Half-metallicity of the inverse Heusler alloy Mn2CoAl(0 0 1) surface: A first-principles study

Applied Surface Science 283 (2013) 876–880

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Half-metallicity of the inverse Heusler alloy Mn2 CoAl(0 0 1) surface: A first-principles study Jincheng Li, Yingjiu Jin ∗ Department of Physics, College of Science, Yanbian University, Yanji, Jilin 133002, China

a r t i c l e

i n f o

Article history: Received 14 November 2012 Received in revised form 10 June 2013 Accepted 9 July 2013 Available online 18 July 2013 Keywords: Half-metallicity Heusler alloy Electronic structure First-principles calculation

a b s t r a c t Half-metals exhibit 100% spin polarization at the Fermi level. Thus, they are promising magnetic electrode candidates in spintronics. We investigated the electronic structures, magnetism, and half-metallicity of the inverse Heusler alloy Mn2 CoAl(0 0 1) surface by the all-electron full-potential linearized augmented plane-wave method within the generalized gradient approximation. Two types of surface terminations were considered, namely, the AlMn terminated (AlMn-term) and CoMn terminated (CoMn-term) surfaces. From the calculated layer-projected density of states, we found that the half-metallicity was preserved on the surface of the AlMn-term. However, the width of the minority-spin gap was significantly reduced because of the surface states located just above the Fermi level. By contrast, the CoMn-term lost its half-metallicity because of the strong surface potential effect on the surface Co atom. The magnetic moments of Mn atoms on the surfaces of both terminations are considerably increased compared with those in the deep inner layers, while that of the surface Co atom on the CoMn-term is slightly increased. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Spintronic devices require an efficient spin injection from a magnetic electrode into a semiconductor [1]. Half-metals, which have 100% spin polarization at the Fermi level (EF ), are thus expected to be ideal magnetic electrode candidates [2]. Numerous materials have been predicted to be half-metals based on first-principles studies [3–5]. For some of these materials, high-spin polarizations have been experimentally measured [6–8]. Half-metallic Heusler alloys are of particular interest because of their high Curie temperature (higher than room temperature) and structures similar to zinc-blende semiconductors [9–11]. Heusler alloys can be classified into two main groups, namely, half-Heusler XYZ alloys and full-Heusler X2 YZ alloys. X and Y are transition metal elements, and Z is an sp element. Full-Heusler X2 YZ alloys generally have two types of structures. One is the Cu2 MnAl (L21 ) structure, which forms when the nuclear charge of X is higher than that of Y in the same period. The other is the Hg2 CuTi structure, which forms under the opposite condition [12,13]. The L21 structure belongs to the Fm3m space group. In this space group, X atoms are located at the A (0, 0, 0) and C ( 12 , 12 , 12 ) sites, whereas Y and Z atoms are located at the B ( 14 , 14 , 14 ) and D ( 34 , 34 , 34 ) sites in Wyckoff positions, respectively. Full-Heusler alloys with the Hg2 CuTi structure, also known as inverse Heusler alloys, have F43m symmetry. In this symmetry, X atoms are located at the A(0, 0, 0) and

∗ Corresponding author. Tel.: +86 4332732221; fax: +86 4332732596. E-mail addresses: [email protected], [email protected] (Y. Jin). 0169-4332/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apsusc.2013.07.036

