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Ab initio investigations of magnetic properties of thin film Heusler alloys
Materials Science and Engineering A 481–482 (2008) 209–213
Ab initio investigations of magnetic properties of thin film Heusler alloys S.E. Kulkova a,b,∗ , S.V. Eremeev a , S.S. Kulkov b , V.A. Skripnyak b a
Institute of Strength Physics and Materials Science of SB RAS, Akademichesky 2/1, Tomsk 634021, Russia b Tomsk State University, Lenina 36, 634050 Tomsk, Russia Received 22 May 2006; received in revised form 21 December 2006; accepted 22 December 2006
Abstract The electronic structure and magnetic properties of several Heusler alloys and their thin films on a GaAs(0 0 1) substrate were investigated using density functional theory calculations. The alteration of the electronic structure and magnetic properties upon defect formation in bulk and surface is discussed. © 2007 Elsevier B.V. All rights reserved. PACS: 71.20 Be; 71.20.−b; 73.20.At Keywords: Heusler alloys; Magnetic films and multilayers; Electronic band structure
1. Introduction Ferromagnetic Heusler alloys (Ni2 MnGa, Ni2 FeGa, Ni2 MnAl, etc.) exhibit interesting magneto-mechanical properties such as magnetic shape memory effect, magnetic field-induced superelasticity, which are subject of current worldwide research [1]. On the other hand, Heusler alloys are very promising materials for spintronics applications because some of them behave as half-metals and, therefore, exhibit 100% spin polarization at the Fermi level. Since a number of Heusler alloys have lattice parameters similar to those of many semiconductors, they could be easily epitaxially grown on semiconductor surfaces. Layered hybrid systems incorporating Heusler alloys are known to be advantageous in comparison to bulk systems because of the small relaxation time for magnetoelastic strains. Unfortunately, the substrate temperature can influence the interfacial reactions, crystal quality, magnetic properties and atomic ordering. The experimental studies indicate the sensitivity of the physical properties of Heusler alloys to structural defects. In particular, the martensitic transformation temperature increases linearly with the increase of Ni content in Ni2+x Mn1−x Ga [2]. In this context the understanding
∗ Corresponding author at: Institute of Strength Physics and Materials Science of SB RAS, Akademichesky 2/1, Tomsk 634021, Russia. Tel.: +7 3822 286952; fax: +7 3822 492576. E-mail address: [email protected] (S.E. Kulkova).
0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.12.197
of the influence of defects on local magnetic properties and the electronic structure of bulk and low-dimensional Heusler alloy systems can be one of the most important problems related to the potential technological applications of these materials. In this work, ab initio calculations of the electronic structure and magnetic properties of several thin film Heusler alloys (with composition X2 YZ, where X = Ni, Co, Y = Mn, Fe and Z = Ga, Si) on a GaAs(0 0 1) substrate are studied with respect to surface termination and defects in the surface layers. The effect of structural defects on the electronic and magnetic properties of bulk alloys is also discussed. 2. Computational details The full-potential linearized augmented plane-wave (FLAPW) method (Wien implementation [3]) within the generalized gradient approximation was used in the band-structure calculations of bulk alloys and thin films. The plane-wave cutoff of RKmax = 9 leads to about 400 basis function. In the interstitial region the potential were expanded in a Fourier series with wave vectors up to Gmax = 14 reciprocal lattice units. The pseudopotential (PP) approach was also applied to calculations of bulk and defective systems. Our supercell consisted of 2 × 2 × 2 times the L21 unit cell and we simulated the X2 YZ(0 0 1) surface using a supercell containing 9–15 atomic layers separated by a vacuum region ∼1 nm. In case of a GaAs substrate, we used multilayers consisting of 6–7 layers of an alloy and 6–10 layers of semiconductor material. It should be
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Fig. 1. Surface DOS for both terminations of Ni2 MnGa(0 0 1), Ni2 FeGa(0 0 1)and Co2 MnGa(0 0 1) in comparison to the bulk DOS.
