First-principle calculations of structural, electronic and magnetic investigations of Mn 2 RuGe 1-x Sn x quaternary Heusler alloys

Abstract

First-principles calculations were used to calculate the structural, electronic and half-metallic ferromagnetism of Mn2RuGe1-xSnx (x=0, 0.25, 0.50, 0.75, 1) Heusler alloys. The Hg2CuTi-type structure is found to be energetic more than Cu2MnAl-type structure for both Mn2RuGe and Mn2RuSn compounds. The calculated lattice constants for Mn2RuGe and Mn2RuSn are 5.91 Å and 6.17 Å, respectively. The electronic band structures and density of states of Mn2RuGe show a half metallic character with total magnetic moments, 2 μB per formula unit that are in good agreement with Slater-Pauling rule with indirect band gap, 0.31 eV along the direction Γ –X. It is observed that the total magnetic moment per cell increases as Sn concentration increases in the Heusler alloys.

Full text

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Chinese Journal of Physics
journal homepage: www.elsevier.com/locate/cjph
First-principle calculations of structural, electronic and magnetic
investigations of Mn
2
RuGe
1-x
Sn
x
quaternary Heusler alloys
F. Semari
a
, F. Dahmane
a,b
, N. Baki
c
, Y. Al-Douri
d,e,⁎
, S. Akbudak
f
,G.Uğur
g
,Ş.Uğur
g
,
A. Bouhemadou
h
, R. Khenata
a
, C.H. Voon
i
a
Laboratoire de Physique Quantique et de Modélisation Mathématique (LPQ3M), Département deTechnologie, Université de Mascara, 29000
Mascara, Algeria
b
Département de SM, Institue des Sciences et des Technologies, Centre Universitaire de Tissemsilt, Tissemsilt 38000, Algeria
c
Laboratoire d’Étude des Matériaux & Instrumentations Optiques, Département Matériaux & Développement Durable, Faculté des Sciences Exactes,
Université Djillali Liabès de Sidi Bel Abbès 22000, Algeria
d
Nanotechnology and Catalysis Research Center (NANOCAT), University of Malaya, 50603 Kuala Lumpur, Malaysia
e
Physics Department, Faculty of Science, University of Sidi-Bel-Abbes, 22000, Algeria
f
Department of Physics, Faculty of Arts and Sciences, Adiyaman University, 02100 Adiyaman, Turkey
g
Department of Physics, Faculty of Science, Gazi University, 06500 Ankara, Turkey
h
Laboratory for Developing New Materials and their Characterization, Department of Physics, Faculty of Science, University of Setif 1, 19000 Setif,
Algeria
i
Institute of Nano Electronic Engineering, University Malaysia Perlis, Kangar, 01000 Perlis, Malaysia
ARTICLE INFO
Keywords:
First-principle calculations
Electronic structure
Heusler alloy
Half-metallic
ABSTRACT
First-principles calculations were used to calculate the structural, electronic and half-metallic
ferromagnetism of Mn
2
RuGe
1-x
Sn
x
(x = 0, 0.25, 0.50, 0.75, 1) Heusler alloys. The Hg
2
CuTi-type
structure is found to be energetic more than Cu
2
MnAl-type structure for both Mn
2
RuGe and
Mn
2
RuSn compounds. The calculated lattice constants for Mn
2
RuGe and Mn
2
RuSn are 5.91 Å and
6.17 Å, respectively. The electronic band structures and density of states of Mn
2
RuGe show a half
metallic character with total magnetic moments, 2 μ
B
per formula unit that are in good agree-
ment with Slater-Pauling rule with indirect band gap, 0.31 eV along the direction Γ–X. It is
observed that the total magnetic moment per cell increases as Sn concentration increases in the
Heusler alloys.