B ( 14 , 14 , 14 ) sites, whereas Y and Z atoms are located at the C ( 12 , 1 1 , ) and D ( 34 , 34 , 34 ) sites in Wyckoff positions, respectively. A 2 2 half-Heusler XYZ alloy crystallizes in the C1b structure and has the same symmetry with the Hg2 CuTi structure. Over the last decade, theoretical and experimental studies have mainly focused on fullHeusler alloys with the L21 structure. However, recent studies have shown that numerous inverse Heusler alloys also belong to the family of half-metals [14–18]. Liu et al. [14] synthesized a Mn2 CoAl alloy by arc-melting and found that the alloy forms the Hg2 CuTi structure. First-principles studies suggest that Mn2 CoAl with the Hg2 CuTi structure has a half-metallic character and a high Curie temperature of 890 K [14–16]. The measured spin polarizations for some half-metals are much lower than the expected value of 100% [6,19], which can be ascribed to the atomic disorder or the surface effect [20,21]. Previous first-principles studies [22,23] have also predicted that Co2 MnSi, Co2 MnGe, and Co2 CrAl alloys with the L21 structure lose their half-metallicity at the (0 0 1) surfaces, except for the pure Mn terminated Co2 MnSi(0 0 1) surface where the half-metallicity preserved. Using the full-potential linearized augmented plane-wave (FLAPW) calculation, Jin et al. [24] showed that the TiSi terminated Co2 TiSi(0 0 1) surface retains the halfmetallicity. However, they did not consider the effect of surface relaxation. Recently, the half-metallicity of Mn2 CoSn(0 0 1) surfaces [25] and Ti2 CoAl(0 0 1) surfaces [26] was investigated by first-principles calculations. It is found that because of surface states, the (0 0 1) surfaces fail to preserve the half-metallicity which can be observed in the bulks. For practical applications, we have studied the electronic

J. Li, Y. Jin / Applied Surface Science 283 (2013) 876–880

and magnetic properties, as well as the half-metallicity of the inverse Heusler alloy Mn2 CoAl(0 0 1) surfaces. 2. Calculation method For the Mn2 CoAl(0 0 1) surface, two types of surface terminations were considered: the AlMn terminated (AlMn-term) and CoMn terminated (CoMn-term) surfaces. Both AlMn-term and CoMn-term are modeled by single slabs of 13 and 15 atomic layers, respectively (Fig. 1). The lattice constant was set to the experimental value of 5.84 A˚ [14]. The structures of the two systems were optimized by total energy and atomic force calculations [27]. The topmost two atomic layers were allowed to be relaxed, and the optimized structure was assumed when the atomic force on each atom ˚ The letters S, S − 1, and C denote the surbecame less than 0.02 eV/A. face, subsurface, and center layers, respectively. The Kohn–Sham equation [28] was self-consistently solved using the all-electron FLAPW [29] method as implemented in the FLEUR code [30] within the generalized gradient approximation (GGA) [31]. Lattice harmonics with ≤8 were used to expand the charge density, potential, and wave functions inside the muffin-tin radii of 1.16 A˚ for Mn and Co atoms, and 1.22 A˚ for Al atom. A plane wave cutoff of 14 Ry was used for the linearized augmented plane-wave basis, and a 210 Ry star-function cutoff was used to depict the charge density and potential in the interstitial region. Integrations inside the Brillouin zone (BZ) were performed by summation over a 12 × 12 k points inside the irreducible two-dimensional BZ. Self-consistency was assumed when the difference between input and output charge (spin) densities was less than 1.0 × 10−5 electrons/(a.u.)3 . 3. Results and discussions 3.1. Atomic displacement and surface energy ˚ with respect to the The calculated atomic displacements (in A) abruptly terminated positions of the AlMn-term and CoMn-term are given in Table 1. The + and − signs indicate upward and downward relaxation, respectively. The subscripts A and B on Mn atoms denote the A and B sites in the Hg2 CuTi structure. Both terminations

877

Table 1 ˚ with respect to the abruptly terminated Calculated atomic displacements (in A) positions for CoMn-term and AlMn-term. z denotes vertical bucking at the surface layers. CoMn-term