noted that one surface was passivated by hydrogen atoms using the PP approach but a symmetrical slab was used in the FLAPW calculations. The atomic positions were fully relaxed except from the atoms in the central layers of the slabs (five layers for symmetrical slabs and three layers for slabs with a hydrogen layer). Both methods reproduced quite well the physical trends of the series of alloys [4]. The theoretical lattice parameters were found to be 0.5813 nm (Ni2 MnGa), 0.5767 nm (Ni2 FeGa), 0.5728 nm (Co2 MnGa), 0.5636 (Co2 MnSi) using the FLAPW method compared to 0.5810, 0.5728, 0.5714 and 0.5620 nm, respectively, obtained by employing the PP approach. 3. Results and discussion In the [0 0 1] direction, the L21 structure consists of alternating X and YZ planes. The electronic structure of both Ni2 MnGa(0 0 1) surface terminations (X and YZ) on the GaAs(0 0 1) substrate was calculated using two models within the PP approach. The calculated spin magnetic moments (μ) for surface and subsurface atoms are found to be in good agreement with results obtained from the FLAPW calculations. In particular, μ of the Mn surface atom is 3.70μB (FLAPW) and 3.77μB , 3.86μB (PP method applied to symmetrical slabs model and using atomic H layer, respectively). The effect of structural relaxation on the magnetic moment is not substantial (within ∼0.05–0.1μB ). The exchange splitting of states with opposite spin combined with the narrowing of the bands at the surface due to decrease of coordination number of nearest neighbors and charge redistribution in the surface layers results in a higher value of spin magnetic moment at the surface atoms in comparison with bulk values. The values of spin magnetic moments of the surface atoms are given in Table 1. As can be seen from this table, Ga and Si surface atoms have weak magnetic moments which are antiparallel to the Mn or Fe atoms (as in bulk alloys). The values of magnetic moments of subsurface Ni and Co atoms are found to be close to their bulk values. The surface densities of states (DOS) for all considered systems are shown in Fig. 1 in comparison with the corresponding bulk DOS. A small difference in the position of the main peaks
for up- and down-spin states with respect to EF is observed for YZ-terminations compared with bulk values, while the DOS structure for X-terminations of surfaces changes considerably more. The hybridization between Mn and Co minority-spin states is the reason for the reduction of the magnetic moment of Mn atoms in bulk Co2 MnGa in comparison to Ni2 MnGa alloy, where Mn states have strongly localized character. Therefore, the change of the Mn magnetic moment at the surface in Cobased alloys is much more pronounced than in Ni2 MnGa(0 0 1). The values of the magnetic moment of Mn subsurface atoms in case of Ni- and Co-terminated surfaces are close to the bulk ones since they are fully coordinated. The surface DOS’s of both MnGa- and FeGa-terminations of Ni-based alloys (0 0 1) surface have finer structure at the Fermi level. One should note that the structural transformations in Ni2 MnGa alloy are connected with peculiarities of the electronic structure around the Fermi level [5–7]. In particular a small DOS peak, which is located just below the Fermi level and associated with the Ni contribution, is split due to the tetragonal distortion leading to a lower energy of the system. Thus, the composition of surface layers and its change due to defects can be critical for structural transformations in thin film Heusler alloys. In order to understand of influence of defects on the surface properties, we first estimated the formation energies of defects in the bulk alloys. Four kinds of defects (X, Y antisites and X–Y or Y–Z swaps) were considered. The calculation of the defect formation energies for Co2 MnSi was performed as test for comparison with results obtained earlier [8] by using the FLAPW method. Total DOS for both defective and ideal alloys are shown in Figs. 2 and 3. Only minor defect-induced changes of the DOS are observed for all alloys in case of Mn or Fe antisites on Ni or Co sites. The modifications of the DOS structure near the Fermi level are entirely due to the Mn or Fe antisites d-states. More pronounced changes in the spin-down DOS structure below the Fermi level were found for Ni antisites on Mn(Fe) sites in Ni2 MnGa and Ni2 FeGa. The calculation of the local DOS showed that Ni spin-down states are responsible for the DOS structure in the energy region just below EF . The shift of spin-down states and disappearance of the pseudo-
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Table 1 Calculated magnetic moments μ (in μB ) of surface and subsurface atoms for different surface terminations Systems
μMn(Fe)
μNi(Co)
μGa(Si)
MnGa/Ni2 MnGa(0 0 1) Ni/Ni2 MnGa(0 0 1) MnMn/Ni2 MnGa(0 0 1) –Ga/Ni2 MnGa(0 0 1) GaGa/Ni2 MnGa(0 0 1)
3.86 [3.37] 3.36 3.91 – 0.03
0.37 [0.35] 0.38 0.52 0.27 0.17
−0.14 [−0.08] −0.08 3.97 0.03 −0.08
FeGa/Ni2 FeGa(0 0 1) Ni/Ni2 FeGa(0 0 1) FeFe/Ni2 FeGa(0 0 1) –Ga/Ni2 FeGa(0 0 1) GaGa/Ni2 FeGa(0 0 1)
3.05 [2.82] 2.84 3.03 – −0.07
0.36 [0.25] 0.46 0.51 0.28 0.08
−0.09 [−0.05] −0.05 3.04 0.04 −0.05
MnGa/Co2 MnGa(0 0 1) Co/Co2 MnGa(0 0 1) MnMn/Co2 MnGa(0 0 1) –Ga/Co2 MnGa(0 0 1) GaGa/Co2 MnGa(0 0 1)
3.69 [2.75] 2.77 3.60 – 0.02
0.82 [0.71] 1.41 1.03 0.27 0.61
−0.12 [−0.08] −0.13 3.76 −0.07 −0.01
MnSi/Co2 MnSi(0 0 1) Co/Co2 MnSi(0 0 1) MnMn/Co2 MnSi(0 0 1) -Si/Co2 MnSi(0 0 1) SiSi/Co2 MnSi(0 0 1)
3.65, 3.59* [2.98] 2.67 3.74, 3.63* – 0.07, 0.05*
0.89, 0.98*[1.02] 1.32 1.04, 1.17* 0.52, 0.52* 0.85, 0.91*
−0.10, −0.09*[−0.03] −0.13 3.84, 3.65* −0.08, −0.06* 0.11, −0.02*
Results in square brackets are bulk magnetic moments. The results obtained in Ref. [9] by using the FLAPW code are marked by a star.