1. Introduction
Heusler alloys show unusual strong ferromagnetism and very important due to their interesting and diverse magnetic properties
[1,2]. Especially, X
2
YZ type Heusler alloy has attracted great attention that is attributed to their exclusive transport and magnetic
properties [3]. These alloys have essential role for spintronic applications because of their half-metallicity [4]. Half metals are
described by metallic electronic having 100% spin polarization at Fermi level (EF). This half-metallicity (HM) is one of the key
ingredients for realization of spintronics as it is known to maximize the spin-injection rate of spin-polarized carriers into semi-
conductors [5]. Based on the band structure calculations of NiMnSb and PtMnSb heusler alloys, Groot et al. [6] have introduced the
concept of half-metallic ferrmagnets. Up to now, many theoretical and experimental studies including heusler compounds [7–10] and
diluted magnetic semiconductors [11–14] were carried out to explain the half-metallic properties.
https://doi.org/10.1016/j.cjph.2018.01.015
Received 24 December 2017; Received in revised form 22 January 2018; Accepted 28 January 2018
⁎
Corresponding author at: Nanotechnology and Catalysis Research Center (NANOCAT), University of Malaya, 50603 Kuala Lumpur, Malaysia.
E-mail addresses: yaldouri@yahoo.com,yarub@um.edu.my (Y. Al-Douri).
Chinese Journal of Physics 56 (2018) 567–573
Available online 02 February 2018
0577-9073/ © 2018 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.
T

Among Mn
2
YZ type heusler alloys, Mn
2
VAl has been studied experimentally and theoretically [15–17], and proposed as HMF.
Later, studies including Mn
2
VZ (Z = Al, Ga, In, Si, Ge, Sn) [18],Mn
2
CuMg [19],Mn
2
CuGe [20],Mn
2
FeB, Mn
2
CoB, Mn
2
NiB [21],
Mn
2
Si
1-x
Ge
x
[22],Mn
2
ZrSi and Mn
2
ZrGe [23],Mn
2
CuSi and Mn
2
ZnSi [24] alloys were obtained from band structure calculations.
In the present work, Mn
2
RuGe
1-x
Sn
x
with concentrations x =0.25, 0.5, 0.75 and 1 is studied. As far as we know, there is no study
about half-metallicity obtained for x = 0.25,x = 0.50 and x = 0.75. So, it is very essential to investigate the structural, electronic,
magnetic properties and half-metallic behaviour of Mn
2
RuGe
1-x
Sn
x
. Organization of this paper is as follows: Section 2 presents
computational method, Section 3 is devoted to results and discussions and finally Section 4 summaries the results.
2. Calculations method
Structural, electronic and magnetic properties of Sn doped Mn
2
RuGe were studied at different concentrations, x = 0.25, 0.5,
0.75,1 using first-principles calculations. For all calculations, full-potential linearized augmented plane-wave (FP-LAPW) method
implemented in the WIEN2K package was used [25,26]. For the exchange correlation potential, the generalized gradient approx-
imation functional proposed by Wu and Cohen (GGA-WC) [27] was used. A cutoffof K
max
= 8.0/R
MT
was used where R
MT
is the
average radius of muffin-tin spheres and K
max
is the largest K vector in the plane wave. The maximum partial wave value inside the
atomic sphere was set as l
max
= 10. The charge density was expanded to G
max
= 14 (a.u.)
−1
using Fourier expansion where G
max
is
the largest vector in the Fourier expansion. A mesh of 64 special k-points was chosen along the Brillouin zone. The cut offenergy was
set to −6 Ry. The MT radii (R
MT
) used in our calculations are for Mn
2
RuGe; R
MT
(Mn) = R
MT
(Ru) = 2.38 Bohr, R
MT
(Ge) = 2.24 Bohr,
and for Mn
2
RuSn; R
MT
(Mn) = R
MT
(Ru) = 2.48 Bohr, R
MT
(Sn )= 2.33 Bohr. Ground state properties were determined from Murna-
ghan's equation of state [28].
=+
′′
−⎡
⎣
⎢⎛
⎝−⎞
⎠+⎛
⎝⎞
⎠−
⎤
⎦
⎥
′
VBV
BB BV
V
V
V
E
E( ) (1)
100
1
B
0(1)
where E
0
is the minimum energy at T = 0 K, Bis the bulk modulus, B’is the derivative of bulk modulus and V
0
is the equilibrium
volume. To simulate Mn
2
RuGe
1-x
Sn
x
(x = 0.25, 0.50, 0.75), supercell with 16 atoms from the most stable structure have been created.
For x = 0.25, we replace one Ge atom by one Sn atom, for x = 0.50 we replece two Ge atoms by two Sn atoms, and lastly for
x = 0.75, we replace three Ge atoms by three Sn atoms.