AlMn-term

Atom

Relaxation

Atom

Relaxation

MnA (S) Co(S) MnB (S − 1) Al(S − 1) z

0.14 −0.12 0.01 −0.02 0.26

MnB (S) Al(S) MnA (S − 1) Co(S − 1) z

−0.14 −0.16 −0.02 −0.04 0.02

exhibit the strongest relaxations on the topmost surface layers. The surface atoms undergo different displacements. For the CoMnterm, the surface MnA atom relaxes outward by 0.14 A˚ whereas ˚ establishing an overthe surface Co atom moves inward by 0.12 A, ˚ A large buckling is also found in the MnSi all buckling of 0.26 A. terminated surface of Co2 MnSi(0 0 1) [23]. As for AlMn-term, the ˚ respecsurface MnB and Al atoms relax inward by 0.14 and 0.16 A, ˚ This small value indicates tively, showing a small buckling of 0.02 A. smoothness of the AlMn terminated surface. On the other hand, the relaxations of subsurface layers for both terminations are relatively ˚ mild, showing small buckling values of ∼0.02 A. The structural stability of surfaces is determined by the surface energy (Es ), which can be calculated with the cleavage energy (Ec ) and the relaxation energy (Erel ) [32,33]. In our calculations the 13 layer AlMn- and 15 layer CoMn-terminated slabs represent together fourteen bulk unit cells. Thus, the Ec can be calculated as follows. Ec =

1 unrel unrel (AlMn) + Eslab (CoMn) − 14Ebulk ] [E 4 slab

(1)

unrel (AlMn) and E unrel (CoMn) are unrelaxed AlMn- and where Eslab slab CoMn-terminated slab energies, Ebulk is the total energy per unit cell of bulk Mn2 CoAl, respectively. The factor of 4 is the number of created surfaces during the cleavage of the alloy into both slabs. The Erel and Es defined as follows.

Erel (B) =

1 rel unrel [E (B) − Eslab (B)] 2 slab

(2)

Es = Ec + Erel (B)

(3)

rel (B) is a relaxed slab energy, B denotes AlMn- or CoMnwhere Eslab terminated slabs. The calculated cleavage, relaxation, and surface energies are presented in Table 2. With cleavage of the alloy along the [0 0 1] direction, both AlMn- and CoMn-terminated surfaces arise simultaneously and the cleavage energy distributes equally between created surfaces, therefore both surfaces have the same cleavage energies of 3.402 eV/surface cell. The Es of AlMn-term is 3.301 eV, slightly lower than that (3.304 eV) of CoMn-term. The small energy difference of the Es between AlMn- and CoMn-term implies that both surfaces are stable and energetically equally favorable. Due to there are no available data on the surface energy for Heusler alloys, we have compared the surface energy of Mn2 CoAl(0 0 1) with some elemental metals. The average surface energy of Mn2 CoAl(0 0 1) is 3.104 J/m2 , which is larger than that of the bcc Mn(0 0 1) [34], hcp Co(0 0 1) [35], and fcc Al(0 0 1) [36], the values are 1.60, 2.74 and 1.35 J/m2 , respectively. A high surface energy implies it does not

Table 2 Calculated cleavage, relaxation, and surface energies (in eV per surface cell).

Fig. 1. Schematic of different surface terminations, where (a) and (b) represent CoMn-term and AlMn-term, respectively. The arrows indicate the directions of atomic relaxations.

Energies

CoMn-term

AlMn-term

Ec Erel Es

3.402 −0.098 3.304

3.402 −0.101 3.301

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J. Li, Y. Jin / Applied Surface Science 283 (2013) 876–880

cleave easily, but rather fractures. It is worth mentioning that the above results are only applied when the surfaces are in a vacuum. When surfaces are in thermodynamic equilibrium with the bulk, the relative stability of surfaces with different stoichiometry can be analyzed by the surface free energy [23]. The surface free energy of Mn2 CoAl(0 0 1) will be discussed in another paper.

