First-Principles Study of Half-Metallic Materials in Double-Perovskite

Aug 8, 2012 - In this work, calculations based on density functional theory were carried out with full structural optimization and using the generaliz...
0 downloads 9 Views 3MB Size
Download PDF
Article pubs.acs.org/JPCC

First-Principles Study of Half-Metallic Materials in Double-Perovskite A2FeMO6 (M = Mo, Re, and W) with IVA Group Elements Set on the A‑Site Position Y. P. Liu Department of Physics, National Taiwan Normal University, Taipei 106, Taiwan

H. R. Fuh Graduate Institute of Applied Physics, National Taiwan University, Taipei 106, Taiwan

Y. K. Wang* Center for General Education and Department of Physics, National Taiwan Normal University, Taipei 106, Taiwan ABSTRACT: In this work, calculations based on density functional theory were carried out with full structural optimization and using the generalized gradient approximation (GGA). In addition, the correlation effect (GGA+U) in the double-perovskite structure A2BB′O6 (A = Si, Ge, Sn, and Pb) is considered. As the valence electrons between IIA (s2) and IVA (p2) are similar, the IVA group of elements is settled on the A-site ion position with fixed BB′ combinations as FeM (M = Mo, Re, and W). The p−d hybridization with double exchange is the main course of the ferrimagnetic half-metallic properties. For M = Mo and Re, all compounds can be half-metallic (HM) materials, with Si2FeReO6 and Ge2FeReO6 recommended for the GGA+U process. For M = W, only A = Sn and Pb are suitable options for HM materials. However, considering that Si, Ge, Sn, and Pb are quite different from Sr, an examination of structural stability is needed. All compounds are found to be stable, except for the Sibased double-perovskite structure.

■

INTRODUCTION Half-metallic (HM) materials with high Curie temperature are found to have great low-field tunneling magnetoresistance (TMR) at room temperature. In ordered double perovskites, Sr2FeMO6 (M = Mo, Re, and W)1−9 are deemed good candidates for such magnetic electrodes. In HM materials, a well-defined gap lies along the majority channel and in the minor spin channel metallic behavior can be obtained. Thus, three characteristic properties can be observed: (1) quantization of magnetic moment, (2) 100% spin polarization at the Fermi level (EF), and (3) zero spin susceptibility. Among these phenomenon, HM materials are used in various applications such as in computer memory, magnetic recording, etc. To find more suitable candidates for such magnetic electrodes, ordered double perovskites A2BB′O6 can be used as a basis structure because a variety of options are available for substituting the A- or B-site elements. On the B-site elements, transition metal ions are used because of their diverse d orbitals at EF. On the A-site elements, alkaline-earth or rare-earth ions, such as Ca, Sr, Ba, and La, are often used as HMs. These compounds are found as Sr2MnMoO6,10 Sr2CuOsO6,11 Sr2VOsO6,12 Sr2NiRuO6,13 Sr2FeTiO6,14 Sr2CrMoO6,15,16 Sr2CoMoO6,16 Sr2CrReO6,8,17 and Sr2CrWO69,18 for the same Sr ion at the B site. Sr2MnMoO6,10 Ba2MnMoO6,19 and La2NiFeO620 stand for the A-site substitution. In this work, we © XXXX American Chemical Society

present IVA group elements sitting on the A-site ion position, which originated from alkaline-earth elements (Ca, Sr, and Ba) with valence electrons similar to the IVA group elements denoted as IIA(s2) and IVA(p2) by fixing the BB′ combinations as FeM (M = Mo, Re, and W). Nevertheless, an examination of structural stability is still needed because the elements in the IVA group are quite different from Sr. Evidently, all compounds are stable, except the Si-based double-perovskite structure. As the binding energy of the SiO2 covalent bond is too strong, the double-perovskite structure cannot be synthesized. Calculations based on density functional theory (DFT) are carried out, verifying the similarity of the electronic structures to Sr2FeMoO6, especially around EF. The common exception in HM materials for A-site IVA elements is carbon because its covalent bond is too strong that its valence is +4 instead of +2. For M = Mo and Re, all compounds can be HM materials, with Si2FeReO6 and Ge2FeReO6 recommended for strong correlation correction. For M = W, only A = Sn and Pb are deemed viable candidates for HM materials. Received: April 16, 2012 Revised: August 7, 2012

