Electronic and magnetic properties of Mn-doped ZnO: Total-energy calculations

Physica B 407 (2012) 3975–3981

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Electronic and magnetic properties of Mn-doped ZnO: Total-energy calculations Ghadah S AlGhamdi, A.Z. AlZahrani n King Abdulaziz University Physics Department Faculty of Science PO Box 80203 Jeddah 21589, Saudi Arabia

a r t i c l e i n f o

abstract

Article history: Received 30 May 2012 Received in revised form 12 June 2012 Accepted 13 June 2012 Available online 21 June 2012

Based on the spin generalized gradient approximation (sGGA) of the density functional theory (DFT), the structural, magnetic, and electronic properties of Mn-doped ZnO structure have thoroughly been investigated. It is found that the Mn atom prefers to substitute one of the Zn atoms, producing the energetically most stable configuration for the Mn-doped ZnO structure. Employing the Hubbard potential within the calculations suggests various changes and modifications to the structural, magnetic and electronic properties of the Mn-doped ZnO. Our calculations reveal that the local magnetic moment at the Mn site using the ordinary sGGA functional is 4.84 mB/Mn, which is smaller than that evaluated by including the Hubbard potential of 5.04 mB/Mn. Overall, the electronic band structure of the system, within the sGGA þ U, is half-metallic, with metallic nature for the majority state and semiconducting nature for the minority state. Simulated scanning tunneling microscopy (STM) images for both unoccupied and occupied states indicate siginficant brightness on both Zn and Mn atoms and much brighter protrusions around the O atoms, respectively. & 2012 Elsevier B.V. All rights reserved.

Keywords: Density functional theory (DFT) Generalized gradient approximation (GGA) Ionic bonds Scanning tunneling microscopy (STM) Band structure Density of states (DOS)

1. Introduction The development of dilute magnetic semiconductors (DMS) is currently interesting for spin-based light-emitting diodes, sensors, transistors and spintronics devices. Among these possible applications of DMSs, spintronic devices represent the most important and promising application. The word ‘‘spintronics’’ (short for ‘‘spin electronics’’) refers to devices that manipulate the spin degree of freedom. In spintronic devices, charge and spin are simultaneously used. Charge, on one hand, is used for the computing while spin, on the other hand, is used for magnetic data storage. Moreover, these devices are quite interesting due to the exhibition of ferromagnetic behavior of nonmagnetic materials doped with transition metals (TMs) [1–3]. The concentration of these TMs controls the magnetic behavior of such materials. In these DMS materials, the substitution of 3d TMs for the cations of the host leads to significant changes in their electronic structure due to the strong interactions of the 3d orbitals of the magnetic ion and the p orbitals of the neighboring anions. One of the most important TMs and a regular candidate for the DMS applications is the manganese (Mn) atoms. Over the past few decades, Mn-doped III–V systems have received great deal and immense interest. Due to their high Curie

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temperature and compatibility with the GaAs host, (Ga,Mn)As structures have received much more interest in both experiments and theory [4–12]. The substitution of the Mn atom for the Ga site in bulk GaAs crystal has been reported to induce a local spin magnetic moment of 5/2, resulting in an acceptor state at about 0.113 eV above the valence band maximum [13]. From ab initio calculations, using the plane wave pseudopotential method and the density functional scheme, AlZahrani et al. [14] have investigated the structural, magnetic and electronic properties of Mndoped GaAs. Within both the spin-polarized generalized gradient approximation (sGGA) and sGGA þU schemes, their calculations suggest that the Mn impurity in bulk GaAs can be described within the 3d4 scenario, with the energy level of the zone center d state lying 0.25 eV above the Fermi level. Due to the presence of a d-wave envelope function in its ground state, Yakunin et al. [15–17] have revealed a high anisotropic spatial feature of the Mn acceptor state in (Ga, Mn)As, suggesting the responsibility of the valence band of the GaAs host. Kitchen et al. [18] have observed the energy splitting of the Mn acceptor states in GaAs by forming Mn pairs using an atom-by-atom substitution technique. Their results suggested that the Mn–Mn interaction decays rapidly and becomes anisotropic with the increase of separation between the Mn acceptors. The Mn-doped IV structures have also received immense interest as well as Mn-doped III–V systems. Park et al. [19] have fabricated ferromagnetic ordering system of nanoclusters Mn11Ge8 thin films embedded in MnxGe1  x dilute matrix grown