of surfaces originating from the surface potential [37,38]. On surfaces, the bulk negative electrostatic potential increases to match the vacuum zero potential level, which results in an overall shift in LDOS of the surface toward higher energies and substantially destroy the minority-spin gap. The LDOS of Mn at the surface, which exhibits strong band narrowing and large exchange splitting, has litter contributions to the minority-spin gap. To our knowledge, all Co terminated (0 0 1) surfaces for half- and full-Heusler alloys lose their half-metallicity because of a shift in the Co minority-spin states toward higher energies, which destroys the minority-spin band gap [22,37,38]. Several studies have indicated that the surface effect penetrates deeper into the slab when Co atoms are on the surface. In the case of AlMn-term (Fig. 2b), the LDOSs of Mn and Al at the surface layer show clear gaps in the minority-spin band, i.e., the half-metallicity persists for AlMn-term. Similar to the CoMn-term, the LDOS of Mn(S) also shows strong band narrowing and large exchange splitting. Meanwhile, the inward relaxation of Mn(S) decreases the Mn(S)–Co(S − 1) bond length, enhancing the hybridization between the Mn(S)–Co(S − 1) atoms, and then strongly suppressing the effect of surface potential on the Co(S − 1) atom. We found that the minority-spin gap was preserved in the Co(S − 1) atom. On the other hand, it was known that the appearance of surface states will kills the half-metallicity. We found that the localized surface states cross the EF before relaxation, while that shifts to a higher energy away from the EF after relaxation. Consequently, half-metallicity persists for AlMn-term, however, the width of the gap decreases with respect to that of the center layer by 0.08 eV because of the lower part of the minority conduction surface states. The surface states are seen to be decreased rapidly away from the surface. To elucidate the origin of the localized surface states, the surface plane (dx2 −y2 + dxy or px + py ) and out-of-plane

3.2. Electronic structure and half-metallicity The half-metallicity on the Mn2 CoAl(0 0 1) surface can be determined from the spin-polarized layer-projected density of states (LDOS). The LDOSs of (a) CoMn-term and (b) AlMn-term are presented in Fig. 2. The solid and dotted lines denote the relaxed and unrelaxed systems, respectively. The LDOSs of the minority-spin states are multiplied by −1 and the EF is set to zero. At the deep inner layers of both terminations, the overall shapes of LDOSs are consistent with the bulk results [14,15] and well reproduce the half-metallic character. The half-metallic band gap is known to originate from the t1u − eu splitting of d − d hybridizations between the Mn at an A site and the Co at a C site, although they are nextnearest-neighbor to each other [14–16]. In the minority-spin bands of the center layers for both terminations, the occupied t1u and unoccupied eu states are located at ∼−0.02 eV below and ∼0.15 eV above the EF , respectively, leading to a band gap with a width of about 0.17 eV. On the other hand, surface electronic structures generally differ significantly with respect to the bulk due to surface effects. A noticeable feature on the Mn2 CoAl(0 0 1) surfaces is that AlMn-term maintains its half-metallicity whereas CoMn-term dose not. For CoMn-term (Fig. 2a), the surface is no longer half-metallic because the minority-spin gap, which exists in the bulk, is filled up mainly by the Co d states. This phenomenon is known as an effect

(a) CoMn-term 3 2 1 0 -1 -2

MnA(S)

2 1 0 -1 -2

MnB(S±1)

2 1 0 -1 -2

MnA(S±2)

2 1 0 -1 -2

MnA(S±6)

2 1 0 -1 -2 -3

MnB(C)

(b) AlMn-term 3 2 1 0 -1 -2

Co(S)

relax unrelax Al(S±1)

0.5

0

DOS (states/eV-atom)

DOS (states/eV-atom)

3 2 1 0 -1 -2

-0.5

2 1 0 -1 -2

Co(S±2)

2 1 0 -1 -2

Co(S±6)

Al(C) 0.5

0 -0.5

-1 -8

-6

-4

-2

0

2

4

-8

-6

Energy (eV)

-4

-2

0

2

4

1 Al(S)

MnB(S)

0.5

0 relax unrelax

-0.5

2 1 0 -1 -2

MnA(S±1)

2 1 0 -1 -2

MnB(S±2)

2 1 0 -1 -2

MnA(S±5)

2 1 0 -1 -2 -3

MnB(C)

2 1 0 -1 -2

Co(S±1)

Al(S±2) 0.5

0 -0.5

2 1 0 -1 -2

Co(S±5)

Al(C) 0.5

0 -0.5

-1 -8

-6

-4

-2

0

2

4

-8

-6

-4

-2

0

2

4

Energy (eV)

Fig. 2. Spin-polarized layer-projected density of states in (a) CoMn-term and (b) AlMn-term. The LDOSs of minority-spin states are multiplied by −1, and the Fermi level is set to zero.