A

dx.doi.org/10.1021/jp303632z | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

■

Article

COMPUTATIONAL METHOD The theoretical calculations performed in the study were based on first-principles DFT.21 The generalized gradient approximation (GGA)22 was used to approach the exchangecorrelation potential. The full-potential projector-augmented wave (PAW)23 method implemented in the VASP code24,25 was used for the full structural optimization process (i.e., relaxation for both lattice constants and atomic positions). The 8 × 8 × 6 k-point grids were set in the Brillouin zone, and the cutoff energy of the plane wave basis was set to 450 eV. The conjugate-gradient (CG) method was used to find stable ionic positions, and the energy convergence criteria for selfconsistent calculations were set to 10−6 eV. Theoretical equilibrium structures were obtained when the forces and stresses acting on all atoms were less than 0.03 eV/Å and 0.9 kBar, respectively. The Wigner−Seitz radius of the atom was set to 2.5 au for the A-site atoms, to 2.1 au for the 3d materials, and to 1.4 au for O. The strong electron correlation systems in transition metal oxides need better a description instead of GGA calculations. However, GGA calculations can be corrected using a strong correlation correction called the GGA(LDA)+U method.26,27 The GGA(LDA)+U scheme is considered a useful approach28−30 that provides quite satisfactory results for many strongly correlated systems. Thus, the GGA+U calculations were performed in this work. The effective parameter adopted in the study was Ueff = U − J, where U and J are the Coulumb and exchange parameters, respectively (U was used in the study instead of Ueff for simplicity.). In transition metals, the near maximum values were selected from the reasonable range of U.31 For example, the range of U for Fe is 3.0−6.0 eV; 5.0 was used in the calculation. Detailed U values are listed in Table 2. In the ordered double-perovskite structure A2BB′O6 (Figure 1),

the structure is reduced from a cubic structure (Fm3m̅ ) to a tetragonal structure (space group I4/mmm, No. 139) with two nonequivalent types of O atoms, as shown in Table 1. Two O1 Table 1. Structural Parameters of the Fully Optimized Structure (I4/mmm, No. 139)a A2Fe[M] O6

a

c/a

V0 (Å3/ f.u.)

O1z

O2x

O2y

Si[Mo] Ge[Mo] Sn[Mo] Pb[Mo] Si[Re] Ge[Re] Sn[Re] Pb[Re] Si[W] Ge[W] Sn[W] Pb[W]

5.5214 5.5439 5.6255 5.6482 5.5241 5.5432 5.6224 5.6474 5.5376 5.5574 5.6399 5.6625

1.4171 1.4141 1.4149 1.4159 1.4135 1.4126 1.4152 1.4151 1.4145 1.4133 1.4154 1.4153

119.27 120.48 125.94 127.57 119.14 120.31 125.77 127.44 120.10 121.29 126.96 128.48

0.2523 0.2526 0.2543 0.2550 0.2546 0.2546 0.2560 0.2564 0.2541 0.2544 0.2564 0.2569

0.2477 0.2473 0.2457 0.2452 0.2454 0.2454 0.2441 0.2436 0.2459 0.2456 0.2436 0.2430

0.2477 0.2473 0.2457 0.2452 0.2454 0.2454 0.2441 0.2436 0.2459 0.2456 0.2436 0.2430

a

A(x,y,z) = (0, 0.5, 0.75); Fe(x,y,z) = (0, 0, 0), M(x,y,z) = (0, 0, 0.5); O1(x,y,z) = (0, 0, O1z); and O2(x,y,z) = (O2x, O2y, 0.5).

atoms are located along the z axis with B and B′ atoms in between, and four O2 atoms are located along the xy plane with similar B and B′ atoms (Figure 1 and Table 1). The angle of B−O−B′ remains at 180° during structural optimization; however, change is observed in the lattice constant and bond length. With the c/a ratio very close to the ideal value of √2, symmetry reduction is deemed rather minor. In the AF state, the tetragonal structure (P4/mmm, No. 123) remains the same during full structural optimization. Investigating structural stability is necessary because Si, Ge, Sn, and Pb are quite different from Sr. In this work, substitution of Sr with Si and Ge is critical because the covalent bond of Si and Ge is still strong. Their valences are nearly +4 instead of +2. As for the other limit, Pb is found to be suitable to be synthesized in a double-perovskite structure such as Pb2MnReO6.33 Nevertheless, all compounds in the study are verified for structural stability. Structural stability can be examined from the energy difference between the doubleperovskite structure and existing materials, such as AO(2) (A = Si, Ge, Sn, and Pb), MO2 (M = Mo, Re, and W), and FeO(2). Hence, the energy difference can be expressed by eqs 1 and 2, where the total energy of each compound is denoted by Etot(f.u.).

