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Electronic energy gaps and optical properties of LaMnO3
Physics Letters A 375 (2011) 1477–1480
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Electronic energy gaps and optical properties of LaMnO3 Sai Gong a,b , Bang-Gui Liu a,b,∗ a b
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China
a r t i c l e
i n f o
Article history: Received 5 February 2011 Accepted 11 February 2011 Available online 15 February 2011 Communicated by V.M. Agranovich Keywords: Manganite Magnetism Optical property Density functional theory
a b s t r a c t We investigate electronic structure and optical properties of LaMnO3 through density-functional-theory calculations with a recent improved exchange potential. Calculated gaps are consistent with recent experimental values, and calculated optical conductivities and dielectric constants as functions of photon energy are in excellent agreement with low-temperature experimental results. These lead to a satisfactory theoretical understanding of the electronic gaps and optical properties of LaMnO3 without tuning atomic parameters and can help elucidate electronic structures and magnetic properties of other manganite materials. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Because of colossal magnetoresistance effect [1,2], manganite materials have been applied in various spintronic devices [3–6]. Recent femtosecond spin excitation experiment [7] shows that higher than 95% spin polarization can be sustained above room temperature in La0.67 Sr0.33 MnO3 and CrO2 [8,9]. Because LaMnO3 is the most important end member of the manganites, a complete understanding of it is crucial to explore high-spin-polarized ferromagnetism in the doped manganites for spintronic applications [1,2,6,10]. Great efforts have been made to elucidate the magnetic properties and electronic structure of LaMnO3 [6,10–19]. It has been established that the spin configuration is A-type antiferromagnetic (AFM) ordering below 140 K and there is a Jahn–Teller lattice distortion which, in addition to the electron correlation, makes LaMnO3 insulating [10,13–15,19], but a satisfactory description of the electronic properties is still lacking. As for the energy gap of LaMnO3 , early resistivity measurement gave 0.24 eV [12], but recent optical experiments produced approximately 1.2 eV [16,17]. On the theoretical side, density-functional theory (DFT) [20] calculations with both local-density approximation (LDA) [21] and generalized-gradient approximation (GGA) [22] under-estimate the gap [6,11]. Consequently, there are substantial discrepancies between DFT calculated optical properties and experimental results. Although considering electron correlations in the scheme of LDA + U or GGA + U can lead to some improvement in some
*
Corresponding author at: Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. Tel.: +86 10 82649437; fax: +86 10 82649531. E-mail address: [email protected] (B.-G. Liu). 0375-9601/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2011.02.027
aspects by tuning atomic orbital parameters [11], a better DFT approach without tuning atomic parameters is needed to achieve a satisfactory description of LaMnO3 and related materials. In this Letter, we investigate electronic structure and optical properties of LaMnO3 through DFT calculations with a modified Becke–Johnson (mBJ) exchange potential proposed by Tran and Blaha [23]. As preparations, our GGA calculations confirm that the ground-state spin configuration is A-type AFM ordering. Our mBJ calculated minimal gap and direct one of the AFM LaMnO3 are wider than GGA and other results, but are in much better agreement with recent experimental values. Calculated optical conductivities and dielectric constants as functions of photon energy are in excellent agreement with experimental results. More detailed results will be presented in the following. These lead to a satisfactory theoretical understanding of the electronic structure and optical properties of LaMnO3 without tuning atomic parameters and are useful to elucidate electronic structures and magnetic properties of other manganite materials. The rest of this Letter is organized as follows. We shall describe our computational details in the second section. We shall present our main calculated results and analysis in the third section. Finally, we shall make some necessary discussion and give our conclusion in the fourth section. 2. Computational details We use the full-potential linearized augmented-plane-wave method within DFT [20], as implemented in package WIEN2k [24]. We use mBJ approximation [23] for the exchange potential, taking LDA [21] for the correlation potential. In addition, we also use GGA (PBE version) [22] for comparative calculations. Full relativistic ef-