J. Li, Y. Jin / Applied Surface Science 283 (2013) 876–880

DOS (states/eV-atom)

(a) out of plane 3 2 1 0 -1 -2

(b) in plane 3 2 1 0 -1 -2

MnB(S) 8×Al(S)

MnA(S-1) Co(S-1)

2 1 0 -1 -2 -3 -6

-4

-2

0

879

MnB(S) 8×Al(S)

MnA(S-1) Co(S-1)

2 1 0 -1 -2 -3 2

4

-6

-4

Energy (eV)

-2

0

2

4

Fig. 3. Surface plane (dx2 −y2 + dxy or px + py ) and out-of-plane (dz2 + dzx + dyz or pz ) decomposed Mn-, Co-3d and Al-3p states at the surface and subsurface layers of AlMn-term. The density of states of Al-3p states are multiplied by 8 for clarity.

Table 3 Layer-by-layer magnetic moments (in B ) of atoms for CoMn-term and AlMn-term in relaxed geometries. The magnetic moments of atoms in the bulk are also listed for comparison. CoMn-term

AlMn-term

Bulk

Atom

M

Atom

M

Atom

M

MnA (S) Co(S) MnB (S − 1) Al(S − 1) MnA (S − 2) Co(S − 2) MnA (S − 6) Co(S − 6) MnB (C) Al(C)

−3.79 1.09 2.78 −0.03 −1.82 0.96 −1.82 1.04 2.81 −0.03

MnB (S) Al(S) MnA (S − 1) Co(S − 1) MnB (S − 2) Al(S − 2) MnA (S − 5) Co(S − 5) MnB (C) Al(C)

3.46 −0.01 −1.04 1.10 2.74 −0.04 −1.80 1.06 2.80 −0.03

MnA MnB Co Al Total

−1.81 (−1.98a , −1.59b ) 2.81 (3.08a , 2.69b ) 1.06 (0.92a , 0.94b ) −0.03 (−0.02a , −0.05b ) 2.00 (2.00a , 1.99b )

a and b denote the references of 14 and 16, respectively.

(dz2 + dzx + dyz or pz ) decomposed Mn-, Co-3d and Al-3p states at the surface and subsurface layers of AlMn-term are plotted in Fig. 3. The localized surface states, mainly Mn-(dz2 , dyz + dzx ) and Al-pz characters, originate from the surface-induced symmetry breaking. The symmetry of the bulk is reduced on the surface from tetrahedral Td to C2v , which further splits the double and triple d orbitals of Mn into (dz2 , dx2 −y2 ) and (dxy , dyz + dzx ) orbitals, respectively. Previous theoretical studies on Co2 MnSi(0 0 1) surfaces have suggested that the MnSi terminated surface loses its half-metallicity because of a single surface band, which is mostly derived from subsurface Co d states appearing at the EF . By contrast, a pure Mn terminated surface retains its half-metallicity [23,37]. The CrAl terminated surfaces of Co2 CrAl(0 0 1) [22] and Co2 Cr0.5 Fe0.5 Al(0 0 1) [39] are also reported not half-metallic but maintain high spin polarizations at the EF . 3.3. Magnetic moments The reduction of atomic coordination numbers on surfaces may weaken the hybridization which enhances the exchange splitting and band narrowing for surface atoms (Fig. 2). Consequently, the magnetic moments of the surface atoms are enhanced compared with the bulk values. This behavior can be observed in the layer-bylayer magnetic moments of atoms for both terminations (Table 3). For comparison, the magnetic moments of atoms in the bulk are also