Figure 1. Ideal ordered double-perovskite structure A2FeMO6.

ΔE = Etot(A 2FeMO6 ) − [Etot(AO2 ) × 2 + Etot(FeO) + Etot(MO)]

four magnetic phases, namely, ferromagnetic (FM), ferrimagnetic (FiM), antimagnetic (AF), and nonmagnetic (NM), exist and are controlled by the spin state of the two B and B′ ions.

(1)

ΔE = Etot(A 2FeMO6 ) − [Etot(AO) × 2 + Etot(FeO2 )

■

+ Etot(MO2 )]

RESULTS AND DISCUSSIONS In the FM/FiM state of the ideal cubic structure (Fm3m̅ , No. 225), the B and B′ ions are in the order of NaCl configuration and can be described by a face-centered cubic (fcc) with lattice constant 2a. Each B(B′) is coordinated with B′(B), and each has an O ion in between. Hence, six B−O−B′ bonds are present per unit cell with the lengths of B−O and B′−O being equal. We consider a large unit cell with 2 f.u. to allow the structure to relax to a reduced symmetry during structural optimization calculations.32 After full structural optimization,

(2)

SiO2, GeO2, SnO2, PbO2, SnO, PbO, FeO, FeO2, and MO2 are existing materials that can be easily calculated. The case of MO is tricky because MO2 is the one that actually exists and not MO. Thus, the energy of MO can be calculated from the average of MO2 and M bulk, which can be expressed as Etot(MO) = [Etot(M) + Etot(MO2 )] × 0.5

(3)

The results indicate that all compounds remained stable, except the Si-based double-perovskite structure. The energy differB

dx.doi.org/10.1021/jp303632z | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

Table 2. Calculated Physical Properties of A2FeMO6 in the Double-Perovskite Structure with Full Structural Optimization Calculation of GGA(+U) spin magnetic moment (μB/f.u.)

ΔE (meV/f.u.)

N (EF)

band gap

A2Fe[M]O6

U(Fe, M)

MFe

MM

mtot

Fe

M

states/eV/f.u.

eV

FM-AF

FM-NM

Si[Mo]

(0,0) (5,2) (0,0) (5,2) (0,0) (5,2) (0,0) (5,2) (0,0) (5,2) (0,0) (5,2) (0,0) (5,2) (0,0) (5,2) (0,0) (5,2) (0,0) (5,2) (0,0) (5,2) (0,0) (5,2)

3.777 4.197 3.775 4.188 3.758 4.144 3.756 4.135 3.750 4.176 3.742 4.168 3.703 4.119 3.698 4.11 3.769 4.157 3.752 4.133 3.704 4.042 3.699 4.028

−0.309 −0.557 −0.323 −0.577 −0.309 −0.580 −0.310 −0.572 −0.644 −1.132 −0.741 −1.175 −0.851 −1.204 −0.854 −1.199 −0.137 −0.255 −0.159 −0.293 −0.178 −0.347 −0.174 −0.337

4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 3.274 3.000 3.142 3.000 3.000 3.000 3.000 3.000 4.054 4.105 4.033 4.072 4.000 4.000 4.000 4.000

4.878/1.132 5.038/0.877 4.875/1.132 5.030/0.878 4.856/1.129 4.995/0.887 4.851/1.126 4.986/0.887 4.868/1.150 5.021/0.881 4.864/1.154 5.051/0.883 4.841/1.170 4.984/0.900 4.835/1.169 4.975/0.901 4.879/1.139 5.021/0.899 4.875/1.150 5.030/0.914 4.847/1.172 4.974/0.965 4.842/1.173 4.965/0.971

1.940/2.283 1.814/2.394 1.929/2.285 1.801/2.399 1.922/2.261 1.786/2.384 1.913/2.252 1.781/2.371 1.760/2.425 1.529/2.667 1.714/2.471 1.508/2.687 1.655/2.518 1.488/2.694 1.647/2.512 1.483/2.683 1.977/2.150 1.894/2.174 1.964/2.157 1.875/2.191 1.942/2.150 1.839/2.203 1.937/2.140 1.836/2.189