Fig. 2. Total spin DOS for defective (solid line) Ni2 MnGa, Ni2 FeGa and Co2 MnGa alloys with Mn or Fe (upper panel) and Ni or Co (lower panel) antisites in comparison to the DOS of ideal alloys (dashed lines).
Fig. 3. Total spin DOS of defective systems (solid line) with Mn–Ni and Fe–Ni swaps in comparison to ideal Ni2 MnGa and Ni2 FeGa alloys (dashed lines).
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Fig. 4. Surface spin DOS of Ni2 FeGa(0 0 1) (top) and Ni2 MnGa(0 0 1) (bottom) with different terminations and with defects in the surface layer.
band gap below EF is connected with filling of the Ni band due to an increase of the Ni content. In the case of Co-based alloys, the local DOS in Fig. 2c reveals a sharp peak at EF that is formed by Co-antisites d spin-down states. Namely, Co-antisites states destroy half-metallicity in Co2 MnSi [8]. The formation of Ni antisites (0.33 eV) is found more preferable in Ni2 MnGa in comparison with Mn antisites (0.62 eV). This allows us to suggest that Ni antisites can be easily formed during Ni2 MnGa alloy growth. It is necessary to point out that the smallest values of formation energy of Co2 MnGa(Si) alloys were obtained for Mn antisites (0.22 and 0.25 eV, respectively). Here we present results obtained within the pseudopotential approach. We would like to emphasize that atomic positions and volume of a defective cell were relaxed but the lattice constant was kept fixed in Ref. [8]. The formation energy of Mn antisite in Co2 MnSi is only slightly less than the value (0.33 eV) obtained in Ref. [8]. Other kind of defects is connected with the atomic interchange. The defect-induced changes of the DOS are more pronounced in the case of d-metal interchange (X–Y) but they are insignificant for a Y–Z swap. Our finding is different from results of Ref. [8] because the disordering involving Si and Mn atoms seems to be slightly preferable than an Mn–Co swap. The difference in the formation energy between two kinds of swaps (Y–Z and X–Y) is more substantial for Co2 MnGa (0.67 and 1.42 eV) and Ni2 MnGa (0.68 and 1.06 eV) than that for Co2 MnSi (1.03 and 1.09 eV). It should be noted that the Ni–Fe swap is found to be preferable by 0.6 eV in comparison to an Fe–Ga swap. The large changes in magnetization at defect sites and their nearest neighbors are observed. The magnetic moment at Mn and Fe antisites are −2.59μB and 2.09μB in Ni2 MnGa and Ni2 FeGa, but they are 2.95 and 2.82μB on own sites near the defect. The decrease of magnetic moments is observed at Ni antisites in both alloys (0.26 and 0.05μB ). So, our calculations showed that the defects can affect the magnetic behavior as well as the structure in the DOS around the Fermi level. Furthermore, we considered Ni- and Co-based Heusler alloy (0 0 1) surface with different compositions in its first layer. Sur-
face DOS of Ni2 MnGa and Ni2 FeGa alloys with MnMn(FeFe), GaGa, and –Ga terminations, where the subsurface layer consist of Ni atoms, are shown in Fig. 4. It is known that in case of half-metallic alloys, the intermixing with substrate atoms or poor layer-by-layer growth leads to formation of magnetically dead layers in the interface as well as the loss of half-metallicity at the surface, which can be crucial for their possible applications. The changes in the DOS in both cases (defects at surfaces or in metal–semiconductors interfaces) are not so significant for Ni2 MnGa and Ni2 FeGa alloys. Basically all important features which were discussed for the bulk electronic structure in connection with structural transformations [5–7] can be found in the surface DOS of the defective systems considered here. As is obvious from the local spin-down DOS of Ni and Mn atoms (see Fig. 4a), the small peak near the Fermi level caused by the Ni contribution does not change, and Mn antisite on Ga site gives additional density of states above the Fermi level in the same region as Mn at its own site. In the case of the FeFe termination at the Ni2 FeGa(0 0 1) surface, the peak at the Fermi level is mainly contributed by Fe atom as in the bulk. It is possible to suggest that influence of surface and considered defects on the martensitic transformation can be insignificant. The