listed. In the bulk phase, the calculated magnetic moments of both inequivalent Mn atoms in our case are larger by ∼0.2 B than those given by Meinert et al. [16], who used the spin-polarized relativistic Korringa–Kohn–Rostoker method. Meanwhile, our values are smaller by ∼0.2 B than those of Liu et al. [14], who used the FLAPW method. Nevertheless, the total magnetic moment and density of states well agree with previous reports. The magnetic moments of the Mn, Co and Al atoms in the deep inner layers are close to the bulk values. At the surface layers of both terminations, compared with the deep inner layers, the magnetic moments of Mn(S) atoms increase by 109% and 23% to −3.79 and 3.46 B for CoMnterm and AlMn-term, respectively, whereas the magnetic moment of Co(S) in CoMn-term slightly increases by 3% to −1.09 B . On the other hand, the magnetic moment of the Mn(S − 1) atom in AlMnterm markedly decreases to −1.04 B , which can be ascribed to the increased covalent hybridizations between the d states of the subsurface and surface Mn atoms. The total magnetic moment of AlMn-term is an integer, 18 B , which also reveals its half-metallic character. 4. Summary We investigated the electronic structures, magnetism, and halfmetallicity of the inverse Heusler alloy Mn2 CoAl(0 0 1) surface by the all-electron FLAPW method within the GGA. We considered two

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J. Li, Y. Jin / Applied Surface Science 283 (2013) 876–880

types of surface terminations: AlMn-term and CoMn-term. From the calculated LDOS, half-metallicity was found to be preserved on the AlMn-term. Given the surface states located just above the EF , the width of the minority-spin gap decreased compared with the bulk value. By contrast, on the CoMn-term, the strong surface potential effect shifts the minority-spin Co d states toward higher energies and filled up the minority-spin gap. Thus, the surface lost its half-metallicity. The integer value of the total magnetic moment of AlMn-term also indicates the half-metallic behavior of AlMn-term. At the surface layers for both terminations, the LDOSs of Mn atoms showed strong band narrowing and increased exchange splitting because of the reduced coordination number. The reduced dimensionality enhances the magnetic moments of surface Mn atoms to −3.76 and 3.46 B for CoAl-term and AlMnterm, respectively, whereas the magnetic moment of the surface Co on CoMn-term slightly increased to −1.09 B . On the other hand, the magnetic moment of the subsurface Mn atom in AlMn-term markedly decreased to −1.04 B because of the increased covalent hybridizations between the d states of the subsurface and surface Mn atoms. Acknowledgment This work was supported by the National Nature Science Foundation of China under Grant Nos. 10664005, 11064015, and 11264041. References [1] S.A. Wolf, D.D. Awschalom, R.A. Buhrman, J.M. Daughton, S. von Molnar, M.L. Roukes, A.Y. Chtchelkanova, D.M. Treger, Science 294 (2001) 1488. [2] M.I. Katsnelson, V.Y. Irkhin, L. Chioncel, A.I. Lichtenstein, R.A. de Groot, Reviews of Modern Physics 80 (2008) 315. [3] R.A. de Groot, F.M. Mueller, P.G. van Engen, K.H.J. Buschow, Physical Review Letters 50 (1983) 2024. [4] I. Galanakis, P.H. Dederichs, N. Papanikolaou, Physical Review B 66 (2002) 174429. [5] H.C. Kandpal, G.H. Fecher, C. Felser, Physical Review B 73 (2006) 094422. [6] R.J. Soulen Jr., J.M. Byers, M.S. Osofsky, B. Nadgorny, T. Ambrose, S.F. Cheng, P.R. Broussard, C.T. Tanaka, J. Nowak, J.S. Moodera, A. Barry, J.M.D. Coey, Science 282 (1998) 85. [7] J.H. Park, E. Vescovo, H.J. Kim, C. Kwon, R. Ramesh, T. Venkatesan, Nature 392 (1998) 794. [8] Y. Ji, G.J. Strijkers, F.Y. Yang, C.L. Chien, J.M. Byers, A. Anguelouch, G. Xiao, A. Gupta, Physical Review Letters 86 (2001) 5585.