↓3.128 ↓3.391 ↓2.980 ↓4.194 ↓3.243 ↓2.652 ↓2.421 ↓2.613 ↑2.139↓1.972 ↑3.391 ↑1.775↓2.823 ↓2.273 ↓3.201 ↓2.386 ↓3.202 ↓3.348 ↑0.205↓3.048 ↑0.423↓2.887 ↑0.142↓3.080 ↑0.278↓2.892 ↓3.184 ↓3.280 ↓3.336 ↓4.048

↑0.150 ↑1.550 ↑0.300 ↑1.700 ↑0.725 ↑1.950 ↑0.800 ↑2.300

−117.5 −113.5 −120.6 −124.8 −120.1 −127.3 −121.6 −127.8 −84.9 −151.4 −76.9 −150.3 −59.3 −131.5 −63.5 −139.0 −125.0 −126.6 −131.2 −133.6 −128.2 258.5 −130.8 −135.7

156.5 −1407.1 42.8 −1460.6 −361.6 −1588.5 −467.6 −1642.2 −359.3 −1762.4 −469.5 −1836.0 −876.0 −1955.4 −979.7 −2015.1 14.8 −1159.8 −90.2 −1171.6 −1891.6 −1249.2 −605.8 −1287.1

materials

Ge[Mo] Sn[Mo] Pb[Mo] Si[Re] Ge[Re] Sn[Re] Pb[Re] Si[W] Ge[W] Sn[W] Pb[W]

d orbital electrons↑/↓

↑1.925 ↑2.025 ↑0.825 ↑1.900 ↑0.925 ↑2.625

↑1.100 ↑2.225 ↑1.375 ↑2.275

FiM state is found to be far more stable than the NM state. For the Sn2FeWO6 in GGA+U(5,2) scheme, the AF state is more favorable than the FiM state by 258.5 meV. However, at different effective parameters U, where the values of U are lower than U(5,2), the FiM state is more stable than the AF state. For example, U(4,0) and U(4,2) are more stable by 119.9 and 138.6 meV, respectively. When the value of U is higher than U(5,2), the AF state is more stable by 506.4 meV in U(6,3). In A2FeMoO6 and A2FeReO6, the HM characteristics can be obtained from the energy gap at the spin-up channel with total magnetic moments (mtot) of 4.0 and 3.0 μB in the GGA calculation, respectively, whereas Si 2FeReO6 and Ge2FeReO6 are in the GGA+U scheme. For A2FeWO6, the HM characteristics are obtained in Si2FeWO6 and Pb2FeWO6 with mtot = 4.0 μB and an energy gap at the spin-up channel. The dependence of mtot origin on the local magnetic moment (LMM) with oxygen must be considered. However, the LMM of Fe has the greatest effect, and the M atom has a small but opposite LMM that makes up the entire material in FiM state. In fact, the negative LMM of M atoms are induced by Fe moments through hybridization of 4d(5d)−3d orbitals. Another opinion is to consider all of them in the FM state because the M atoms are intrinsically nonmagnetic that their magnetic polarization cannot countenance spontaneously. For A2FeMoO6, the LMMs of Mo are about −0.3(−0.6) μB in the GGA(GGA+U) process whereas the LMMs of Re for A2FeReO6 are about −0.6(−1.2) μB in the GGA(GGA+U) process. These two structures are similar in electronic structure in many ways (Figure 2). For A2FeWO6, the LMMs of W are about −0.1(−0.3) μB in the GGA(GGA+U) process. The LMMs of Fe in all compounds are about 0.3(0.4) μB in the GGA(GGA+U) process.