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S. Gong, B.-G. Liu / Physics Letters A 375 (2011) 1477–1480
fects are calculated with the Dirac equations for core states, and the scalar relativistic approximation is used for valence states [25]. The spin–orbit coupling is neglected because it has little effect on our results. We use 2000 k points in the first Brillouin zone for LaMnO3 . We make harmonic expansion up to lmax = 10, and set R mt × K max = 8. The radii of the O, Mn, and La atomic spheres are set to 1.68, 1.89, and 2.43 bohr. The self-consistent calculations are considered to be converged only when the integration of absolute charge-density difference per formula unit between the successive loops is less than 0.0001|e |, where e is the electron charge. 3. Calculated results and analysis LaMnO3 assumes an orthorhombic structure with space group Pnma (No. 62) at low temperatures, and we use experimental lattice constants, namely a = 5.742 Å, b = 5.532 Å, and c = 7.668 Å, and internal parameters measured at 4.2 K [10]. At first, we calculate PBE total energies of the ferromagnetic structure and three AFM ones, the calculated results confirming that A-type AFM is the ground-state phase. Then, we calculate spin-resolved densities of states (DOSs) and energy bands of LaMnO3 using both PBE and mBJ potentials. In Fig. 1 we present the spin-resolved total DOS
and atomic DOSs between −6.5 and 4 eV calculated with mBJ. The empty La f states are between 1.8 and 3.6 eV, and the filled O p states between −6.5 and −2 eV. The filled Mn t 2g states are between −2.5 and −1.8 eV, and the empty ones between 2.1 and 2.9 eV. The filled Mn e g states are between −1.3 and 0.0 eV, and the empty ones between 1.02 and 2.00 eV. It is clear that there is a gap of 1.02 eV across the Fermi level for both of the spin channels. Because the low energy excitations are between the two states in the e g doublet, this is a d–d orbital transition gap. Fig. 2 shows corresponding spin-dependent energy bands with Mn1 d character. It can be seen that the bottom of the conduction bands is at Γ point, and the top of the valence bands in between T and Z points. Consequently, the minimal gap across the Fermi level is an indirect gap. It is interesting to compare the DOSs and bands calculated with mBJ and those with popular GGA [22]. The main difference is that the GGA spin exchange splitting is smaller than the mBJ value, the GGA gap is smaller, and the GGA band structure between −2.5 and 2.5 eV is different. We present in Table 1 the minimal gap (G M ), direct gap (G D ), and Mn moment (M) calculated with GGA (PBE) [22], GGA + U [11], and mBJ. Also shown are experimental results available. It is clear that the GGA values of G M and G D are substantially smaller than the experimental results. The GGA + U values are better than the GGA ones, but still too small. Fortunately, the mBJ values describe the experimental results very satisfactorily. As for the Mn moment, the mBJ value is the best among the three calculated values compared to the experimental result. Numerous optical measurements have been done on LaMnO3 at various temperatures. Because low-temperature optical conductivities and dielectric constants as functions of photon energy are
Table 1 Minimal gaps (G M ), direct gaps (G D ) and Mn magnetic moments (M) of LaMnO3 calculated with different methods and corresponding experimental results available. Fig. 1. (Color online.) Spin-resolved total density of states (DOS, thick solid) and the partial DOSs of La (dash-dotted), Mn1 (dotted), Mn2 (dashed), and O (thin solid) atoms (state/eV per unit cell), calculated with mBJ. The upper part is for majorityspin channel and the lower for minority-spin one.
Method
GGA
GGA + U
mBJ
Exp.
G M (eV) G D (eV) M (μ B )
0.28 0.95 3.33
0.81 [11] 1.18 [11] 3.46 [11]
1.02 1.58 3.59
0.24 [12], ∼1.2 [17] 1.1 [13], 1.7 [14] 3.42 [15], 3.7 ± 0.1 [10]
Fig. 2. The spin-resolved energy bands with Mn d character (described by thickness) between −6.5 and 4 eV, calculated with mBJ. The left panel shows the majority-spin bands, and the right the minority-spin ones.