magnetic moments at atoms for the considered defective surface terminations are given in Table 1. As one can see, the magnetization of the subsurface Ni atoms increases slightly by the increasing number of Mn atoms at the surface. The same trend was found in Co-based alloys [9]. It should be noted that the magnetization of Co surface atoms increases significantly in comparison to the bulk values. The values of the magnetic moment of the Co surface atoms are ∼1.30–1.40μB in Co2 MnSi(Ga)-(0 0 1) films if Co is the interface atom also. This value is a little bit larger than 1.20μB found in experiment [10]. Note that the magnetic moment depends strongly on the planar lattice parameter. Several calculations have been performed in the case of Coterminated films using different interlayers (Mn–Ga, Mn–As, Mn–Si). In all cases, the change of μ at the Co surface and Mn subsurface atoms are within 0.05–0.1μB . The same trend
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was found for both Ni-based systems. The increase of magnetic moment of Ni surface atoms at the Ni2 MnGa(0 0 1) surface is not substantial and is caused by the tetragonal distortion of the film by the GaAs substrate. This alteration is the same order as found for tetragonal distorted bulk alloys in Ref. [6]. 4. Conclusions In summary, ab initio calculations of the electronic structure and magnetic properties of Ni- and Co-based thin film Heusler alloys on a GaAs(0 0 1) substrate were performed. Different ideal and defective terminations of the (0 0 1) surface were considered. We estimated the effect of structural relaxation on magnetic properties and found that it is insignificant (by ∼0.05–0.1μB ) for the systems considered here. It was shown that the magnetic moments of the transition metal surface atoms are increased in comparison to corresponding bulk values. The increase of the magnetic moment of Co surface atoms up to 1.30μB in the case of Ga–Co interlayer and its variation within ∼0.1μB in the case of other interlayers, was found for Co2 MnGa(0 0 1) thin film. The magnetic moment of Mn subsurface atoms varies slightly from intermediate layers and is ∼2.60–2.70μB in good agreement with experimental data [10]. It was shown that the electronic structure of defective terminations of Ni2 MnGa(0 0 1) and Ni2 FeGa(0 0 1) surfaces changes significantly less in comparison to Co-based systems especially with half-metallic behavior. The main features of the electronic structure around the Fermi level remain basically the same as in the bulk systems. This allows to suggest that the influence of
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surface and considered defects on the martensitic transformation will not be so significant. At the same time we found that the formation of Ni antisites at the Mn sites is more preferable in the bulk Ni2 MnGa alloy, but NiGa termination at the surface is less stable than considered above. In general, the results obtained allow to understand the microscopic origin of the change of magnetic properties due to structural defects in the bulk and at surfaces and interfaces. Acknowledgement This work was supported by the Russian Foundation for Basic Research under grant 05-02-16074a. References [1] K. Kakeshita, K. Ullakko, MRS Bull. 27 (2002) 105–108. [2] V. Khovailo, V. Novosad, T. Takagi, D. Filippov, R. Levitin, A. Vasil’eV, Phys. Rev. B 70 (2004) 174413. [3] P. Blaha, K. Schwarz, G.K.M. Madsen, D. Kvasnicka, J. Luits, Wien 2k, Vienna University of Technology, Austria, 2001, ISBN 3-9501031-1-2. [4] S. Kulkova, S. Eremeev, T. Kakeshita, S. Kulkov, G. Rudenskiy, Mater. Trans. 47 (2006) 599–606. [5] S. Fujii, S. Ishida, S. Asano, J. Phys. Soc. Japn. 58 (1989) 3657. [6] A. Ayuela, J. Enkovaara, R.M. Nieminen, J. Phys.: Condens. Matter 14 (2002) 5325. [7] A.T. Zayak, P. Entel, J. Enkovaara, A. Ayuela, R.M. Nieminen, J. Phys.: Condens. Matter 15 (2003) 159. [8] S. Picozzi, A. Continenza, A.J. Freeman, Phys. Rev. B 69 (2004) 094423. [9] S. Hashemifar, P. Kratzer, M. Scheffler, Phys. Rev. Lett. 94 (2005) 96402. [10] W.H. Wang, M. Przybylski, W. Kush, L. Chelaru, J. Wang, Y.F. Lu, J. Bartel, H.L. Meyerheim, J. Kirschner, Phys. Rev. B 71 (2005) 144416.