ences (ΔE) for Si, Ge, Sn, and Pb of A2FeMO6 are from about 7 to 9 eV/f.u., −1 to −3 eV/f.u., −8 to −10 eV/f.u., and −9 to −13 eV/f.u., respectively. We believe that the crystal ionic radius for Si4+ is too small that after oxidation the bond of the electrons remains close to the Si4+ ion, thereby producing a covalent bond. The binding energy of the covalent bond of SiO2 is too strong that the double-perovskite structure cannot be synthesized. Sr2FeMoO6 is found to stable as well. We present the Si-based double-perovskite structure to ensure the integrity of our work. In the FM and FiM states, each B and B′ ions ha similar a spin state (i.e., (B, B, B′, B′) = (m, m, m′, m′) = FM or (m, m, −m′, −m′) = FiM) that can lead to the assumption of the HM state. During the self-consistent process, the initial FM and FiM states all converge to the FiM state. In the AF state, the spin state of (B, B, B′, B′) is (m, −m, m′, −m′). The induced equivalence in the charges is Q↑ [B (B′)] = Q↓ [B (B′)], which can be observed from the symmetry of the spin up and spin down in the total density of state (DOS). Thus, no HM feature can be found. In the NM state, no spin polarization is observed, resulting in the absence of magnetic properties. To determine the most stable magnetic phase, calculations for all four magnetic phases are performed. Full structural optimization with high convergence criteria is also performed to guarantee the accuracy of the calculation result. From the energy difference on the order of from 101 to 102 meV/f.u. (Table 2), most of the FiM states are more favorable than the AF and NM states, except the following three compounds: Si2FeMoO6, Ge2FeMoO6, and Si2FeWO6. In the GGA calculation, the NM state is found to be more stable than the FiM state for Si2FeMoO6 and Ge2FeMoO6 by 156.5 and 42.8 meV, respectively. However, in the GGA+U scheme, the C

dx.doi.org/10.1021/jp303632z | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

Figure 2. Calculated total spin and site decomposition density of states in GGA of (a) A2FeMoO6 and (b) A2FeReO6.

and as the IVA group of elements at the A-site atom shows strong covalent characteristics near the top of the periodic table, the ionic characteristics appear stronger in that the valence from carbon to lead is noted as +4 to +2 (the others are in between) as we go deeper. Hence, in Si2FeReO6 and Ge2FeReO6, too many valence electrons are available for the p orbital of oxygen. The electrons flow into other orbitals (Re t2g), thereby inducing metallic characteristics on the compound. Hence, every carbon in the A site has no half metallicity. In Table 1, we can observe that the lattice constant and the volume of the unit cell rises with the A site atom from silicon to lead. This behavior will narrow the electron band structure and will enlarge the energy gap (Table 2). According to the calculated electron numbers, the electron configuration of A2FeReO6 is Fe3+(t2g3eg2) at S = 5/2 and Re5+(t2g2) at S = −1. Figure 3 shows the DOS of A2FeWO6 in the GGA calculations. The O-2p orbital extends from about −9 to −2

From the DOS of A2FeMoO6 and A2FeReO6 (Figure 2) in the GGA calculations, we can deduce the similarity among the electronic structures, as they share the same mechanism underlying their HM characteristics. In A2FeMo(Re)O6, the p orbital of O is extended from about −9 to −2 eV and from 0.5 to 3 eV. The Fe t2g orbital in the spin-up channel extends from about −6 to −2 eV. The eg orbital is below the Fermi level (EF) that creates the band gap with the Mo(Re) t2g orbital above EF. In the spin-down channel, the Fe and Mo(Re) t2g orbitals coexist at the EF and the main peak is observed at the same energy level just above EF (about 1 eV). In the ionic illustration, the formal valence of FeM is +8 and the electron configurations are Fe3+(t2g3eg2) at S = 5/2 and Mo5+(t2g 1) at S = −1/2 for A2FeMoO6 according to the calculated electron numbers. For Si2FeReO6 and Ge2FeReO6, the Re t2g orbitals slightly cross EF that the band gap does not exist. As the number of valence electron of Re(5d56s2) is greater than that of Mo(4d55s1) by 1 D

dx.doi.org/10.1021/jp303632z | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