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at low temperature (  300 1C). Their measurements of the magnetization reveal that the clusters dominate the magnetic properties, while the matrix itself controls the transport properties. Zhang et al. [20] have found that Mn0.05 Si0.95 thin films showed ferromagnetic behavior above room temperature (  400 1K). Their structural analysis, using X-ray diffraction (XRD), of Mn0.05 Si0.95 thin films have verified the single phase crystallization and incorporation of the Mn atoms in the film, with semiconducting behaviour of the system. Zhang et al. [21] have investigated the magnetic and electrical properties of Mn-doped silicon using the superconducting quantum interference device (SQUID). Their results indicated that the materials contain two ferromagnetic phases with Curie temperatures of around 55 K and over 250 K. Miura et al. [22] have reported that Mn cluster is more stable than isolated Mn impurity in bulk Si. Moreover, Yabuuchi et al. [23] have investigated the effects of strain on Mn impurities in Si using first-principles density functional calculations. They have reported that the tensile strain stabilizes the substitutional Mn and retains the magnetic moment. Within the framework of density functional theory in its generalized gradient approximation, AlZahrani [24] has presented theoretical results for the structural, magnetic, and electronic properties of Mn-doped Si. It has been found that the tetrahedral interstitial position is energetically favored over the hexagonal interstitial and substitutional doping sites. For substitutional site, it was found that the local magnetic moment at the Mn site of 2.95 mB/Mn in the sGGA þU is slightly smaller than that in the sGGA of 3.05 mB/Mn. Similarly, it was found that the local magnetic moment of 3.07 mB/ Mn within the sGGA scheme increases to 3.60 mB/Mn within the sGGA þU frame for the interstitial doping site. Although there are many available experimental and theoretical studies on the behaviour of Mn-doped III–V and IV semiconductors, a few little investigations has been carried out towards the Mn-doped II–VI semiconducting materials such as Mn-doped ZnO. Due to the strong coupling between the magnetic ions 3d states and the coupling to the host p states, diluted magnetic oxide semiconductors have been predicted and observed to show hole-mediated ferromagnetic behaviour above room temperatures. As a result, doping ZnO with Mn atoms has been a popular technique to manipulate and control ZnO’s extrinsic properties for various magnetoelectronics applications. Within the framework of the generalized gradient approximation (GGA) of the density functional theory (DFT), Reber et al. [25] have reported on doping of Co atoms in a small cluster of ZnO. It has been found that doping of Co ions leads to ferromagnetic coupling due to the direct exchange interaction. For small Mn–Mn separation, Liu et al. [26] have found that the Mn-doped ZnO yields an antiferromagnetic (AFM) ground state structure. For large Mn–Mn distance, ferromagnetic (FM) and AFM states have been found to be degenerate. Recently, Cheng and Wang have investigated the structural and magnetic properties of several ZnO doped with 3d transition ions using GGA [27] scheme. They have reported that most of the dopants present the ground-state structure either in paramagnetic or in AFM state, except Co and Ni, where the ferromagnetic and AFM states are found to be energetically stable. Ganguli et al. [28] have studied the energetic and magnetic interactions in 3d transition metals doped ZnO using the GGAþU method. Their calculations suggested that all the 3d atoms antiferromagnetically couple in a pristine ZnO cluster with the possible exception of Ti ions. Very recently, Mn substituted ZnO nanoparticles with various compositional formulae were synthesized by sol–gel method by Dole et al. [29]. Using XRD measurements, grain size, X-ray density and atomic packing fraction (APF) were evaluated. Their experimental results indicated that grain size increases while X-ray density and APF decrease with the increase of the dopant concentration.

To get deep understanding of the structural, magnetic, and electronic properties of Mn-doped ZnO, DFT calculations for Zn1  x Mnx O within both the ordinary sGGA functional and sGGAþ U approaches will be carried out in the present article.

