16710
J. Phys. Chem. C 2010, 114, 16710–16715
A New Half-Metallic Ferromagnet La2NiFeO6: Predicted from First-Principles Calculations Shuhui Lv,†,‡ Hongping Li,†,‡ Xiaojuan Liu,*,† Deming Han,† Zhijian Wu,† and Jian Meng*,† State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China, and Graduate School, Chinese Academy of Sciences, Beijing 100049, P. R. China ReceiVed: May 20, 2010; ReVised Manuscript ReceiVed: July 19, 2010
Electronic structure calculations based on density functional theory in both optimized monoclinic (No. 14 P21/n) and rhombohedral (No. 148 R3j) phases of La2NiFeO6 have been performed using full-potential linearized augmented plane wave method. The result indicates that La2NiFeO6 is a half-metallic ferromagnet within both crystal structures, and electronic correlation (U) plays a vital role in stabilizing the ferromagnetic ground state. Substitution of Mn4+ with Fe3+ induces a hole on Ni, making the transition of semiconducting La2Ni2+Mn4+O6 to half-metallic La2Ni3+Fe3+O6. Moreover, the half-metallicity is found to be robust under the compressive and tensile strains for both phases. The magnetic interaction constant is calculated according to the Heisenberg model, from which the Curie temperature is estimated within the mean field approximation. The Curie temperature is predicted to be as large as 495 and 474 K in P21/n and R3j, respectively, making this system interesting candidates in spintronic devices. 1. Introduction Spintronics is currently a rather hot topic because it offers opportunities for a new generation of multifunctional devices.1,2 The main task to boost the development of spintronics and to design new materials is how to efficiently manipulate the spin polarization of current. Half-metals (HMs), which are metallic for one spin channel and insulating for the other, are considered as the key ingredients for future high-performance spintronic devices. For HM, the spin polarization is 100% at the Fermi level without any external operation. Since the first discovery of half-metallic ferromagnets (HMF) by de Groot et al. in 1983,3 the intensive searches for these kinds of materials, in particular with high Curie temperature (TC), have been conducted. To find new HMs with TC above room temperature is important in both fundamental science and technological applications. Up to now, half-metallic properties have been found in diverse compounds, such as spinel Fe3O4;4 Heusler alloys NiMnSb5 and Co2MnSi;6 rutile CrO2;7 mixed-valence perovskite La0.7Sr0.3MnO3;8 double perovskites Sr2FeMoO69 and Sr2CrReO6;10,11 and zinc-blende structure compounds MnBi,12 CrSb,13 Al1-xCrxAs,14 etc. Unlike superconductors, metals, semiconductors, or insulators, where there is a clear indication in electrical transport, halfmetals have features that are quite different from conventional ferromagnetic metals because the half-metallic property is not easily detected by the experiments. Therefore, band structure calculations are important in identifying HMs and exploring new half-metallic compounds. Recently La2NiMnO6 (LNMO)15,16 was found to be a ferromagnetic insulator with a Curie temperature close to room temperature with Ni2+ and Mn4+. It is expected that if Mn is substituted by Fe, that is, La2NiFeO6 (LNFO), half-metallic property may be realized, since Fe is prone to exist in +3 or +5 state, which will induce a hole or electron on Ni sites. Thus, * Corresponding authors. E-mail:
[email protected] (J.M.) and lxjuan@ ciac.jl.cn (X.L.). Telephone: +86-431-85262030; +86-431-85262415. Fax: +86-431-85698041. † Changchun Institute of Applied Chemistry. ‡ Graduate School.