S. Gong, B.-G. Liu / Physics Letters A 375 (2011) 1477–1480
1479
the E ||c cases in Fig. 3, the PBE results are far from the experimental curves between 0 and 1.5 eV, which is due to the too small PBE gap, but excellent agreement is achieved between the mBJ calculated spectra and corresponding experimental results below 3 eV. For the dielectric functions ε1 (ω) in Fig. 4, the mBJ results are in excellent agreement with the experimental curves measured at 20 K [18], but the PBE E ||ab results (xx and yy) are far from the experimental curve below 2 eV and the PBE E ||c result is too large below 3 eV. 4. Discussion and conclusion
Fig. 3. (Color online.) The optical conductivity σ (ω) (in 103 Ω −1 cm−1 ) of LaMnO3 for photon energy ω = 0–4.5 eV when the field is in the ab plane (a) and along the c axis (b). The mBJ calculated results and experimental ones (exp1997 at room temperature [16], exp2001 at 10 K [17]) are shown with thick lines; and the PBE calculated results with thin lines.
The above comparisons show that our mBJ gaps and the optical properties are in excellent agreement with recent experimental results. The present results can be explained by observing that mBJ exchange potential yields accurate crystal field effects and spin exchange splitting and by noticing that mBJ can yield accurate energy gaps for semiconductors and insulators, including transition-metal oxides [23,26]. Actually, the gaps of LaMnO3 are orbital excitation gaps, directly caused by both the enhanced orbital splitting of Mn e g doublet and the strong spin exchange splitting of Mn e g and t 2g . Because the optical properties in the photon energy ranges in Figs. 3 and 4 are determined mainly by the electronic states between −2.5 and 2.5 eV, naturally the mBJ optical conductivities and dielectric functions are much more accurate compared to the experimental results. In summary, our mBJ calculated minimal and direct gaps are consistent with recent experimental values, our mBJ calculated optical conductivities and dielectric constants as functions of photon energy are in excellent agreement with recent experimental results. Therefore, we have achieved a satisfactory DFT understanding of the electronic gaps and optical properties of LaMnO3 without tuning atomic parameters. This approach can be used to elucidate electronic structures and magnetic properties of other manganite materials. Acknowledgements This work is supported by Nature Science Foundation of China (Grant Nos. 10874232 and 10774180), by the Chinese Academy of Sciences (Grant No. KJCX2.YW.W09-5), and by Chinese Department of Science and Technology (Grant No. 2005CB623602). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
Fig. 4. (Color online.) The real part ε1 (ω) of the dielectric function spectra of LaMnO3 for photon energy ω = 0–6 eV when the field is in the ab plane (a) and along the c axis (b). The mBJ results and experimental ones at 20 K [18] are shown with thick lines; and the PBE results with thin lines.
[11] [12]
already available [17,18], we present our mBJ and PBE calculated optical conductivities σ (ω) and dielectric constants ε1 (ω) (real parts) as functions of photon energy ω in Figs. 3 and 4, respectively, and compare them with the experimental results available. For the optical conductivities in both of the E ||ab (xx and yy) and
[13] [14] [15] [16] [17] [18] [19] [20]
S. Jin, et al., Science 264 (1994) 413. A.P. Ramirez, J. Phys. Condens. Matter 9 (1997) 8171. S.A. Wolf, et al., Science 294 (2001) 1488. W.E. Pickett, J.S. Moodera, Phys. Today 54 (5) (2001) 39. R.A. de Groot, F.M. Mueller, P.G. van Engen, K.H.J. Buschow, Phys. Rev. Lett. 50 (1983) 2024. W.E. Pickett, D.J. Singh, Phys. Rev. B 53 (1996) 1146. G.M. Muller, et al., Nature Mater. 8 (2009) 56. K. Schwarz, J. Phys. F 16 (1986) L211. S.M. Watts, S. Wirth, S. von Molnar, A. Barry, J.M.D. Coey, Phys. Rev. B 61 (2000) 9621. J.B.A.A. Elemans, B.V. Laar, K.R.V.D. Veen, B.O. Loopstra, J. Solid State Chem. 3 (1971) 238. T. Hashimoto, S. Ishibashi, K. Terakura, Phys. Rev. B 82 (2010) 045124. R. Mahendiran, A.K. Raychaudhuri, A. Chainani, D.D. Sarma, S.B. Roy, Appl. Phys. Lett. 66 (1995) 233. T. Arima, Y. Tokura, J.B. Torrance, Phys. Rev. B 48 (1993) 17006. T. Saitoh, et al., Phys. Rev. B 51 (1995) 13942. B.C. Hauback, H. Fjellvag, N. Sakai, J. Solid State Chem. 124 (1996) 43. J.H. Jung, et al., Phys. Rev. B 55 (1997) 15489. K. Tobe, T. Kimura, Y. Okimoto, Y. Tokura, Phys. Rev. B 64 (2001) 184421. N.N. Kovaleva, et al., Phys. Rev. B 81 (2010) 235130. I. Loa, et al., Phys. Rev. Lett. 87 (2001) 125501. P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864;