2. Computational method We carried out the present calculations within the density functional theory [30] using the spin-polarized version of a generalized gradient approximation (DFT–sGGA). The Perdew– Burke–Ernzerhof exchange–correlation scheme [31] was considered to treat electron–electron interactions. Electron–ion interactions were treated by using the ultrasoft pseudopotentials [32]. Single-particle Kohn–Sham [33] wavefunctions were expanded in the framework of a plane wave basis set with a kinetic energy cutoff of 35 Ryd (480 eV) which is sufficient enough to obtain well-converged results. Self-consistent solutions of the Kohn– Sham equations were obtained by employing 2  2  1 k-points Monkhorst–Pack sets [34] within the bulk Brillouin zone. Our theoretically calculated lattice constants of a ¼b¼ 3.28092 A˚ and c¼5.282275 A˚ were used for the hexagonal ZnO unit cell. We have relaxed all the atoms in the unit cell using the total energy and Hellmann–Feynman force minimization method. The force tolerance in the minimization procedure was set to ˚ approximately 0.005 eV/A. To compare the various structural models that are initially considered for the Mn-doped ZnO structure with different stoichiometric either Zn or O atoms, we introduce the following formula

DE ¼ EMnZnO EZnO þ DNi mi mMn, where EMn ZnO is the total energy of the Mn-doped ZnO structure, EZnO is the total energy of the clean ZnO structure, DNi is the difference in number of ith atomic species, mi is the chemical potential of the ith atomic species (Zn and O), and mMn is the chemical potential of Mn atom. The ferromagnetic (FM) state is theoretically prepared by assigning suitable initial magnetic moment values at the Mn sites. Quantitatively, we assigned magnetic moments of þ0.7 mB at the Mn site within the unit cell. Changing the initial value of 0.7 mB to 0.5 mB (or to 1.0 mB) does not alter the final result of the magnetization. For all calculations reported here with the inclusion of Hubbard potential U, the value of the Hubbard correlation was chosen to be 4.0 eV. This value is in agreement with those found in different literatures [14,24,35].

3. Results and discussion Following the normal procedure, we considered three initial structural models for the Mn-doped ZnO structure with dopant concentration of 6.25%: Mn substitutes one of the Zn atoms (ZnMn structure), Mn substitutes one of the O atoms (OMn structure), and Mn being interstitially doped (Mnint structure), as shown in Fig. 1. Our total energy calculation reveals that the energetically most stable structure corresponds to the ZnMn structure with an energy gain of about 0.63 and 0.53 eV/Mn with respect to OMn and Mnint structures, respectively. This substitutional site is somehow predicted since the atomic size of the Mn atom is quite similar to that of the Zn atom. 3.1. Structural and magnetic properties The optimized (relaxed) geometry of the most stable structure, schematically shown in panel (a) of Fig. 2, indicates that the

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Mn O Zn

Fig. 1. The structural models of studies ZnMnO system (a) Mn substitutes one of the Zn atoms (b) Mn substitutes one of the O atoms and (c) Mn interstitially doped.

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˚ indicating weak bond formation. This value is in become 1.94 A, excellent agreement with the value obtained by Ganguli et al. [28] ˚ Moreover, the Zn–O bond length categorizes into two of 1.95 A. classes: one with O atom close to Mn atom and the other with O atom far from the Mn atom. The Zn–O bond length, with O atom close to the Mn atom, is 1.85 A˚ while the other Zn–O bond length ˚ This suggests that the Zn–O bond becomes slightly is 1.87 A. stronger upon the doping of Mn atom. However, these values are slightly smaller than the Zn–O bond length in pure ZnO [36]. The O–Mn–O and O–Zn–O bond angles are found to be 1201 and 1221, respectively. Furthermore, the doping of Mn atom leads to a ˚ reduction in the vertical distance by approximately 0.003 A, comparing with the undoped ZnO. Employing both nonmagnetic (NM) and ferromagnetic (FM) schemes, our total-energy calculations suggest that the FM phase is the ground state configuration for the Mn-doped ZnO structure. Our calculations reveal that the local magnetic moment at the Mn site using the ordinary XC functional is approximately 4.84 mB/Mn, which is slightly smaller than that measured by including the Hubbard potential of 5.04 mB/Mn. It is noted that the inclusion of U in the calculations modifies the magnetic properties of Mn-doped ZnO. It is interesting to note that the magnetic moment of the system without U is quite smaller than the value obtained for the Mn in the rocksalt MnO crystal of approximately 4.93 mB/Mn.