a comprehensive investigation including the crystal structures, covalent states of Ni and Fe, electronic structure, and transition temperature of magnetic coupling on LNFO has been carried out. The crystal structures are based on the experimentally determined structure of LNMO, and other relevant calculated results are also compared with corresponding determinations of LNMO if possible. 2. Computational Methods Geometry predictions were performed within the CASTEP code17 based on the experimentally synthesized compound LNMO. It was found that the structure of LNMO is rhombohedral (R3j) at high temperature and transforms to monoclinic (P21/n) at low temperature. Then our calculations on LNFO were performed on these two space groups. The Vanderbilt ultrasoft pseudopotential,18 which describes the interaction of valence electrons with ions, was used with the cutoff energy of 340 eV. The exchange and correlation functional were treated by the generalized gradient approximation by Perdew, Burke, and Ernzerhof (GGA-PBE).19 The unit cell was fully relaxed, until the self-consistent field convergence per atom, tolerances for total energy, root-mean-square (rms) displacement of atoms, the maximum ionic Hellmann-Feynman force, and the stress tensor were less than 1.0 × 10-6 eV, 1.0 × 10-5 eV, 0.001 Å, 0.03 eV/Å, and 0.05 GPa, respectively. The electronic and magnetic properties were calculated within the framework of density functional theory (DFT) using the fullpotential linearized augmented plane wave (FPLAPW) plus local orbital method (LO),20,21 as implemented in the WIEN2K code.22 In this method, the space is divided into nonoverlapping muffintin spheres surrounding the atoms and an interstitial region. Most important, this method assumes no shape approximation of the potential, wave functions, or charge density. The spherical harmonic expansion of the potential was performed up to lmax ) 10. The value of RmtKmax (the smallest muffin-tin radius multiplied by the maximum k value in the expansion of plane waves in the basis set), which determines the accuracy of the basis set used, is set to 7.0. The nonoverlapping muffin-tin radii
10.1021/jp104617q 2010 American Chemical Society Published on Web 09/10/2010
A New Half-Metallic Ferromagnet La2NiFeO6
J. Phys. Chem. C, Vol. 114, No. 39, 2010 16711
Figure 1. Crystal structures of (a) the P21/n phase and (b) the R3j phase (represented by the conventional hexagonal unit cell) for La2NiFeO6.
TABLE 1: Optimized Structure Parameters of Spin-Polarized La2NiFeO6 in Rhombohedral (R3j) and Monoclinic (P21/n) Phases lattice parameters a ) 5.502 Å R ) 61.146°
b ) 5.502 Å β ) 61.146°
a ) 5.588 Å R ) 90.000°
b ) 5.527 Å β ) 90.653°
atom Rhombohedral c ) 5.502 Å La γ ) 61.146° Ni Fe O c ) 7.899 Å γ ) 90.000°
Monoclinic La Ni Fe O1 O2 O3
(RMT) used are 2.38, 1.95, 1.90, and 1.68 bohrs for La, Ni, Fe, and O, respectively. For the exchange-correlation energy functional, the GGA-PBE was also employed.19 In the whole Brillouin zone, 1000 k points were used. The Brillouin zone integration is carried out with a modified tetrahedron method.23 The self-consistent calculations were considered to be converged when the energy convergence is less than 10-5 Ry. It is well-known that GGA often underestimates the energy band gap for systems with strongly localized d orbitals or that even metallic behavior is predicted for materials that are known to be insulators.24 The main reason for this failure is the selfinteraction error (the electrostatic interaction of an electron with itself) that is contained in these approximate functions and their associated potentials (functional derivative).25 To improve the description of solids containing localized d (or f) electrons, onsite Coulomb repulsion has to be taken into account in the calculations of correlated electron systems by the “+U method”, based on the Hubbard’s model. The +U method requires two parameters, the Hubbard parameter U and the exchange interaction J. The parameter U gives the strength of the Coulomb repulsion between these orbitals, while J describes the on-site exchange interaction between these orbitals. Since there is no unique way in how to choose a reasonable Hubbard term within the DFT framework, several different approaches are available which give similar results. In this work we use the approach described by Dudarev et al.,26 where only an effective Hubbard parameter Ueff ) U - J determines an orbital-dependent correction to the DFT energy. For simplicity, we use the U to represent the effective parameter Ueff in the following paper.