1480
[21] [22] [23] [24]
S. Gong, B.-G. Liu / Physics Letters A 375 (2011) 1477–1480
W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133. J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. F. Tran, P. Blaha, Phys. Rev. Lett. 102 (2009) 226401. P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Proper-
ties, Karlheinz Schwarz, Techn. Universitat Wien, Austria, ISBN 3-9501031-1-2, 2001. [25] A.H. MacDonald, W.E. Pickett, D.D. Koelling, J. Phys. C 13 (1980) 2675; J. Kunes, P. Novak, R. Schmid, P. Blaha, K. Schwarz, Phys. Rev. B 64 (2001) 153102. [26] D.J. Singh, Phys. Rev. B 82 (2010) 205102.
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Electronic energy gaps and optical properties of LaMnO3 Sai Gong a,b , Bang-Gui Liu a,b,∗ a b
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China
a r t i c l e
i n f o
Article history: Received 5 February 2011 Accepted 11 February 2011 Available online 15 February 2011 Communicated by V.M. Agranovich Keywords: Manganite Magnetism Optical property Density functional theory
a b s t r a c t We investigate electronic structure and optical properties of LaMnO3 through density-functional-theory calculations with a recent improved exchange potential. Calculated gaps are consistent with recent experimental values, and calculated optical conductivities and dielectric constants as functions of photon energy are in excellent agreement with low-temperature experimental results. These lead to a satisfactory theoretical understanding of the electronic gaps and optical properties of LaMnO3 without tuning atomic parameters and can help elucidate electronic structures and magnetic properties of other manganite materials. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Because of colossal magnetoresistance effect [1,2], manganite materials have been applied in various spintronic devices [3–6]. Recent femtosecond spin excitation experiment [7] shows that higher than 95% spin polarization can be sustained above room temperature in La0.67 Sr0.33 MnO3 and CrO2 [8,9]. Because LaMnO3 is the most important end member of the manganites, a complete understanding of it is crucial to explore high-spin-polarized ferromagnetism in the doped manganites for spintronic applications [1,2,6,10]. Great efforts have been made to elucidate the magnetic properties and electronic structure of LaMnO3 [6,10–19]. It has been established that the spin configuration is A-type antiferromagnetic (AFM) ordering below 140 K and there is a Jahn–Teller lattice distortion which, in addition to the electron correlation, makes LaMnO3 insulating [10,13–15,19], but a satisfactory description of the electronic properties is still lacking. As for the energy gap of LaMnO3 , early resistivity measurement gave 0.24 eV [12], but recent optical experiments produced approximately 1.2 eV [16,17]. On the theoretical side, density-functional theory (DFT) [20] calculations with both local-density approximation (LDA) [21] and generalized-gradient approximation (GGA) [22] under-estimate the gap [6,11]. Consequently, there are substantial discrepancies between DFT calculated optical properties and experimental results. Although considering electron correlations in the scheme of LDA + U or GGA + U can lead to some improvement in some
*
Corresponding author at: Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. Tel.: +86 10 82649437; fax: +86 10 82649531. E-mail address: [email protected] (B.-G. Liu). 0375-9601/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2011.02.027
aspects by tuning atomic orbital parameters [11], a better DFT approach without tuning atomic parameters is needed to achieve a satisfactory description of LaMnO3 and related materials. In this Letter, we investigate electronic structure and optical properties of LaMnO3 through DFT calculations with a modified Becke–Johnson (mBJ) exchange potential proposed by Tran and Blaha [23]. As preparations, our GGA calculations confirm that the ground-state spin configuration is A-type AFM ordering. Our mBJ calculated minimal gap and direct one of the AFM LaMnO3 are wider than GGA and other results, but are in much better agreement with recent experimental values. Calculated optical conductivities and dielectric constants as functions of photon energy are in excellent agreement with experimental results. More detailed results will be presented in the following. These lead to a satisfactory theoretical understanding of the electronic structure and optical properties of LaMnO3 without tuning atomic parameters and are useful to elucidate electronic structures and magnetic properties of other manganite materials. The rest of this Letter is organized as follows. We shall describe our computational details in the second section. We shall present our main calculated results and analysis in the third section. Finally, we shall make some necessary discussion and give our conclusion in the fourth section. 