1.8

7

3.2. Electronic properties

121

7

1.8 120

120

1.8

7

1.89

122

To point out the fundamental electronic changes of the ZnO structure due to the doping of the Mn atom, we prefer to present the electronic band structure of the pure ZnO structure, as shown in Fig. 3. It is clearly shown that the structure is semiconducting with a direct band gap of 1.27 eV, which is much better than the recently-reported value of 0.75 eV [36]. At 2.2 eV above the Fermi level, we clearly find degeneracy at point A which is also observed at 3.3 eV. These degeneracies are also defined in other theoretical works which are characteristic properties of ZnO. Below the Fermi level, there are a number of dispersive curves along the whole direction, indicating very good conducting behavior. At the G point, a few number of bands are degenerate with zero effective masses just around the point (i.e., the bands conduct a linear E-k behavior or nondispersive bands). Similar energetic degeneracy is also observed at the edges of the Brillouin zone. The electronic band structures for both the majority and minority spin channels of the Mn-doped ZnO in the vicinity of the fundamental band gap region are depicted in Fig. 4. Panels (a) and (b) show the majority and minority channels, respectively,

1.85

120 1.94

Fig. 2. The relaxed structures the most stable configuration of the ZnMnO (a) without U and (b) with U.

nearest-neighbour O atoms have slightly moved away from the ˚ Mn atom. The calculated Mn–O bond length is found to be 1.89 A, which is very comparable with the summation of the species ˚ A little reduction in the Zn–O bond length covalent radii of 1.9 A. is observed upon the doping of Mn atom. The calculations suggest ˚ which is smaller than the that the Zn–O bond length is 1.87 A, reported value of 1.89 A˚ [36]. The O–Mn–O and O–Zn–O bond angles are found to be 1201 and 1211, respectively, indicating a tiny expansion in the O–Zn–O angle. Upon the inclusion of Hubbard potential, the fundamental structural parameters have significantly changed, as shown in Fig. 2(b). The Mn–O bond length has been elongated by 0.05 A˚ to

Fig. 3. Band structure plot of ZnO along the high symmetry direction. The zero energy is set at the Fermi level. A sketch of the Brillouin zone is inserted in the inset.

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Fig. 4. Electronic band structure of ZnMnO, along the highly symmetry direction of Brillouin Zone, for (a) the majority and (b) minority channels. These calculations were performed without U.

in the absence of the Hubbard correction. Turning our attention to the majority spin channel, we clearly find that the LUMO state of the ZnO is now pushed down upon the doping of Mn atom, crossing the Fermi level which suggests metallic nature. It is noted that the degeneracy of the two lowest unoccupied states at point A of the Brillouin zone is now removed. It is also noted that there are two new occupied states (acceptor states) in the interval EF 1.2 eV. These states are degenerate at the G point. It is important to note that the band structure above the Fermi level is quite similar to that of the undoped ZnO structure. The minority spin channel, on the other hand, is metallic with the LUMO state crosses the Fermi level around the G point. Less dispersive bands are now observed in the interval 1.8–3.0 eV above the Fermi level. These bands are believed to be originated from the hybridization between the Mn d states and p states of the environment. Below the Fermi level, the electronic band structure retains the fundamental behaviour of ZnO structure. It is rather important to note that a significant change in the electronic band structure has been revealed upon the inclusion of U in the calculations. It is clearly noted, in Fig. 5(a), that the unoccupied bands have been shifted upward while the occupied states have been shifted downwards, leading the majority channel to nearly cross the Fermi level which indicates metallic behaviour. It is also noted that the acceptor states that are created at approximately 1.2 eV below the Fermi level, have slightly been shifted down. These states along with the magnetic moment suggest that the electronic scenario of Mn–ZnO system can be explained by 3d5 þ acceptor. This conclusion is different from that