x
y
z
0.249 85 0.0 0.5 0.809 47
0.249 85 0.0 0.5 0.692 28
0.249 85 0.0 0.5 0.250 20
0.004 12 0.0 0.5 0.269 37 0.271 40 0.566 83
0.025 98 0.5 0.0 0.271 61 0.270 59 -0.007 73
0.243 31 0.0 0.0 0.036 93 0.463 87 0.249 86
The +U method has been successfully applied to describe the electronic structure of strong correlated systems.27,28 3. Results and Discussion Crystal Structure. The crystal structures for both P21/n and R3j phases were optimized with and without spin polarization. The calculated results show that the total energies with spin polarization are always lower than that without spin polarization, suggesting that the ground state of La2NiFeO6 is spin-polarized. Therefore, only the results from spin-polarized situation are given below. The two optimized crystals structures (P21/n and R3j) of LNFO are shown in Figure 1a,b and the optimized lattice parameters and atomic positions are given in Table 1. The result indicates that P21/n is the lower energy crystal structure, which is about 7.0 meV lower than that of R3j. On the basis of this result and the existing experimental determination on LNMO, we can conclude that LNFO also probably exists as two crystal structures of R3j and P21/n, with R3j being the high-temperature structure and P21/n the low-temperature structure. It is seen that for both Ni and Fe sites all the Ni-O (Fe-O) bond distances are the same with 1.983 Å (1.996 Å) in R3j phase while they are split into three different bond distances which are 2.016, 1.980, and 1.985 Å (2.005, 2.002, and 1.999 Å) in P21/n phase due to its further distortion. Consequently, Ni and Fe 3d orbitals split differently in these two phase: in the R3j phase five 3d orbitals split into 3z2 - r2, {x2 - y2, xy}, {xz, yz}, while the five 3d orbitals are completely split in the P21/n phase. In these two phases, each NiO6 octahedron is tilted with
16712
J. Phys. Chem. C, Vol. 114, No. 39, 2010
Lv et al.
TABLE 2: Calculated Total Energy Differences of FiM Relative to FM Configuration Per Formula Unit (fu) for La2NiFeO6 in the Monoclinic Phase within Both GGA+U and LSDA+U Methods; Magnetic Moments of Ni, Fe, and O; and the Total Magnetic Moment at FM Ordering Per Formula Unit M (µB) UNi/UFe (eV)
∆E (eV/fu)
0.0/0.0 5.0/4.0 6.0/4.0 7.0/4.0 6.0/3.0 6.0/5.0
-0.06 0.32 0.48 0.60 0.53 0.42
0.0/0.0 5.0/4.0 6.0/4.0 7.0/4.0 6.0/3.0 6.0/5.0
-0.29 0.22 0.32 0.41 0.35 0.29
Ni
Fe
O
total
GGA+U 0.74 1.52 1.58 1.63 1.60 1.57
3.05 3.91 3.90 3.88 3.79 3.98
0.08 0.05 0.04 0.04 0.05 0.04
4.60 6.00 6.00 6.00 6.00 6.00
LDSA+U 1.26 1.46 1.53 1.58 1.55 1.50
3.45 3.86 3.84 3.83 3.74 3.93
0.16 0.07 0.06 0.05 0.07 0.05
6.00 6.00 6.00 6.00 6.00 6.00
respect to the FeO6 octahedron, giving rise to the Ni-O-Fe bond angle of 158.4° and 161.0° in P21/n and R3j, respectively, which is comparable with the corresponding Ni-O-Mn angle of 156.5° and 157.1° in LNMO.15 Although there are some differences in the structural parameters between the two crystal phases, we obtained similar features in the computed density of states and band structures and half-metallic solutions for both P21/n and R3j phases. Thus, in the following, for some results we only provide and discuss the calculated results for P21/n phase and the corresponding similar results for R3j phase are provided in the Supporting Information, while for some outcomes we present the results for both phases when it is necessary. Magnetic Property. Total energy calculations within GGA were performed for both ferromagnetic (FM) and ferrimagnetic (FiM) configurations of Ni and Fe moments. Furthermore, in order to investigate how the magnetic structures depend on electron localization, GGA+U calculations were conducted by using different U values (UNi from 5.0-7.0 eV, UFe from 3.0-5.0 eV). The calculated results are listed in Table 2 for P21/n and the corresponding result for R3j is given in the