3. Results and discussion
The Heusler alloys have different orientations depending on the positions of atoms. Full-Heusler alloys have X-Y-X-Z (Cu
2
MnAl
type structure) atomic sequence and inverse Heusler alloys have X-X-Y-Z (Hg
2
CuTi type structure) atomic orientations. The four
unique crystal sites are A (0, 0, 0), B (0.25, 0.25, 0.25), C (0.50, 0.50, 0.50) and D (0.75, 0.75, 0.75). Generally, the X and Y atoms in
the atomic sequence are chosen from transition metals, while Z atom is selected from sp-elements. Ground state properties such as
equilibrium volume, lattice constant and total energy of Mn
2
RuGe and Mn
2
RuSn compounds are determined from the diagram of
change in energy as a function of volume which is plotted through fitting Murnaghan equation of state [28].
Ahmadian et al. [29] have claimed that, in case, Y has higher atom number than of X atom which is in the same period, an inverse
Heusler structure (F43m, space group no. 216) is observed. In Hg
2
CuTi-type full-Heusler alloy, X atoms occupy A (0, 0, 0) and B
(0.25, 0.25, 0.25) sites, and Y atom occupies C (0.5, 0.5, 0.5) site, and Z atom occupies D (0.75, 0.75, 0.75) site in Wyckoffco-
ordinates. In Hg
2
CuTi-type structure, the X atoms entering sites A and B that are denoted as X (1) and X (2), respectively. Y (Ru) atom
in Mn
2
RuGe compound has higher atomic number, 44 than X (Mn) atom in Mn
2
RuSn compound, 25. Yang et al. [30] have asserted
that the ideal ordered structure of Mn
2
RuGe and Mn
2
RuGa Heusler alloys should include the occupation of two Mn atoms at 4a (0, 0,
0) and 4c (1/4, 1/4, 1/4) Wyckoff-positions, Ru and Ge or Ga atoms locate at 4b (1/2, 1/2, 1/2) and 4d (3/4, 3/4, 3/4) positions,
respectively. According to the previous studies related to Mn
2
VZ and Mn
2
CrZ [31,32], Mn atoms occupy preferentially (A, C) sites in
contrast to the majority of Heusler alloys. And these studies show that Mn atom usually occupies the B site. Energy–Volume (E–V)
curve of Mn
2
RuGe and Mn
2
RuSn in ferromagnetic phase is shown in Fig. 1. The equilibrium volumes of unit cells are 347.9304 and
395.6775 (Bohr)
3
and the calculated lattice constants are 5.91 Å and 6.17 Å for Mn
2
RuGe and Mn
2
RuSn compounds, respectively.
The equilibrium structural parameters such as lattice parameter (a) and bulk modulus (B) are listed in Table 1. To best of our
knowledge, there is no available study in the literature about Mn
2
RuGe
1-x
Sn
x
(x = 0, 0.25, 0.75)
.
Because of this reason, we predict
the lattice parameters by Vegard's law as shown in Eq. (2):
=×+×=
=×+×=
=×+×=
Mn RuGe Sn : a(Å) 5.91 0.75 6.17 0.25 5.975
Mn RuGe Sn : a(Å) 5.91 0.5 6.17 0.5 6.04
Mn RuGe Sn : a(Å) 5.91 0.25 6.17 0.55 6.105
2 0.75 0.25
20.50.5
2 0.25 0.75 (2)
Energy bands of Mn
2
RuGe and Mn
2
RuSn with the most stable structure Hg
2
CuTi along high-symmetry directions in the Brillouin
zone are presented in Fig. 2.InMn
2
RuGe, the minority-spin bands have an indirect band gap, 0.31 eV along the direction Γ–X which
leads to 100% spin polarization at E
F
, whereas the majority-spin bands illustrate an intersection between valence and conduction
bands at the Fermi level, indicating a metallic nature of majority-spin channel. So, Mn
2
RuGe shows a half-metallic behavior at
equilibrium state. For Mn
2
RuSn, it is apparent from Fig. 3 that the structure has metallic intersections at the Fermi level in the spin up
F. Semari et al. Chinese Journal of Physics 56 (2018) 567–573
568

and spin down states, indicating a strong metallic nature for both the majority and minority-spin channel.
Qi et al. [34] have showed that, in Mn
2
FeAs full-Heusler alloy, there is an overlap between valence and conduction bands the
spin-up band structure, and Fermi level goes through overlapping regions leading to the spin-up channel showing metallic character.