Ab initio investigations of magnetic properties of thin film Heusler alloys S.E. Kulkova a,b,∗ , S.V. Eremeev a , S.S. Kulkov b , V.A. Skripnyak b a
Institute of Strength Physics and Materials Science of SB RAS, Akademichesky 2/1, Tomsk 634021, Russia b Tomsk State University, Lenina 36, 634050 Tomsk, Russia Received 22 May 2006; received in revised form 21 December 2006; accepted 22 December 2006
Abstract The electronic structure and magnetic properties of several Heusler alloys and their thin films on a GaAs(0 0 1) substrate were investigated using density functional theory calculations. The alteration of the electronic structure and magnetic properties upon defect formation in bulk and surface is discussed. © 2007 Elsevier B.V. All rights reserved. PACS: 71.20 Be; 71.20.−b; 73.20.At Keywords: Heusler alloys; Magnetic films and multilayers; Electronic band structure
1. Introduction Ferromagnetic Heusler alloys (Ni2 MnGa, Ni2 FeGa, Ni2 MnAl, etc.) exhibit interesting magneto-mechanical properties such as magnetic shape memory effect, magnetic field-induced superelasticity, which are subject of current worldwide research [1]. On the other hand, Heusler alloys are very promising materials for spintronics applications because some of them behave as half-metals and, therefore, exhibit 100% spin polarization at the Fermi level. Since a number of Heusler alloys have lattice parameters similar to those of many semiconductors, they could be easily epitaxially grown on semiconductor surfaces. Layered hybrid systems incorporating Heusler alloys are known to be advantageous in comparison to bulk systems because of the small relaxation time for magnetoelastic strains. Unfortunately, the substrate temperature can influence the interfacial reactions, crystal quality, magnetic properties and atomic ordering. The experimental studies indicate the sensitivity of the physical properties of Heusler alloys to structural defects. In particular, the martensitic transformation temperature increases linearly with the increase of Ni content in Ni2+x Mn1−x Ga [2]. In this context the understanding
∗ Corresponding author at: Institute of Strength Physics and Materials Science of SB RAS, Akademichesky 2/1, Tomsk 634021, Russia. Tel.: +7 3822 286952; fax: +7 3822 492576. E-mail address: [email protected] (S.E. Kulkova).
0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.12.197
of the influence of defects on local magnetic properties and the electronic structure of bulk and low-dimensional Heusler alloy systems can be one of the most important problems related to the potential technological applications of these materials. In this work, ab initio calculations of the electronic structure and magnetic properties of several thin film Heusler alloys (with composition X2 YZ, where X = Ni, Co, Y = Mn, Fe and Z = Ga, Si) on a GaAs(0 0 1) substrate are studied with respect to surface termination and defects in the surface layers. The effect of structural defects on the electronic and magnetic properties of bulk alloys is also discussed. 2. Computational details The full-potential linearized augmented plane-wave (FLAPW) method (Wien implementation [3]) within the generalized gradient approximation was used in the band-structure calculations of bulk alloys and thin films. The plane-wave cutoff of RKmax = 9 leads to about 400 basis function. In the interstitial region the potential were expanded in a Fourier series with wave vectors up to Gmax = 14 reciprocal lattice units. The pseudopotential (PP) approach was also applied to calculations of bulk and defective systems. Our supercell consisted of 2 × 2 × 2 times the L21 unit cell and we simulated the X2 YZ(0 0 1) surface using a supercell containing 9–15 atomic layers separated by a vacuum region ∼1 nm. In case of a GaAs substrate, we used multilayers consisting of 6–7 layers of an alloy and 6–10 layers of semiconductor material. It should be
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Fig. 1. Surface DOS for both terminations of Ni2 MnGa(0 0 1), Ni2 FeGa(0 0 1)and Co2 MnGa(0 0 1) in comparison to the bulk DOS.