Fig. 5. Electronic band structure of ZnMnO, along the highly symmetry direction of Brillouin zone, for (a) the majority and (b) minority channels. These calculations were performed with U.

drawn for Mn-doped GaAs [14]. It is found that the possible electronic configuration for such a Mn–GaAs system is 3d4 þ hole. The degeneracy of these acceptor states at the G point has not been removed upon the inclusion of the Hubbard potential. The lowest unoccupied state of the minority channel, as indicated in Fig. 5(b), slightly touches the Fermi level, suggesting a semiconducting nature with a direct band gap of approximately 1.32 eV. Overall, the Mn–ZnO system is half-metallic with the help of the Hubbard potential. From the previous, it is obviously noted that the Coulomb potential U plays a dominant role in the interaction of Mn d states with ZnO host valence bands. This leads us to conclude that the use of the standard XC functional (LSDA or sGGA) is not enough to sufficiently describe the electronic structure of DMS. We have examined the orbital natures of the electronic states slightly below the Fermi level by plotting their partial charge densities, as shown in Fig. 6. Panels (a) and (b) show the partial charge density plots for the two highest occupied states (shown in Fig. 5(a)) at the zone edge (point M). It is found that the highest band is entirely contributed by the Mn dxy orbital (Fig. 6(a)), while the second highest occupied state mainly originates from the O pz orbital (Fig. 6(b)). To easily reveal the essential changes in the electronic properties of pure ZnO structure upon the incorporation of Mn atom, we have plotted the total density of states (DOS) for both channels along with the DOS of the clean ZnO structure, as shown in Fig. 7. It is clear that some peaks in both the majority and minority

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[100]

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[001]

[010]

[100]

Fig. 6. The partial charge density plots of the (a) highest occupied state and (b) the second highest occupied state (shown in Fig. 5(a)) at the zone edge (point M).

Fig. 7. The total density of state (DOS) of the Mn-doped ZnO structure for both spin-up and spin-down channels. For comparison, the DOS of pure ZnO is depicted. The inset shows a magnification in small energy interval, close to Fermi level.

states are appreciably shifted from their original positions when the adatom has been doped. For the spin-up channel diagram, we observe two small shoulders appear in the regions 2.0–3.0 eV below the Fermi level. Moreover, a birth of new developed peaks at EF 0.6 and EF  5.0 eV is noticed. These peaks have also been observed in a previous work [28]. The minority state, however, produces the following changes. (i) The peak at about 1.0 eV below the Fermi level is removed upon the doping of Mn atom, (ii) a well-developed peak is now created at about EF þ4.0 eV, and (iii) the peak at EF þ3.0 eV is now turned into a shoulder at approximately the same energetic position. These observations are supportive of the band structure calculations. In Fig. 8, we have shown the total charge density along the lines joining the Mn atom with its neighboring O atom. It is obviously shown that there is a clear bond formation between Mn and O atoms. This bond has little degree of covalency, but shows a large amount of ionic nature. It is also shown that a large amount of charge is condensed around the Mn atoms. For comparison, we have calculated the total charge density of the rocksalt MnO structure. We have plotted the charge density along the Mn–O bond. It is clearly noted that the charge ratio (Mn/O) is approximately 3.5 which is typical for these species. The bond formation

Fig. 8. The total charge density along the Mn–O bond of the Mn-doped ZnO structure (solid curve) and of the rocksalt MnO structure (dashed curve).

between the atoms is quite ionic. Comparing this with our studied system we conclude that the bond formation between Mn and O atoms in ZnMnO is quite similar to the typical Mn–O bond but with smaller charge ratio of 3.1. Furthermore, it is found that, upon the doping of Mn atom, the total charge density along the O–Zn–O bond is slightly different from that of the clean ZnO structure, as shown in Fig. 9. There is little spreading (redistribution) of the charge around the Zn atom, leading the peak to be slightly expanded. This suggests that the wavefunction of Zn atom is less localized upon the doping of Mn atom. However, the bond retains its ionic nature with slight redistribution of charge around the O atoms. To elucidate the charge accumulation around the atomic species of the Mn-doped ZnO structure, we have performed contour plot for the total charge density in the xy plane, as shown in Fig. 10. Unlike the charge density of the pure ZnO structure [36], it is clearly shown that there is much more amount of charge being localized around the O components. Moreover, it is revealed that a large amount of charge is localized around the Mn atom. The density at electron cloud between Mn and O atoms is larger than that between Zn and O, indicating stronger interaction occurs between the dopont and O atoms. Moreover, we have simulated scanning tunneling microscopy (STM) images of the Mn-doped ZnO structure. Our theoretical STM

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Fig. 9. The total charge density along the line joining the Zn atom with its nearest neighbors O atoms of the Mn-doped ZnO structure.