2. Computational details We use the full-potential linearized augmented-plane-wave method within DFT [20], as implemented in package WIEN2k [24]. We use mBJ approximation [23] for the exchange potential, taking LDA [21] for the correlation potential. In addition, we also use GGA (PBE version) [22] for comparative calculations. Full relativistic ef-
1478
S. Gong, B.-G. Liu / Physics Letters A 375 (2011) 1477–1480
fects are calculated with the Dirac equations for core states, and the scalar relativistic approximation is used for valence states [25]. The spin–orbit coupling is neglected because it has little effect on our results. We use 2000 k points in the first Brillouin zone for LaMnO3 . We make harmonic expansion up to lmax = 10, and set R mt × K max = 8. The radii of the O, Mn, and La atomic spheres are set to 1.68, 1.89, and 2.43 bohr. The self-consistent calculations are considered to be converged only when the integration of absolute charge-density difference per formula unit between the successive loops is less than 0.0001|e |, where e is the electron charge. 3. Calculated results and analysis LaMnO3 assumes an orthorhombic structure with space group Pnma (No. 62) at low temperatures, and we use experimental lattice constants, namely a = 5.742 Å, b = 5.532 Å, and c = 7.668 Å, and internal parameters measured at 4.2 K [10]. At first, we calculate PBE total energies of the ferromagnetic structure and three AFM ones, the calculated results confirming that A-type AFM is the ground-state phase. Then, we calculate spin-resolved densities of states (DOSs) and energy bands of LaMnO3 using both PBE and mBJ potentials. In Fig. 1 we present the spin-resolved total DOS
and atomic DOSs between −6.5 and 4 eV calculated with mBJ. The empty La f states are between 1.8 and 3.6 eV, and the filled O p states between −6.5 and −2 eV. The filled Mn t 2g states are between −2.5 and −1.8 eV, and the empty ones between 2.1 and 2.9 eV. The filled Mn e g states are between −1.3 and 0.0 eV, and the empty ones between 1.02 and 2.00 eV. It is clear that there is a gap of 1.02 eV across the Fermi level for both of the spin channels. Because the low energy excitations are between the two states in the e g doublet, this is a d–d orbital transition gap. Fig. 2 shows corresponding spin-dependent energy bands with Mn1 d character. It can be seen that the bottom of the conduction bands is at Γ point, and the top of the valence bands in between T and Z points. Consequently, the minimal gap across the Fermi level is an indirect gap. It is interesting to compare the DOSs and bands calculated with mBJ and those with popular GGA [22]. The main difference is that the GGA spin exchange splitting is smaller than the mBJ value, the GGA gap is smaller, and the GGA band structure between −2.5 and 2.5 eV is different. We present in Table 1 the minimal gap (G M ), direct gap (G D ), and Mn moment (M) calculated with GGA (PBE) [22], GGA + U [11], and mBJ. Also shown are experimental results available. It is clear that the GGA values of G M and G D are substantially smaller than the experimental results. The GGA + U values are better than the GGA ones, but still too small. Fortunately, the mBJ values describe the experimental results very satisfactorily. As for the Mn moment, the mBJ value is the best among the three calculated values compared to the experimental result. Numerous optical measurements have been done on LaMnO3 at various temperatures. Because low-temperature optical conductivities and dielectric constants as functions of photon energy are
Table 1 Minimal gaps (G M ), direct gaps (G D ) and Mn magnetic moments (M) of LaMnO3 calculated with different methods and corresponding experimental results available. Fig. 1. (Color online.) Spin-resolved total density of states (DOS, thick solid) and the partial DOSs of La (dash-dotted), Mn1 (dotted), Mn2 (dashed), and O (thin solid) atoms (state/eV per unit cell), calculated with mBJ. The upper part is for majorityspin channel and the lower for minority-spin one.