Supporting Information (Table S1). It is shown that for both phases the total energy with FiM ordering is lower than that with FM ordering in GGA (UNi ) UFe ) 0.0 eV) calculation. Nevertheless, contrary to the results of GGA, FM configuration becomes more stable by GGA+U calculation within any combination of UNi and UFe. This means that the ground state magnetic order is sensitive to the local Coulomb repulsion U. Similar phenomena were also observed for the structural change of MnV2O4 upon U, in which, among the two space groups considered (i.e., I41/amd and I41/a), I41/amd is more stable when the U - J is smaller than 1 eV, while for U - J > 1 eV, I41/a is more stable.29 Furthermore, it is found that with the increase of U, FM becomes more stable than FiM due to larger energy difference between FM and FiM. Since the local Coulomb repulsion U is important for both Fe and Ni, we conclude that the ground state of LNFO should be FM, which is the same as that in LNMO.15,16 From Table 2, we note that the magnetic moments mainly come from Ni and Fe sites in FM configuration. Oxygen carries a small but nonvanishing moment due to large hybridization with magnetic ions. The total magnetic moment value per unit cell is an integer (6.0 µB) at GGA+U calculation, which is a characteristic feature of HMs.
It is well-known that it is very difficult to choose a reasonable U to reproduce the experimental data because the parameter U is system-dependent and its variation with its environment is not well understood. Usually, the application of parameter U will enhance the localization of transition-metal elements (thereby increasing the magnetic moment) and push unoccupied states to a high energy level (thereby producing or increasing the energy gap). Therefore, if the energy gap is available experimentally, U can be selected by fitting the experimental value. In the case in which the energy gap is not available, like LNFO, it is hard to find a reasonable U. Generally, the parameter U is selected from the previous theoretical studies containing Fe and/or Ni. In addition, a series of U values is also necessary to find a suitable U. Since the electronic correlations gradually strengthen as the atomic number of transition metal increase from Ti to Cu, we considered different U values for Fe and Ni, where UFe is from 3.0 to 5.0 eV and UNi from 5.0 to 7.0 eV, as listed in Table 2 within GGA+U methods in P21/n phase. We note that the magnetic moment of Ni increases as UNi increases from 5.0 to 7.0 eV with UFe being fixed at 4.0 eV in the meantime. Similarly, the magnetic moment of Fe is also enhanced as UFe increase from 3.0 to 5.0 eV with UNi fixed at 6.0 eV. However, the calculated total magnetic moment for each formula unit remains nearly unchanged, i.e., 6.0 µB (see Table 2). Actually, for different U combinations, they all show quite similar half-metallic behavior. Thus, together with the U values adopted by previous studies,28,30 we choose the results from UFe ) 4.0 eV and UNi ) 6.0 eV for further discussions below. The same calculations are also performed on the basis of LSDA and LSDA+U methods (see Table 2). Similar results are obtained within LSDA+U calculations for the two phases as those of GGA+U results. Taking P21/n phase as an example, FiM state energy is lower by -0.29 eV than that of FM within LSDA while within LSDA+U the FM state is more stable by 0.32 eV (UNi/UFe ) 6.0/4.0 eV) than the FiM state (See Table 2). The band gap enlarged from 1.85 to 2.34 eV for UNi/UFe from 6.0/ 3.0 eV to 6.0/5.0 eV. On the basis of these results, it can be safely concluded that LNFO is a half-metallic ferromagnet. Electronic Structure. We now discuss the electronic structures of LNFO. The GGA+U band structure and the spindependent total and orbital projected density of states (DOS) are presented in Figure 2 for the P21/n phase. For