As a nonmagnetic element is between the magnetic elements of Fe, the F(i)M stabilization mechanism was proposed by Terakura et al.34 Their study indicated that p−d hybridization and double exchange are the main causes of half metallicity. The fully spin-polarized magnetic elements are denoted as d states, whereas the nonmagnetic element between the spin-split d states is denoted as the p state as EF goes through the p band. When we consider the p−d hybridization, the d state pushes the p state upward (downward) at the spin-up (spin-down) channel. To keep the EF value constant, a number of electron switch spin states produces nonmagnetic elements to contribute negative moments and stabilize the F(i)M state. If such p−d hybridization is strong enough, the p state can be pushed above the EF at the spin-up channel and with the double exchange effect, the band is extended to the spin-down channel along with the EF. As such p−d hybridization does not exist in the AF configurations, the FiM states are more favored than the AF states. Fe represents the spin-split d-state magnetic elements, and M = Mo(Re) represents the p-state nonmagnetic elements. As the M = W and W-t2 g orbitals at the spin-down channel are slightly above the Fe t2g orbitals, an empty t2g band is produced and electron transfer does not occur. Given the remaining negative moments by W, p−d hybridization is still possible. As the 5d orbital of W is more extended than the 4d orbital of Mo, the energy level pushed by the hybridization of O-2p and W-5d will be more than that of Mo-4d. This hypothesis is supported by the deeper p−d bonding area of M = W compared with M = Mo. Although Mo and W are in the same row in the periodic table, reaction of Re is more similar to that of Mo rather than to that of W because the number of d electrons of Re (5d56s2) is greater than that of W (5d46s2) by 1. The result is an energy scheme for A2FeReO6 that is more similar to A2FeMoO6 than to A2FeWO6.

Figure 3. Calculated total, spin, and site-decomposed density of states of A2FeWO6 in GGA.

eV and from 0.5 to 3 eV. The Fe t2g orbital in the spin-up channel extends from about −6 to −2 eV. The eg orbital is below the Fermi level (EF) that creates the band gap at the spin-up channel with the W t2g orbital above EF. In the spindown channel, the Fe and W t2g orbitals coexist near EF, where the main difference between M = W and M = Mo(Re) is the main peak of the W t2g orbital at the spin-down channel slightly above the Fe t2g orbitals. Half metallicity appears for A = Sn, Pb(GGA), and Ge(GGA+U). The reason is the same as that for M = Re, which was described earlier in the previous paragraph. The electron configurations for A2FeWO6 are Fe3+(t2g 3eg2) at S = 5/2 and W5+(t2g1) at S = −1/2 according to the calculated electron numbers. The effects of the exchange correlation correction are similar in all compounds. Figure 4 shows the GGA+U calculations for

■

CONCLUSION Assuming that the valence electrons of IIA(s2) and IV(p2) are similar, calculations based on DFT were performed on the double-perovskite structure A2BB′O6 with fixed BB′ combinations and with FeM (M = Mo, Re, and W) and IVA group elements (Si, Ge, Sn, and Pb) lying at the A-site ion. Examination of the structural stability revealed that all compounds were stable, except the Si-based double-perovskite structure, such as that of Si2FeMO6. Thus, in A2FeMO6 (A = Ge, Sn, and Pb), with M = Mo and Re, all compounds can be HM materials, except Ge2FeReO6, for which the GGA+U process is recommended. For M = W, only A = Sn and Pb were found to be viable options for HM materials. The main courses of the HM-FiM properties were the p−d with double exchanges. We hope that the present work will encourage further experimental studies on HM materials and promote more studies on HM materials in the IVA-group double perovskites.

Figure 4. Calculated total, spin, and site-decomposed density of states of Pb2FeMO6 in GGA+U(5,2).

■

Pb2FeMO6. When the exchange correlation effect is considered, the Fe eg band is pushed deeper and becomes more localized whereas the M t2g orbitals are pushed higher in the spin-up channel. Thus, the band gap becomes wider. For example, the band gaps of Pb2FeWO6 for the GGA and GGA+U processes are 0.80 and 2.30 eV, respectively. For Si2FeReO6, no energy gap is observed in the EF that lies on the edge of the Re t2g orbitals for the GGA calculation. In the GGA+U process, the Re t2g orbitals are pushed up, thereby opening a gap with a width of 1.93 eV.

AUTHOR INFORMATION

Corresponding Author

*Phone: +886-2-7734-1130. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors gratefully acknowledge the support from the National Science Council (99B0320) and the Computational E

dx.doi.org/10.1021/jp303632z | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

Materials Research Focus Group (CMRFG). We also thank the National Center for High-Performance Computing (NCHC) of Taiwan for providing CPU time. Gratitude is extended to Drs. Zhi-Ren Xiao and Yiing-Rei Chen for consultation on the examination of structural stability. Finally, Y. K. Wang thanks Dr. Chun-Yen Chang and the Center for General Education of the National Normal University for their financial support.

