnetic field by comparing two samples. They were annealed at a lower temperature of 873K and a higher temperature of 1323K, referred as samples A and B, respectively. The maximum value of magnetic entropy change of 2.1J/(kgK) for the sample A is larger than that of 1.0J/(kgK) for the sample B. However, a wider working temperature span and a larger refrigerant capacity were obtained in the sample B, indicating that the sample annealed at a higher temperature is superior to the one annealed at a lower temperature in practical application as a refrigeration material.