the R3j phase, we present the corresponding results in the Supporting Information (Figure S1). It is clear that LNFO is half-metallic with the spin-up channel being metallic and the spin-down channel being insulating. The metallic behavior in the majority spin channel is mainly due to the hybridization of Ni 3d and O 2p at the Fermi energy level (see the inset of the middle panel in Figure 2). Fe 3d states are located in the lower energy region from -8 to -6 eV in the spin-up channel, while it is nearly empty for spin-down channel. The narrow band indicates the highly localized electrons. For the spin-up channel, the top of the valence band is mainly attributed to Ni 3d states, hybridized with O 2p, while the bottom of the conduction band is primarily attributed to Fe 3d states. Due to the exchange splitting of Fe 3d states, the minority spin states of Fe 3d are pushed completely above the Fermi level and give a direct energy gap of 2.30 eV. Within the LSDA+U method, we only present the relevant total and partial density of states in Figure 3, which is similar to the results within GGA+U (see Figure 2, middle). We further comparatively analyze the partial DOS (PDOS) of the 3d states of Fe and Ni and the O 2p states in the two phases, which is shown in Figure 4a for P21/n and Figure 4b for R3j. At the P21/n phase (See Figure 4a), the bands at the
A New Half-Metallic Ferromagnet La2NiFeO6
J. Phys. Chem. C, Vol. 114, No. 39, 2010 16713
Figure 2. GGA+U (UNi ) 6.0 eV, UFe ) 4.0 eV) band structure for La2NiFeO6 in the P21/n phase: left panel, minority spin; right panel, majority spin. The horizontal red line denotes the Fermi energy level. The middle panel is the total density of states (black solid line) and density of states projected on the Ni 3d (green dashed dotted line), Fe 3d (blue short dashed line), and O 2p (red solid line with shadow).
Figure 3. LSDA+U (UNi ) 6.0 eV, UFe ) 4.0 eV) calculated total density of states (black solid line) and partial density of states for La2NiFeO6 in the P21/n phase: Ni 3d (green dashed dotted line), Fe 3d (blue short dashed line), and O 2p (red solid line with shadow). The vertical red line denotes the Fermi energy level.
Fermi level mainly come from the hybridization between Ni 3d and O px and py orbitals. The completely splitting five Fe 3d orbitals are all occupied for spin-up, while they are all above the Fermi level for spin-down. Quantitative analysis on electronic occupation for Fe 3d orbitals are (dz2)0.89(dx2-y2)0.9(dxy)0.8(dxz)0.97(dyz)0.9 for the spin-up channel, while they are zero for the spin-down channel; thus, the total covalent electron number is 4.46, that is, the covalent state of Fe is Fe3.54+. For Ni, the electronic occupation is (dz2)0.89(dx2-y2)0.94(dxy)0.88(dxz)0.94(dyz)0.93 for the spin-up channel while they are (dz2)0.18(dx2-y2)0.93(dxy)0.16(dxz)0.89(dyz)0.90 for the spin-down channel. Then the total covalent electron number is 7.65, resulting in the covalent state of Ni being Ni2.36+. Similarly for the R3j phase, the bands at the Fermi level are also mainly from the hybridization between Ni 3d orbitals with O px and pz orbitals. The five 3d states of Fe are occupied with a narrow bandwidth in the spin-up channel. For Ni 3d orbitals, the double occupation of dz2 allows a considerable reduction of the intra-atomic Coulomb repulsion.32,32 The two doubly degenerate orbitals {dx2-y2, dxy} and {dxz, dyz} are occupied by electrons in both spin channels and they ({dx2-y2, dxy} and {dxz, dyz}) are nearly degenerate. A similar situation was also discovered in previous studies.33,34 Further quantitative analysis on the electronic occupation for Ni 3d orbitals are (dz2)0.92(dx2-y2 + dxy)1.82(dxz + dyz)1.79 for the spin-up channel and (dz2)0.92(dx2-y2 + dxy)1.29(dxz + dyz)0.81 for the spin-down channel. For Fe it is (dz2)0.92(dx2-y2 + dxy)1.79(dxz + dyz)1.77 for the spin-up channel and zero for the spin-down channel. These results give the valence state of Ni being +2.45 and Fe +3.52. Thus, in