■

REFERENCES

(1) Kobayashi, K. I.; Kimura, T.; Sawada, H.; Terakura, K.; Tokura, Y. Nature 1998, 395, 677−680. (2) Kobayashi, K. I.; Kimura, T.; Sawada, H.; Terakura, K.; Tokura, Y. Phys. Rev. B 1999, 59, 11159−11162. (3) Chan, T. S.; Liu, R. S.; Guo, G. Y.; Hu, S. F.; Lin, J. G.; Chen, J. M.; Chang, C.-R. Solid State Commun. 2005, 133, 265−270. (4) Fang, Z.; Terakura, K.; Kanamori, J. Phys. Rev. B 2001, 63, 180407(R). (5) Itoh, M.; Ohta, I.; Inaguma, Y. Mater. Sci. Eng., B 1996, 41, 55. (6) Moritomo, Y.; Kusura, H.; Akimoto, T.; Machida, A. Jpn. J. Appl. Phys. 2000, 39, L360−L362. (7) Tomioka, Y.; Okuda, T.; Okimoto, Y.; Kumai, R.; Kobayashi, K. I.; Tokura, Y. Phys. Rev. B 2000, 61, 422−427. (8) Kato, H.; Okuda, T.; Okimoto, Y.; Tomioka, Y. Phys. Rev. B 2004, 69, 184412. (9) Jeng, H. T.; Guo, G. Y. Phys. Rev. B 2003, 67, 094438. (10) Solovyev, I. V. J. Magn. Magn. Mater. 2004, 268, 194−197. (11) Song, W.; Wang, J.; Wu, Z. Chem. Phys. Lett. 2009, 482, 246− 248. (12) Wang, J.; Wu, Z. Chem. Phys. Lett. 2011, 501, 324−329. (13) Yousif, S. E. A.; Yassin, O. A. J. Alloys Compd. 2010, 506, 456. (14) Bannikov, V. V.; Shein, I. R.; Kozhevnikov, V. L.; Ivanovsky, A. L. J. Struct. Chem. 2008, 49 (5), 781. (15) Bonillaa, C. M.; et al. Physica B 2007, 398, 208−211. (16) Hua, W. Phys. Rev. B 2001, 64, 125126. (17) Tang, C. Q.; Zhang, Y.; Dai, J. Solid State Commun. 2005, 133, 219−222. (18) Philipp, J. B.; et al. Phys. Rev. B 2003, 68, 144431. (19) Cardona, R.; et al. J. Magn. Magn. Mater. 2008, 320, e85−e87. (20) Lv, S.; Li, H.; Liu, X.; Han, D.; Wu, Z.; Meng, J. J. Phys. Chem. C 2010, 114, 16710−16715. (21) Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864. Kohn, W.; Sham, L. J. Phys. Rev. 1965, 140, A1133. (22) Blöchl, P. E. Phys. Rev. B 1994, 50, 17953. (23) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865−3868. (24) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 48, 13115. (25) Kresse, G.; Furthmüller, J. Comput. Mater. Sci. 1996, 6, 15; Phys. Rev. B 1996, 54, 11169. (26) Anisimov, V. I.; Zaanen, J.; Andersen., O. K. Phys. Rev. B 1991, 44, 943−954. (27) Lichtenstein, A. I.; Anisimov, V. I.; Zaanen, J. Phys. Rev. B 1995, 52, R5467. (28) Anisimov, V. I.; Aryasetiawan, F.; Lichtenstein, A. I. J. Phys.: Condens. Matter 1997, 9, 767−808. (29) Jeng, H. T.; Guo, G. Y.; Huang, D. J. Phys. Rev. Lett. 2004, 93, 156403. (30) Jiang, X.; Guo, G. Y. Phys. Rev. B 2004, 70, 035110. (31) Solovyev, I. V.; Dederichs, P. H.; Anisimov, V. I. Phys. Rev. B. 1994, 50, 16861. (32) Wang, Y. K.; Lee, P. H.; Guo, G. Y. Phys. Rev. B. 2009, 80, 224418. (33) Blasco, J.; et al. Dalton Trans. 2011, 40, 3211. (34) Terakura, K.; Fang, Z.; Kanamori, J. J. Phys. Chem. Solids. 2002, 63, 907−912.

F

dx.doi.org/10.1021/jp303632z | J. Phys. Chem. C XXXX, XXX, XXX−XXX