In contrast to spin-up channel, a semiconducting band gap around the Fermi level is observed in the spin-down band structure having
a direct energy gap, 0.46 eV in the spin-down channel. In the study case related to Mn
2
CuMg [35], there is a real gap in the spin-down
states for the full-Heusler alloy, and the width of band gap is 0.53 eV. The Fermi level just falls within the gap in the spin-down band
indicating semiconductor properties, which keeps a perfect 100% spin polarization of conduction electrons at the Fermi level. The
local density of state (LDOS) and total density of state (TDOS) of the herein interested material are presented in Fig. 3 to clarify the
nature of the band structure.
It is very important to give an extra attention to the origin of the band gap which shows a representative character for the half-
metallic Heusler alloys. The source of band gap can be mainly divided into three categories: (1) covalent band gap, (2) d–d band gap,
and (3) charge transfer band gap [36]. The covalent band gap has been found to be in half-Heusler alloys with C
1b
structure, such as
NiMnSb [37]. The d–d band gap is responsible for the half-metallic quality of the full-Heusler alloys with L
21
structure. Usually, the
origin of band gap in the Heusler alloy is always ascribed to the covalence hybridization between the lower-energy d states of the
high-valence transition metal atom and the higher-energy d states of the low-valence transition metal atom [38].
The total density of states and the spin-polarized band structure along high-symmetry directions of the first Brillouin zone (spin
up, spin dn) for Mn
2
Ru
1-x
Ge
x
(x =0.25, 0.50, 0.75) are presented in Fig. 4. The Fermi level is placed to 0.0eV. For all alloys, the spin
up is metallic, whereas the minority spin band included an energy gap not at the Fermi level (E
F
), which is semiconducting character.
This shows that Mn
2
Ru
1-x
Ge
x
Sn (x = 0.25, 0.50, 0.75) are half metals (HM) of type III with energy gap, 0.289 eV, 0.134 eV and
0.110 eV for x = 0.25, 0.50, and 0.75, respectively.
Slater and Pauling [39,40] have observed that the magnetic moment “m”of 3d elements and their binary alloys can be
Fig. 1. Total energy as a function of unit cell volume for Mn
2
RuGe and Mn
2
RuSn with Hg
2
CuTi and Cu
2
MnAl.
Table 1
Calculated lattice constant a (Å), bulk modulus B (GPa) for Mn
2
RuGe
1-x
Sn
x
.
Compound Structure a (Å) B (GPa)
Mn
2
RuGe Hg
2
CuTi 5.91 168.6772
5.92 [30]
Cu
2
MnAl 6.08 134.7154
Mn
2
RuSn Hg
2
CuTi 6.17 223.6790
6.15 [33]
Cu
2
MnAl 6.30 146.1184
Mn
2
RuGe
0.75
Sn
0.25
5.98 783.2711
Mn
2
RuGe
0.50
Sn
0.50
6.04 632.0719
Mn
2
RuGe
0.25
Sn
0.75
6.15 551.4391
F. Semari et al. Chinese Journal of Physics 56 (2018) 567–573
569

determined according to average valence electron number (n
V
) per atom [39,40,41].Table 2 illustrates the calculated total atom-
resolved magnetic moments contribution of interstitial regions in the unit cell (interstitial moments) for Mn
2
RuGe
1-x
Sn
x
. The
Mn
2
RuGe Heusler alloy has 26 valence electrons per unit cell ( = × ++=n(72)8426
V), so =−=mμ26 24 2
B
. For Mn
2
RuSn, the
total magnetic moment is not integer, 6.93 and this confirms the metallic character of the alloy. We should keep in mind that Mn
atoms are responsible for the majority part of the total magnetic moment. This is due to big exchange splitting between the majority
and minority spin states of Mn atom and small magnetic moment on the interstitial region of Sn (Ge) atom.
The dissimilar local magnetic moments of two Mn atoms in the Mn
2
RuGe compounds with Hg
2
CuTi structure are consequence of
different atomic surroundings, i.e., Mn1 atom has four nearest Mn2 atoms and four nearest Ge atoms as well as six second nearest Ru
atoms, while Mn2 atom has four nearest Mn1 atoms and four nearest Ru atoms as well as six second nearest Ge atoms.