both crystal phases we can figure out that Ni and Fe show the same covalent state, with Ni being about 3+ (Ni3+: d7) and Fe being about 3+ (Fe3+: d5). From PDOS of both parts a and b of Figure 4, we can see that there is some mixture between spin-up and spin-down channels for Ni, which leads to the calculated magnetic moments (about 1.58 µB) being largely reduced from their expected values (Ni3+: d7 with 3 µB). The detailed analysis above reveals the microscopic mechanism of the transition from semiconducting LNMO to half-metallic LNFO. In LNMO, the covalent state of Mn is +4 and Ni +2. Nevertheless, when Fe replaces Mn ion, namely LNFO, Fe ion is prone to be +3, as shown above, which induces a hole on Ni sites. Consequently, the covalent state of Ni is changed from +2 for LNMO to +3 for LNFO, resulting in the half-metallic property of LNFO. Since the breathing distortion of the octahedron in double perovskite plays a very important role in physical properties,35 we have studied the robustness of the half-metallic ground state with respect to the compressive and tensile strains. We consider that if LNFO is supposed to be a film material, then the lattice constant will be slightly reduced or elongated due to a biaxial strain. To examine the effect of the in-plane strain on the electronic properties, we perform band electronic structure calculations with GGA+U on LNFO at a 5% compression as well as 5% expansion of its equilibrium lattice constant. In both cases volume is kept fixed. We optimized all the atom positions to reach the energy minimum. In Figure 5, taking R3j as an example, we show the total DOS of LNFO in both compressive and tensile strains. We note that it remains metallic in the spinup channel, while spin gaps of 2.0 and 1.5 eV are obtained in the spin-down channel in compressive and tensile situations, respectively. Further, it is known to us that an important property of HMs is their half-metallic gap, which is defined as the minimum between the lowest energy of majority-spin (or minority-spin) conduction bands with respect to the Fermi level and the absolute values of the highest energy of the majorityspin (or minority-spin) valence bands also with respect to the Fermi level.13 The GGA+U-predicted half-metallic gap for LNFO at its equilibrium constants is 0.91 eV (see Figure 2), which is comparable with the large half-metallic gap of CrTe (0.88 eV).36 When external strains are imposed, the half-metallic gap persists to be nonzero, giving the value of 0.82 eV for compression and 0.40 eV for elongation, which indicates the robustness of the half-metallicity. Note that the half-metallic gap decreases larger in elongation than that in compression. This is because the Fermi level moves downward for elongation, but
16714
J. Phys. Chem. C, Vol. 114, No. 39, 2010
Lv et al.
Figure 4. The orbital-decomposed partial density of states for (a) the P21/n phase and (b) the R3j phase obtained from the GGA+U method. The vertical red line denotes the Fermi energy level.
H)-
∑ JijSiSj
(1)
where Jij is the exchange parameter between two transition metal sites (i, j), which can be extracted by comparing the total energies for different magnetic configurations. J < 0 (J > 0) represents AFM (FM) interactions, and Si ) 3/2 on the Ni sites and 5/2 on the Fe sites. For LNFO, we only consider the nearestneighbor Ni and Fe atoms in determining their exchange interaction. From the coupling constant we then estimate the magnetic ordering temperature within the mean-field approximation (MFA).37 In the MFA method, the Curie temperature is given by Figure 5. Total density of states of LNFO under biaxial strain: (a) under tensile strain and (b) under compressive strain.