[9] S. Wurmehl, G.H. Fecher, H.C. Kandpal, V. Ksenofontov, C. Felser, H.J. Lin, J. Morais, Physical Review B 72 (2005) 184434. [10] I. Galanakis, P. Mavropoulos, P.H. Dederichs, Journal of Physics D: Applied Physics 39 (2006) 765. [11] J. Kübler, G.H. Fecher, C. Felser, Physical Review B 76 (2007) 024414. [12] T.J. Burch, T. Litrenta, J.I. Budnick, Physical Review Letters 33 (1974) 421. [13] H.C. Kandpal, G.H. Fecher, C. Felser, Journal of Physics D: Applied Physics 40 (2007) 1507. [14] G.D. Liu, X.F. Dai, H.Y. Liu, J.L. Chen, X.Y. Li, G. Xiao, G.H. Wu, Physical Review B 77 (2008) 014424. [15] H. Luo, Z. Zhu, L. Ma, S. Xu, X. Zhu, C. Jiang, H. Xu, G. Wu, Journal of Physics D: Applied Physics 41 (2008) 055010. [16] M. Meinert, J.M. Schmalhorst, G. Reiss, Journal of Physics: Condensed Matter 23 (2011) 116005. [17] M. Meinert, J.M. Schmalhorst, C. Klewe, G. Reiss, E. Arenholz, T. Böhnert, K. Nielsch, Physical Review B 84 (2011) 132405. [18] N. Zheng, Y. Jin, Journal of Magnetism and Magnetic Materials 324 (2012) 3099. [19] L.J. Singh, Z.H. Barder, Y. Miyoshi, Y. Bugoslavsky, W.R. Branford, L.F. Cohen, Applied Physics Letters 84 (2004) 2367. [20] M.P. Raphael, B. Ravel, Q. Huang, M.A. Willard, S.F. Cheng, B.N. Das, R.M. Stroud, K.M. Bussmann, J.H. Claassen, V.G. Harris, Physical Review B 66 (2002) 104429. [21] J.-P. Wüstenberg, M. Cinchetti, M. Sánchez Albaneda, M. Bauer, M. Aeschlimann, Journal of Magnetism and Magnetic Materials 316 (2007) e411. [22] I. Galanakis, Journal of Physics: Condensed Matter 14 (2002) 6329. [23] S.J. Hashemifar, P. Kratzer, M. Scheffler, Physical Review Letters 94 (2005) 096402. [24] Y.J. Jin, J.I. Lee, Physica Status Solidi (a) 205 (2008) 1824. [25] J.M. Khalaf Al-zyadi, G.Y. Gao, K.L. Yao, Journal of Alloys and Compounds 565 (2013) 17. [26] Y. Feng, B. Wu, H. Yuan, A. Kuang, H. Chen, Journal of Alloys and Compounds 557 (2013) 202. [27] W. Mannstadt, A.J. Freeman, Physical Review B 55 (1997) 13298. [28] W. Kohn, L.J. Sham, Physical Review 140 (1965) A1133. [29] E. Wimmer, H. Krakauer, M. Weinert, A.J. Freeman, Physical Review B 24 (1981) 864, and references therein; M. Weinert, E. Wimmer, A.J. Freeman, Physical Review B 26 (1982) 4571. [30] http://www.flapw.de [31] J.P. Perdew, K. Burke, M. Ernzerhof, Physical Review Letters 77 (1996) 3865, Physical Review Letters 78 (1997) 1396(E). [32] E. Heifets, R.I. Eglitis, E.A. Kotomin, J. Maier, G. Borstel, Physical Review B 64 (2001) 235417. [33] L. Guan, J. Zuo, G. Jia, Q. Liu, W. Wei, J. Guo, X. Dai, B. Liu, Y. Wang, G. Fu, Applied Surface Science 264 (2013) 570. [34] M. Aldén, H.L. Skriver, S. Mirbt, B. Johansson, Physical Review Letters 69 (1992) 2296. [35] M. Aldén, S. Mirbt, H.L. Skriver, N.M. Rosengaard, B. Johansson, Physical Review B 46 (1992) 6303. [36] L. Vito, A.V. Ruban, H.L. Skriver, J. Kollár, Surface Science 411 (1998) 186. [37] B. Wu, H. Yuan, A. Kuang, H. Chen, Y. Feng, Applied Surface Science 258 (2012) 4945. [38] Sh. Khosravizadeh, S.J. Hashemifar, H. Akbarzadeh, Physical Review B 79 (2009) 235203. [39] S. Zarei, S.J. Hashemifar, H. Akbarzadeh, Z. Hafari, Journal of Physics: Condensed Matter 21 (2009) 055002.