noted that one surface was passivated by hydrogen atoms using the PP approach but a symmetrical slab was used in the FLAPW calculations. The atomic positions were fully relaxed except from the atoms in the central layers of the slabs (five layers for symmetrical slabs and three layers for slabs with a hydrogen layer). Both methods reproduced quite well the physical trends of the series of alloys [4]. The theoretical lattice parameters were found to be 0.5813 nm (Ni2 MnGa), 0.5767 nm (Ni2 FeGa), 0.5728 nm (Co2 MnGa), 0.5636 (Co2 MnSi) using the FLAPW method compared to 0.5810, 0.5728, 0.5714 and 0.5620 nm, respectively, obtained by employing the PP approach. 3. Results and discussion In the [0 0 1] direction, the L21 structure consists of alternating X and YZ planes. The electronic structure of both Ni2 MnGa(0 0 1) surface terminations (X and YZ) on the GaAs(0 0 1) substrate was calculated using two models within the PP approach. The calculated spin magnetic moments (μ) for surface and subsurface atoms are found to be in good agreement with results obtained from the FLAPW calculations. In particular, μ of the Mn surface atom is 3.70μB (FLAPW) and 3.77μB , 3.86μB (PP method applied to symmetrical slabs model and using atomic H layer, respectively). The effect of structural relaxation on the magnetic moment is not substantial (within ∼0.05–0.1μB ). The exchange splitting of states with opposite spin combined with the narrowing of the bands at the surface due to decrease of coordination number of nearest neighbors and charge redistribution in the surface layers results in a higher value of spin magnetic moment at the surface atoms in comparison with bulk values. The values of spin magnetic moments of the surface atoms are given in Table 1. As can be seen from this table, Ga and Si surface atoms have weak magnetic moments which are antiparallel to the Mn or Fe atoms (as in bulk alloys). The values of magnetic moments of subsurface Ni and Co atoms are found to be close to their bulk values. The surface densities of states (DOS) for all considered systems are shown in Fig. 1 in comparison with the corresponding bulk DOS. A small difference in the position of the main peaks
for up- and down-spin states with respect to EF is observed for YZ-terminations compared with bulk values, while the DOS structure for X-terminations of surfaces changes considerably more. The hybridization between Mn and Co minority-spin states is the reason for the reduction of the magnetic moment of Mn atoms in bulk Co2 MnGa in comparison to Ni2 MnGa alloy, where Mn states have strongly localized character. Therefore, the change of the Mn magnetic moment at the surface in Cobased alloys is much more pronounced than in Ni2 MnGa(0 0 1). The values of the magnetic moment of Mn subsurface atoms in case of Ni- and Co-terminated surfaces are close to the bulk ones since they are fully coordinated. The surface DOS’s of both MnGa- and FeGa-terminations of Ni-based alloys (0 0 1) surface have finer structure at the Fermi level. One should note that the structural transformations in Ni2 MnGa alloy are connected with peculiarities of the electronic structure around the Fermi level [5–7]. In particular a small DOS peak, which is located just below the Fermi level and associated with the Ni contribution, is split due to the tetragonal distortion leading to a lower energy of the system. Thus, the composition of surface layers and its change due to defects can be critical for structural transformations in thin film Heusler alloys. In order to understand of influence of defects on the surface properties, we first estimated the formation energies of defects in the bulk alloys. Four kinds of defects (X, Y antisites and X–Y or Y–Z swaps) were considered. The calculation of the defect formation energies for Co2 MnSi was performed as test for comparison with results obtained earlier [8] by using the FLAPW method. Total DOS for both defective and ideal alloys are shown in Figs. 2 and 3. Only minor defect-induced changes of the DOS are observed for all alloys in case of Mn or Fe antisites on Ni or Co sites. The modifications of the DOS structure near the Fermi level are entirely due to the Mn or Fe antisites d-states. More pronounced changes in the spin-down DOS structure below the Fermi level were found for Ni antisites on Mn(Fe) sites in Ni2 MnGa and Ni2 FeGa. The calculation of the local DOS showed that Ni spin-down states are responsible for the DOS structure in the energy region just below EF . The shift of spin-down states and disappearance of the pseudo-
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Table 1 Calculated magnetic moments μ (in μB ) of surface and subsurface atoms for different surface terminations Systems
μMn(Fe)
μNi(Co)
μGa(Si)
MnGa/Ni2 MnGa(0 0 1) Ni/Ni2 MnGa(0 0 1) MnMn/Ni2 MnGa(0 0 1) –Ga/Ni2 MnGa(0 0 1) GaGa/Ni2 MnGa(0 0 1)
3.86 [3.37] 3.36 3.91 – 0.03
0.37 [0.35] 0.38 0.52 0.27 0.17
−0.14 [−0.08] −0.08 3.97 0.03 −0.08
FeGa/Ni2 FeGa(0 0 1) Ni/Ni2 FeGa(0 0 1) FeFe/Ni2 FeGa(0 0 1) –Ga/Ni2 FeGa(0 0 1) GaGa/Ni2 FeGa(0 0 1)
3.05 [2.82] 2.84 3.03 – −0.07
0.36 [0.25] 0.46 0.51 0.28 0.08
−0.09 [−0.05] −0.05 3.04 0.04 −0.05
MnGa/Co2 MnGa(0 0 1) Co/Co2 MnGa(0 0 1) MnMn/Co2 MnGa(0 0 1) –Ga/Co2 MnGa(0 0 1) GaGa/Co2 MnGa(0 0 1)
3.69 [2.75] 2.77 3.60 – 0.02
0.82 [0.71] 1.41 1.03 0.27 0.61
−0.12 [−0.08] −0.13 3.76 −0.07 −0.01
MnSi/Co2 MnSi(0 0 1) Co/Co2 MnSi(0 0 1) MnMn/Co2 MnSi(0 0 1) -Si/Co2 MnSi(0 0 1) SiSi/Co2 MnSi(0 0 1)
3.65, 3.59* [2.98] 2.67 3.74, 3.63* – 0.07, 0.05*
0.89, 0.98*[1.02] 1.32 1.04, 1.17* 0.52, 0.52* 0.85, 0.91*
−0.10, −0.09*[−0.03] −0.13 3.84, 3.65* −0.08, −0.06* 0.11, −0.02*
Results in square brackets are bulk magnetic moments. The results obtained in Ref. [9] by using the FLAPW code are marked by a star.