upward for compression. Therefore, it is concluded that halfmetallicity is preserved with respect to in-plane strains, indicating that LNFO could be a potential candidate for spintronics to be used in practical applications. Exchange Parameters and Curie Temperature. In addition to high-spin polarization of the states at the Fermi level, an important further condition for spintronics materials is a high Curie temperature. Only a system with the Curie temperature over room temperature can be considered for wide device applications. To estimate the magnetic ordering temperature of LNFO, we calculated the intra-atomic exchange interaction according to the effective Heisenberg Hamiltonian
TCMFA )
∑
2 J 3kB j*0 0j
(2)
The calculated exchange parameters of the nearest Ni and Fe sites are 10.67 and 10.22 meV for P21/n and R3j, respectively, indicating the ferromagnetic coupling of the two transition metal elements, which is consistent with the results of the above. From J0, we obtained the magnetic ordering temperature of 495 and 474 K for P21/n and R3j, respectively, which is substantially higher than room temperature. Note that the MFA neglects the effect of fluctuation of the spins from their average values, which tends to decrease the magnetic ordering temperature. Therefore, the MFA often gives an overestimation of the actual ordering temperature.38 After all, our results could provide a theoretical basis for further experimental studies in the future.
A New Half-Metallic Ferromagnet La2NiFeO6 4. Conclusions Electronic and magnetic properties of La2NiFeO6 were predicted by using the density functional theory within GGA (LSDA) and GGA+U (LSDA+U) methods. It is found that P21/n is the lower energy crystal structure, which is similar to its isostructural compound La2NiMnO6. And La2NiFeO6 is predicted to be a ferromagnetic half-metal when reasonable U values are taken into account. Microscopic mechanism of semiconductor to half-metal transition from La2NiMnO6 to La2NiFeO6 is revealed due to the hole injection by the substitution of Mn4+ with Fe3+. The half-metallic property is robust with respect to both compression and elongation induced by in-plane strain, which suggests that La2NiFeO6 has potential applications. Further, the predicted magnetic ordering temperature is higher than room temperature, which indicates that La2NiFeO6 could be a promising candidate for future spintronic applications. Acknowledgment. This project was supported by National Natural Science Foundation of China (Grant Nos. 20831004, 90922015, 20921002, and 21071141). We appreciate the constructive advice of reviewers on this paper. Supporting Information Available: Additional information as discussed in the text. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Wolf, S. A.; Awschalom, D. D.; Buhrman, R. A.; Daughton, J. M.; von Molna´r, S.; Roukes, M. L.; Chtchelkanova, A. Y.; Treger, D. M. Science 2001, 294, 1488. (2) Zˇutic´, I.; Fabian, J.; Sarma, S. D. ReV. Mod. Phys. 2004, 76, 323. (3) de Groot, R. A.; Mueller, F. M.; van Engen, P. G.; Buschow, K. H. J. Phys. ReV. Lett. 1983, 50, 2024. (4) Yanase, A.; Siratori, K. J. Phys. Soc. Jpn. 1984, 53, 312. (5) Tanaka, C. T.; Nowak, J.; Moodera, J. S. J. Appl. Phys. 1999, 86, 6239. (6) Burzo, E.; Balazs, I.; Chioncel, L.; Arrigoni, E.; Beiuseanu, F. Phys. ReV. B 2009, 80, 214422. (7) Watts, S. M.; Wirth, S.; von Molna´r, S.; Barry, A.; Coey, J. M. D. Phys. ReV. B 2000, 61, 9621. (8) Coey, J. M. D.; Viret, M.; von Molna´r, S. AdV. Phys. 1999, 48, 167. (9) Kobayashi, K.-I.; Kimura, T.; Sawada, H.; Terakura, K.; Tokura, Y. Nature (London) 1998, 395, 677.