Fig. 10. Contour plot of the total charge density in the [1 1 0] plane for ZnMnO structure.

images are performed using the Tersoff–Hamann method [37] in the constant-height mode. The tunneling current is derived from the local density of states close to the Fermi energy EF. Using this model, we have simulated STM images for both the filled and empty states from the electronic energy calculations by integrating over the energy range EF to EF þeVB, where VB is the bias voltage. Considering a bias voltage of 2.0 V below and above the Fermi level EF, we have performed and shown the STM images in Fig. 11. The plotting plane of the simulated STM images has been chosen to be slightly above the Mn atom forming the zigzag chain with its neighbors. Our simulated STM image of the empty state, shown in Fig. 11(a), clearly indicates significantly large values of brightness on both Zn and Mn atoms, suggesting that these protrusions are significantly contributed by the electronic charge transfer. The occupied STM image, shown in Fig. 11(b), is brighter around the O atoms with two levels of brightness as clearly seen in the top and bottom zigzag chains shown in the figure.

Fig. 11. The simulated scanning tunneling microscopy (STM) images for both the (a) empty and (b) filled states of the Mn-doped ZnO structure with a bias voltage of 7 2.0 V.

4. Summary and conclusion In the present article we have performed calculations for the ZnO structure upon the doping of 6.25% of Mn atoms. The calculations were carried out within both the sGGA and sGGA þU approaches. We have shown that the use of Hubbard potential U in such a system plays an important role in determining the accurate electronic and structural properties. Within the sGGAþ U method, it was found that the Mn–O bond length has ˚ Moreover, it was been elongated by 0.05 A˚ to become 1.94 A. measured that the Zn–O bond lengths, with O atom close to the

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˚ Mn atom, is 1.85 A˚ while the other Zn–O bond length is 1.87 A. The magnetic moment has been also modified to become 5.04 mB/ Mn. This indicates that the electronic scenario of Mn–ZnO system can be explained by 3d5 þacceptor states scenario, which is different from that of Mn-doped GaAs where the system was described by 3d4 þ hole state. The overall system behaves like half metallic with metallic nature in the spin-up channel and semiconducting nature for the spin-down channel. Several empty and filled peaks were observed in the density of states (DOS) with appreciable redistribution of the pure ZnO peaks upon the incorporation of Mn atom. Scanning tunneling microscopy (STM) images for both unoccupied and occupied states indicate large values of brightness on both Zn and Mn atoms and much brighter protrusions around the O atoms, respectively.

References [1] P. Kacman, Sci. Technol. 16 (2001) R25. [2] S.A. Wolf, D.D. Awschalom, R.A. Buhrman, J.M. Daughton, S. von Molna´r, M.L. Roukes, A.Y. Chtchelkanova, D.M. Treger, Science 294 (2001) 1488. [3] S.J. Pearton, C.R. Abernathy, M.E. Overberg, G.T. Thaler, D.P. Norton, N. Theodoropoulou, A.F. Hebard, Y.D. Park, F. Ren, J. Kim, L.A. Boatner, J. Appl. Phys. 93 (2003) 1. [4] H. Ohno, Science 281 (1998) 951. [5] Y. Ohno, D.K. Young, B. Beschoten, F. Matsukura, H. Ohno, D.D. Awschalom, Nature 402 (1999) 790. [6] G. Prinz, J. Krebs, Appl. Phys. Lett. 39 (1981) 397. [7] H. Wu, M. Hortamani, P. Kratzer, M. Scheffler, Phys. Rev. Lett. 92 (2004) 237202. [8] H. Wu, P. Kratzer, M. Scheffler, Phys. Rev. B 72 (2005) 144425. [9] R.A. de Groot, F.M. Mueller, P.G. van Engen, K.H.J. Buschow, Phys. Rev. Lett. 50 (1983) 2024. [10] M. Hortamani, H. Wu, P. Kratzer, M. Scheffler, Phys. Rev. B 74 (2006) 205305. [11] 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 (1988) 85.