We can see that the total magnetic moment per cell increases with Sn concentration in Heusler alloys having values 2 μ
B
,8μ
B
/16
atoms, 20 μ
B
/16 atoms, 25 μ
B
/16 atoms and 6.93772 μ
B
for x = 0, 0.25, 0.50, 0.75, and 1 respectively.
4. Conclusions
First-principles calculations at FP-LAPW level within the generalized gradient approximation have been used to investigate the
electronic structure and magnetism of Heusler alloys. For both Mn
2
RuGe and Mn
2
RuSn compounds, the Hg
2
CuTi-type structure is
found to be energetic more than Cu
2
MnAl-type structure. The lattice constants are 5.91 Å and 6.17 Å for Mn
2
RuGe and Mn
2
RuSn
Fig. 2. The spin-polarized band structure of Mn
2
RuGe and Mn
2
RuSn.
F. Semari et al. Chinese Journal of Physics 56 (2018) 567–573
570

compounds, respectively. The density of states, electronic and band structures of Mn
2
RuGe exhibit half metallic character and have
total magnetic moments, 2.0 μ
B
which is in good agreement with Slater-Pauling. It is observed that the total magnetic moment per
cell increases as Sn concentration increases in Heusler alloys.
Fig. 3. Spin-polarized total and partial densities of state (DOS) of Mn
2
RuGe and Mn
2
RuSn.
F. Semari et al. Chinese Journal of Physics 56 (2018) 567–573
571

References
[1] S.K. Bose, J. Kudrnovský, Y. Liu, Structure and physical properties of quaternary Heusler alloy NiMnCuSb, J. Magn. Magn. Mater. 444 (2017) 338–343.
[2] O. Canko, F. Taşkın, M. Atiş, N. Kervan, S.K. Kervan, Magnetism and half-metallicity in the Fe2ZrP Heusler alloy, J. Supercond. Nov. Magn. 29 (2016)
2573–2578.
[3] N. Fukatani, H. Fujita, T. Miyawaki, K. Ueda, H. Asano, Structural and magnetic properties of antiferromagnetic Heusler Ru
2
MnGe Epitaxial thin films, J. Korean
Phys. Soc. 63 (2013) 711–715.
[4] T. Van Quang, J. Lee, M. Kim, Electronic structure and magneto-optical properties of Co
2
MnX alloys where X = Ge, Sn and Pb: a First-principles investigation in
the LDA+U approach, J. Korean Phys. Soc. 62 (2013) 2184–2187.
[5] M. Kim, J.I. Lee, Surface and correlation effect on the half-metallicity of the Co
2
FeSi Heusler alloy, J. Korean Phys. Soc. 60 (2012) 1068–1071.
[6] R.A. De Groot, F.M. Muller, P.G. van Engen, K.H.J. Buschow, New class of materials: half-metallic ferromagnets, Phys. Rev. Lett. 50 (1983) 2024–2027.
[7] M. Ameri, A. Touia, R. Khenata, Y. Al-Douri, H. Baltache, Structural and optoelectronic properties of NiTiX and CoVX (X = Sb and Sn) half-Heusler compounds:
an ab initio study, Optik 124 (2013) 570–574.
[8] A. Missoum, T. Seddik, G. Murtaza, R. Khenata, A. Bouhemadou, Y. Al-Douri, A. Abdiche, H. Meradji, H. Baltache, Ab initio study of the structural and
optoelectronic properties of the half-Heusler CoCr Z (Z =Al, Ga), Can. J. Phys. 92 (2014) 1105–1112.
[9] B. Abderrahim, M. Ameri, D. Bensaid, Y. Azaz, B. Doumi, Y. Al-Douri, F. Benzoudji, Half-metallic magnetism of quaternary Heusler compounds Co
2
Fe
x
Mn
1−x
Si
(x=0,0.5, and 1): first-principles calculations, J. Supercond. Novel Magn. 29 (2016) 277–283.
[10] D. Bensaid, T. Hellal, M. Ameri, Y. Azzaz, B. Doumi, Y. Al-Douri, B. Abderrahim, F. Benzoudji, First-principle investigation of structural, electronic and magnetic
properties in Mn
2
RhZ (Z = Si, Ge, and Sn) Heusler alloys, J. Supercond. Novel Magn. 29 (2016) 1843–1850.
[11] I.E. Yahiaoui, A. Lazreg, Z. Dridi, Y. Al-Douri, B. Bouhafs, Electronic and magnetic properties of Co
2
CrGa
1-x
Si
x
Heusler alloys, J. Supercond. Novel Magn. 30
(2017) 421–424.