J. Phys. Chem. C, Vol. 114, No. 39, 2010 16715 (10) Kato, H.; Okuda, T.; Okimoto, Y.; Tomioka, Y.; Takenoya, Y.; Ohkubo, A.; Kawasaki, M.; Tokura, Y. Appl. Phys. Lett. 2002, 81, 328. (11) Vaitheeswaran, G.; Kanchana, V. Appl. Phys. Lett. 2005, 86, 032513. (12) Xu, Y.-Q.; Liu, B.-G.; Pettifor, D. G. Phys. ReV. B 2002, 66, 184435. (13) Liu, B.-G. Phys. ReV. B 2003, 67, 172411. (14) Zhao, Y.-H.; Zhao, G.-P.; Liu, Y.; Liu, B.-G. Phys. ReV. B 2009, 80, 224417. (15) Rogado, S.; Li, J.; Sleight, A. W.; Subramanian, M. A. AdV. Mater. 2005, 17, 2225. (16) Das, H.; Waghmare, U. V.; Saha-Dasgupta, T.; Sarma, D. D. Phys. ReV. Lett. 2008, 100, 186402. (17) Segall, M. D.; Lindan, P. L. D.; Probert, M. J.; Pickard, C. J.; Hasnip, P. J.; Clark, S. J.; Payne, M. C. J. J. Phys.: Condens. Matter 2002, 14, 2717. (18) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892. (19) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (20) Singh, D. J.; Nordstrom, L. PlanewaVes, Pseudopotentials and the LAPW Method, 2nd ed.; Springer: Berlin, 2006. (21) Singh, D. Phys. ReV. B 1991, 43, 6388. (22) Blaha, P.; Schwarz, K.; Madsen, G. K. H.; Kvasnicka, D.; Luitz, J. WIEN2K, An Augmented Plane WaVe and Local Orbitals Program for Calculating Crystal Properties; Technical University Wien: Vienna, 2001. (23) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953. (24) Terakura, K.; Oguchi, T.; Williams, A. R.; Ku¨bler, J. Phys. ReV. B 1984, 30, 4734. (25) Perdew, J. P.; Zunger, A. Phys. ReV. B 1981, 23, 5048. (26) Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Phys. ReV. B 1998, 57, 1505. (27) Hao, X. F.; Xu, Y. H.; Wu, Z. J.; Zhou, D. F.; Liu, X. J.; Meng, J. Phys. ReV. B 2007, 76, 1. (28) Hao, X. F.; Xu, Y. H.; Gao, F. M.; Zhou, D. F.; Meng, J. Phys. ReV. B 2009, 79, 113101. (29) Sartar, S.; Maitra, T.; Valenti, R.; Saha-Dasgupta, T. Phys. ReV. Lett. 2009, 102, 216405. (30) Yamamoto, S.; Fujiwara, T. J. Phys. Soc. Jpn. 2002, 71, 1226. (31) Xiang, H. J.; Wei, S.-H.; Whangbo, M.-H. Phys. ReV. Lett. 2008, 100, 167207. (32) Pruneda, J. M.; I´n˜iguez, J.; Canadell, E.; Kageyama, H.; Takano, M. Phys. ReV. B 2008, 78, 115101. (33) Liu, X. J.; Xiang, H. P.; Cai, P.; Hao, X. F.; Wu, Z. J.; Meng, J. J. Mater. Chem. 2006, 16, 4243. (34) Xiang, H. P.; Liu, X. J.; Zhao, E. J.; Meng, J.; Wu, Z. J. Inorg. Chem. 2007, 46, 9575. (35) Solovyev, I. V. Phys. ReV. B 2002, 65, 144446. (36) Xie, W.-H.; Xu, Y.-Q.; Liu, B.-G.; Pettifor, D. G. Phys. ReV. Lett. 2003, 91, 037204. (37) Morrish, A. H. The Physical Principles of Magnetism; Wiley-IEEE: New York, 2001. (38) Baetting, P.; Ederer, C.; Spaldin, N. A. Phys. ReV. B 2005, 72, 214105.
JP104617Q