Fig. 2. Total spin DOS for defective (solid line) Ni2 MnGa, Ni2 FeGa and Co2 MnGa alloys with Mn or Fe (upper panel) and Ni or Co (lower panel) antisites in comparison to the DOS of ideal alloys (dashed lines).
Fig. 3. Total spin DOS of defective systems (solid line) with Mn–Ni and Fe–Ni swaps in comparison to ideal Ni2 MnGa and Ni2 FeGa alloys (dashed lines).
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Fig. 4. Surface spin DOS of Ni2 FeGa(0 0 1) (top) and Ni2 MnGa(0 0 1) (bottom) with different terminations and with defects in the surface layer.
band gap below EF is connected with filling of the Ni band due to an increase of the Ni content. In the case of Co-based alloys, the local DOS in Fig. 2c reveals a sharp peak at EF that is formed by Co-antisites d spin-down states. Namely, Co-antisites states destroy half-metallicity in Co2 MnSi [8]. The formation of Ni antisites (0.33 eV) is found more preferable in Ni2 MnGa in comparison with Mn antisites (0.62 eV). This allows us to suggest that Ni antisites can be easily formed during Ni2 MnGa alloy growth. It is necessary to point out that the smallest values of formation energy of Co2 MnGa(Si) alloys were obtained for Mn antisites (0.22 and 0.25 eV, respectively). Here we present results obtained within the pseudopotential approach. We would like to emphasize that atomic positions and volume of a defective cell were relaxed but the lattice constant was kept fixed in Ref. [8]. The formation energy of Mn antisite in Co2 MnSi is only slightly less than the value (0.33 eV) obtained in Ref. [8]. Other kind of defects is connected with the atomic interchange. The defect-induced changes of the DOS are more pronounced in the case of d-metal interchange (X–Y) but they are insignificant for a Y–Z swap. Our finding is different from results of Ref. [8] because the disordering involving Si and Mn atoms seems to be slightly preferable than an Mn–Co swap. The difference in the formation energy between two kinds of swaps (Y–Z and X–Y) is more substantial for Co2 MnGa (0.67 and 1.42 eV) and Ni2 MnGa (0.68 and 1.06 eV) than that for Co2 MnSi (1.03 and 1.09 eV). It should be noted that the Ni–Fe swap is found to be preferable by 0.6 eV in comparison to an Fe–Ga swap. The large changes in magnetization at defect sites and their nearest neighbors are observed. The magnetic moment at Mn and Fe antisites are −2.59μB and 2.09μB in Ni2 MnGa and Ni2 FeGa, but they are 2.95 and 2.82μB on own sites near the defect. The decrease of magnetic moments is observed at Ni antisites in both alloys (0.26 and 0.05μB ). So, our calculations showed that the defects can affect the magnetic behavior as well as the structure in the DOS around the Fermi level. Furthermore, we considered Ni- and Co-based Heusler alloy (0 0 1) surface with different compositions in its first layer. Sur-
face DOS of Ni2 MnGa and Ni2 FeGa alloys with MnMn(FeFe), GaGa, and –Ga terminations, where the subsurface layer consist of Ni atoms, are shown in Fig. 4. It is known that in case of half-metallic alloys, the intermixing with substrate atoms or poor layer-by-layer growth leads to formation of magnetically dead layers in the interface as well as the loss of half-metallicity at the surface, which can be crucial for their possible applications. The changes in the DOS in both cases (defects at surfaces or in metal–semiconductors interfaces) are not so significant for Ni2 MnGa and Ni2 FeGa alloys. Basically all important features which were discussed for the bulk electronic structure in connection with structural transformations [5–7] can be found in the surface DOS of the defective systems considered here. As is obvious from the local spin-down DOS of Ni and Mn atoms (see Fig. 4a), the small peak near the Fermi level caused by the Ni contribution does not change, and Mn antisite on Ga site gives additional density of states above the Fermi level in the same region as Mn at its own site. In the case of the FeFe termination at the Ni2 FeGa(0 0 1) surface, the peak at the Fermi level is mainly contributed by Fe atom as in the bulk. It is possible to suggest that influence of surface and considered defects on the martensitic transformation can be insignificant. The