[12] B. Fadila, M. Ameri, D. Bensaid, M. Noureddine, I. Ameri, S. Mesbah, Y. Al-Douri, Structural, magnetic, electronic and mechanical properties of full-Heusler
alloys Co
2
YAl (Y= Fe, Ti): first principles calculations with different exchange-correlation potentials, J. Magn. Magn. Mater. 448 (2018) 208–220.
[13] F. Dahmane, A. Tadjer, B. Doumi, D. Mesri, H. Aourag, A. Sayede, First principles study of the electronic structures and magnetic properties of transition metal-
doped cubic indium nitride, Mater. Sci. Semicond. Process. 21 (2014) 66–73.
[14] F. Dahmane, A. Tadjer, B. Doumi, H. Aourag, First-principle calculations of structural, electronic, and magnetic properties of cubic Al
1−x
TM
x
N (TM = V, Cr, Mn,
Fe), J. Supercond. Nov. Magn. 27 (2014) 2647–2654.
[15] Hongzhi Luo, Zhiyong Zhu, Guodong Liu, Shifeng Xu, Guangheng Wu, Heyan Liu, Jingping Qu, Yangxian Li, Prediction of half-metallic properties for the Heusler
Fig. 4. Density of state of Mn
2
Ru
1-x
Ge
x
(x = 0.25, 0.50, 0.75).
Table 2
The total and partial magnetic moments of Mn
2
RuGe
1-x
Sn
x
.
Compound M
Mn1
M
Mn2
M
Ru
M
Ge
M
Sn
M
interstitial
M
tot
Mn
2
RuGe Hg
2
CuTi −1.3343 3.0872 0.14280 0.03805 –0.06617 1.99988
2[30]
Cu
2
MnAl 3.2188 3.2188 0.91794 −0.0599 –0.11960 7.41528
Mn
2
RuSn Hg
2
CuTi 3.3522 3.3224 0.29105 –−0.05167 0.02364 6.93772
Cu
2
MnAl 3.3632 3.3632 0.98227 –−0.05106 0.06502 7.72263
Mn
2
RuGe
0.75
Sn
0.25
8.00328
Mn
2
RuGe
0.50
Sn
0.50
20.84920
Mn2RuGe
0.25
Sn
0.75
25.09392
F. Semari et al. Chinese Journal of Physics 56 (2018) 567–573
572

alloys Mn
2
CrZ (Z=Al, Ga, Si, Ge, Sb): a first-principles study, J. Magn. Magn. Mater. 320 (2008) 421–428.
[16] S. Ishida, S. Asano, J. Ishida, Bandstructures and hyperfine fields of Heusler alloys, J. Phys. Soc. Japan 53 (1984) 2718–2725.
[17] H. Itoh, T. Nakamichi, Y. Yamaguchi, N. Kazama, Neutron diffraction study of Heusler type alloy Mn
0.47
V
0.28
Al
0.25
, Trans. Jpn. Inst. Met. 24 (1983) 265–271.
[18] K. Ozdogan, I. Galanakis, E. Sasioglu, B. Aktas, Search for half-metallic ferrimagnetism in V-based Heusler alloys Mn2VZ (Z = Al, Ga, In, Si, Ge, Sn), J. Phys.:
Condens.Matter 18 (2006) 2905–2914.
[19] X.-P. Wei, J.-B. Deng, S.-B. Chu, G.-Y. Mao, T. Lei, X.-R. Hu, Half-metallic ferrimagnetism in full-Heusler alloy Mn
2
CuMg, J. Magn. Magn. Mater. 323 (2011)
186–189.
[20] X.-P. Wei, X.-R. Hu, G.-Y. Mao, S.-B. Chu, T. Lei, L.-B. Hu, J.-B. Deng, Half-metallic ferrimagnetism in Mn
2
CuGe, J. Magn. Magn. Mater. 322 (2010) 3204–3207.
[21] M. Pugaczowa-Michalska, Theoretical prediction of ferrimagnetism in Mn
2
FeB, Mn
2
CoB and Mn
2
NiB, Intermetallics 24 (2012) 128–134.