3981

[12] K.C. Ku, S.J. Potashnik, R.F. Wang, S.H. Chun, P. Schiffer, N. Samarth, M.J. Seong, A. Mascarenhas, E. Johnston-Halperin, R.C. Myers, A.C. Gossard, D.D. Awschalom, Appl. Phys. Lett. 82 (2003) 2302. [13] D. Chiba, K. Takamura, F. Matsukura, H. Ohno, Appl. Phys. Lett. 82 (2003) 3020. [14] A.Z. AlZahrani, G.P. Srivastava, R. Garg, M.A. Migliorato, J. Phys. Condens. Matter 21 (2009) 485504. [15] A.M. Yakunin, A. Yu Silov, P.M. Koenraad, J.H. Wolter, W. Van Roy, J. De Boeck, J.-M. Tang, M.E. Flatte, Phys. Rev. Lett. 92 (2004) 216806. [16] D. Kitchen, A. Richardella, J.-M. Tang, M.E. Flatte, A. Yazdani, Nature 442 (2006) 436. [17] A.M. Yakunin, A. Yu Silov, P.M. Koenraad, J.-M. Tang, M.E. Flatte, J-L. Primus, W. Van Roy, J. De Boeck, A.M. Monakhov, K.S. Romanov, I.E. Panaiotti, N.S. Averkiev, Nat. Mater. 6 (2007) 512. [18] D. Kitchen, A. Richardella, J.-M. Tang, M.E. Flatte, A. Yazdani, Nature 442 (2006) 436. [19] Y.D. Park, A. Wilson, A.T. Hanbicki, J.E. Mattson, T.F. Ambrose, G. Spanos, B.T. Jonker, Appl. Phys. Lett. 78 (2001) 2739. [20] F.M. Zhang, X.C. Liu, J. Gao, X.S. Wu, Y.W. Du, H. Zhu, J.Q. Xiao, P. Chen, Appl. Phys. Lett. 85 (2004) 786. [21] F.M. Zhang, Y. Zeng, J. Gao, X.C. Liu, X.S. Wu, Y.W. Du, J. Magn. Magn. Mater. 282 (2004) 216. [22] Y. Miura, H. Uchida, Y. Oba, K. Nagao, M. Shirai, J. Phys. Condens. Matter 16 (2004) 5735. [23] S. Yabuuchi, E. Ohta, H. Kageshima, A. Taguchi, Physica B 376–377 (2006) 672. [24] A.Z. AlZahrani, Physica B 405 (2010) 4195. [25] A. Reber, S.N. Khanna, J.S. Hunjan, M.R. Beltran, Chem. Phys. Lett. 428 (2006) 376. [26] H.T. Liu, S.Y. Wang, G. Zhou, J. Wu, W.H. Duan, J. Chem. Phys. 124 (2006) 174705. [27] Q. Chen, J. Wang, Chem. Phys. Lett. 474 (2009) 336. [28] N. Ganguli, I. Dasgupta, B. Sanyal, J. Appl. Phys. 108 (2010) 123911. [29] B.N. Dole, V.D. Mote, V.R. Huse, Y. Purushotham, M.K. Lande, K.M. Jadhav, S.S. Shah., Curr. Appl. Phys. 11 (2011) 762. [30] P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864. [31] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [32] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [33] W. Kohn, L. Sham, Phys. Rev. 140 (1965) A1133. [34] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [35] M.A. Gorbunovaa, I.R. Sheinb, Yu.N. Makurina, V.S. Kiikoa, A.L. Ivanovskiib, Physica B 400 (2007) 47. [36] A.S. Mohammadi, S.M. Baizaee, H. Salehi, World Appl. Sci. J. 14 (2011) 1530. [37] J. Tersoff, D.R. Hamann, Phys. Rev. B 31 (1985) 805.