magnetic moments at atoms for the considered defective surface terminations are given in Table 1. As one can see, the magnetization of the subsurface Ni atoms increases slightly by the increasing number of Mn atoms at the surface. The same trend was found in Co-based alloys [9]. It should be noted that the magnetization of Co surface atoms increases significantly in comparison to the bulk values. The values of the magnetic moment of the Co surface atoms are ∼1.30–1.40μB in Co2 MnSi(Ga)-(0 0 1) films if Co is the interface atom also. This value is a little bit larger than 1.20μB found in experiment [10]. Note that the magnetic moment depends strongly on the planar lattice parameter. Several calculations have been performed in the case of Coterminated films using different interlayers (Mn–Ga, Mn–As, Mn–Si). In all cases, the change of μ at the Co surface and Mn subsurface atoms are within 0.05–0.1μB . The same trend
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was found for both Ni-based systems. The increase of magnetic moment of Ni surface atoms at the Ni2 MnGa(0 0 1) surface is not substantial and is caused by the tetragonal distortion of the film by the GaAs substrate. This alteration is the same order as found for tetragonal distorted bulk alloys in Ref. [6]. 4. Conclusions In summary, ab initio calculations of the electronic structure and magnetic properties of Ni- and Co-based thin film Heusler alloys on a GaAs(0 0 1) substrate were performed. Different ideal and defective terminations of the (0 0 1) surface were considered. We estimated the effect of structural relaxation on magnetic properties and found that it is insignificant (by ∼0.05–0.1μB ) for the systems considered here. It was shown that the magnetic moments of the transition metal surface atoms are increased in comparison to corresponding bulk values. The increase of the magnetic moment of Co surface atoms up to 1.30μB in the case of Ga–Co interlayer and its variation within ∼0.1μB in the case of other interlayers, was found for Co2 MnGa(0 0 1) thin film. The magnetic moment of Mn subsurface atoms varies slightly from intermediate layers and is ∼2.60–2.70μB in good agreement with experimental data [10]. It was shown that the electronic structure of defective terminations of Ni2 MnGa(0 0 1) and Ni2 FeGa(0 0 1) surfaces changes significantly less in comparison to Co-based systems especially with half-metallic behavior. The main features of the electronic structure around the Fermi level remain basically the same as in the bulk systems. This allows to suggest that the influence of
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surface and considered defects on the martensitic transformation will not be so significant. At the same time we found that the formation of Ni antisites at the Mn sites is more preferable in the bulk Ni2 MnGa alloy, but NiGa termination at the surface is less stable than considered above. In general, the results obtained allow to understand the microscopic origin of the change of magnetic properties due to structural defects in the bulk and at surfaces and interfaces. Acknowledgement This work was supported by the Russian Foundation for Basic Research under grant 05-02-16074a. References [1] K. Kakeshita, K. Ullakko, MRS Bull. 27 (2002) 105–108. [2] V. Khovailo, V. Novosad, T. Takagi, D. Filippov, R. Levitin, A. Vasil’eV, Phys. Rev. B 70 (2004) 174413. [3] P. Blaha, K. Schwarz, G.K.M. Madsen, D. Kvasnicka, J. Luits, Wien 2k, Vienna University of Technology, Austria, 2001, ISBN 3-9501031-1-2. [4] S. Kulkova, S. Eremeev, T. Kakeshita, S. Kulkov, G. Rudenskiy, Mater. Trans. 47 (2006) 599–606. [5] S. Fujii, S. Ishida, S. Asano, J. Phys. Soc. Japn. 58 (1989) 3657. [6] A. Ayuela, J. Enkovaara, R.M. Nieminen, J. Phys.: Condens. Matter 14 (2002) 5325. [7] A.T. Zayak, P. Entel, J. Enkovaara, A. Ayuela, R.M. Nieminen, J. Phys.: Condens. Matter 15 (2003) 159. [8] S. Picozzi, A. Continenza, A.J. Freeman, Phys. Rev. B 69 (2004) 094423. [9] S. Hashemifar, P. Kratzer, M. Scheffler, Phys. Rev. Lett. 94 (2005) 96402. [10] W.H. Wang, M. Przybylski, W. Kush, L. Chelaru, J. Wang, Y.F. Lu, J. Bartel, H.L. Meyerheim, J. Kirschner, Phys. Rev. B 71 (2005) 144416.