[22] Y.J. Zhang, Z.H. Liu, G.D. Liu, X.Q. Ma, Half-metallic fully compensated ferrimagnetism in C1
b
-type half Heusler compounds Mn
2
Si
1−x
Ge
x
, J. Magn. Magn.
Mater. 387 (2015) 67–71.
[23] A. Abada, K. Amara, S. Hiadsi, B. Amrani, First principles study of a new half-metallic ferrimagnets Mn
2
-based full Heusler compounds: Mn
2
ZrSi and Mn
2
ZrGe, J.
Magn. Magn. Mater. 388 (2015) 59–67.
[24] I.H. Bhat, S. Yousuf, T.M. Bhat, D.C. Gupta, Investigation of electronic structure, magnetic and transport properties of half-metallic Mn
2
CuSi and Mn
2
ZnSi
Heusler alloys, J. Magn. Magn. Mater. 395 (2015) 81–88.
[25] W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. A 140 (1965) 1133–1138.
[26] P. Blaha, K. Schwarz, G.K.H Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented Plane Wave Plus Local Orbitals Program For Calculating Crystal Properties,
Vienna University of Technology, Vienna, 2001.
[27] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett 77 (1996) 3865–3868.
[28] F.D. Murnaghan, The compressibility of media under extreme pressures, Proc. Natl. Acad. Sci. USA 30 (1944) 5390–5399.
[29] F. Ahmadian, A. Salary, Half-metallicity in the Inverse Heusler compounds Sc
2
MnZ (Z = C, Si, Ge, and Sn), Intermetallics 46 (2014) 243–249.
[30] L. Yang, B. Liu, F. Meng, H. Liu, H. Luo, E. Liu, W. Wang, G. Wu, Magnetic properties of Heusler alloy Mn
2
RuGe and Mn
2
RuGa ribbons, J. Magn. Magn. Mater.
379 (2015) 1–5.
[31] H. Zenasni, H.I. Faraoun, C. Esling, First-principle prediction of half-metallic ferrimagnetism in Mn-based full-Heusler alloys with highly ordered structure, J.
Magn. Magn. Mater. 333 (2013) 162–168.
[32] H.Z. Luo, Z.Y. Zhu, G.D. Liu, S.F. Xu, G.H. Wu, H.Y. Liu, J.P. Qu, Y.X. Li, Prediction of half-metallic properties for the Heusler alloys Mn
2
CrZ (Z=Al, Ga, Si, Ge,
Sb): A first-principles study, J. Magn. Magn. Mater. 320 (2008) 421–428.
[33] L. Yang, B. Liu, H. Luo, F. Meng, H. Liu, E. Liu, W. Wang, G. Wu, Investigation of the site preference in Mn
2
RuSn using KKR-CPA-LDA calculation, J. Magn. Magn.
Mater. 382 (2015) 247–251.
[34] S. Qi, C.-H. Zhang, B. Chen, J. Shen, N. Chen, First-principles study on the ferrimagnetic half-metallic Mn
2
FeAs alloy, J. Solid State Chem. 225 (2015) 8–12.
[35] X.-P. Wei, J.-B. Deng, S.-B. Chu, G.-Y. Mao, T. Lei, X.-R. Hu, Half-metallic ferrimagnetism in Full-Heusler alloy Mn
2
CuMg, J. Magn. Magn. Mater. 323 (2011)
186–189.
[36] C.M. Fang, G.A. de Wijs, R.A. de Groot, Spin-polarization in half-metals, J. Appl. Phys. 91 (2002) 8340–8344.
[37] I. Galanakis, P.H. Dederichs, N. Papanikolaou, Origin and properties of the gap in the half-ferromagnetic Heusler alloys, Phys. Rev. B 66 (2002) 134428–134432.
[38] I. Galanakis, P.H. Dederichs, N. Papanikolaou, Slater-Pauling behavior and origin of the half-metallicity of the full-Heusler alloys, Phys. Rev. B 66 (2002)
174429–174437.
[39] L. Pauling, The Nature of the Interatomic Forces in Metals, Phs. Rev. 54 (1938) 899–904.
[40] J.C. Slater, The Ferromagnetism of Nickel II. Temperature Effects, Phys. Rev. 49 (1936) 931–937.
[41] K.H.J. Buschow, Handbook of Magnetic Materials, Elsevier publishing, Amsterdam, 2013.
F. Semari et al. Chinese Journal of Physics 56 (2018) 567–573
573