Method
GGA
GGA + U
mBJ
Exp.
G M (eV) G D (eV) M (μ B )
0.28 0.95 3.33
0.81 [11] 1.18 [11] 3.46 [11]
1.02 1.58 3.59
0.24 [12], ∼1.2 [17] 1.1 [13], 1.7 [14] 3.42 [15], 3.7 ± 0.1 [10]
Fig. 2. The spin-resolved energy bands with Mn d character (described by thickness) between −6.5 and 4 eV, calculated with mBJ. The left panel shows the majority-spin bands, and the right the minority-spin ones.
S. Gong, B.-G. Liu / Physics Letters A 375 (2011) 1477–1480
1479
the E ||c cases in Fig. 3, the PBE results are far from the experimental curves between 0 and 1.5 eV, which is due to the too small PBE gap, but excellent agreement is achieved between the mBJ calculated spectra and corresponding experimental results below 3 eV. For the dielectric functions ε1 (ω) in Fig. 4, the mBJ results are in excellent agreement with the experimental curves measured at 20 K [18], but the PBE E ||ab results (xx and yy) are far from the experimental curve below 2 eV and the PBE E ||c result is too large below 3 eV. 4. Discussion and conclusion
Fig. 3. (Color online.) The optical conductivity σ (ω) (in 103 Ω −1 cm−1 ) of LaMnO3 for photon energy ω = 0–4.5 eV when the field is in the ab plane (a) and along the c axis (b). The mBJ calculated results and experimental ones (exp1997 at room temperature [16], exp2001 at 10 K [17]) are shown with thick lines; and the PBE calculated results with thin lines.
The above comparisons show that our mBJ gaps and the optical properties are in excellent agreement with recent experimental results. The present results can be explained by observing that mBJ exchange potential yields accurate crystal field effects and spin exchange splitting and by noticing that mBJ can yield accurate energy gaps for semiconductors and insulators, including transition-metal oxides [23,26]. Actually, the gaps of LaMnO3 are orbital excitation gaps, directly caused by both the enhanced orbital splitting of Mn e g doublet and the strong spin exchange splitting of Mn e g and t 2g . Because the optical properties in the photon energy ranges in Figs. 3 and 4 are determined mainly by the electronic states between −2.5 and 2.5 eV, naturally the mBJ optical conductivities and dielectric functions are much more accurate compared to the experimental results. In summary, our mBJ calculated minimal and direct gaps are consistent with recent experimental values, our mBJ calculated optical conductivities and dielectric constants as functions of photon energy are in excellent agreement with recent experimental results. Therefore, we have achieved a satisfactory DFT understanding of the electronic gaps and optical properties of LaMnO3 without tuning atomic parameters. This approach can be used to elucidate electronic structures and magnetic properties of other manganite materials. Acknowledgements This work is supported by Nature Science Foundation of China (Grant Nos. 10874232 and 10774180), by the Chinese Academy of Sciences (Grant No. KJCX2.YW.W09-5), and by Chinese Department of Science and Technology (Grant No. 2005CB623602). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
Fig. 4. (Color online.) The real part ε1 (ω) of the dielectric function spectra of LaMnO3 for photon energy ω = 0–6 eV when the field is in the ab plane (a) and along the c axis (b). The mBJ results and experimental ones at 20 K [18] are shown with thick lines; and the PBE results with thin lines.
[11] [12]
already available [17,18], we present our mBJ and PBE calculated optical conductivities σ (ω) and dielectric constants ε1 (ω) (real parts) as functions of photon energy ω in Figs. 3 and 4, respectively, and compare them with the experimental results available. For the optical conductivities in both of the E ||ab (xx and yy) and
[13] [14] [15] [16] [17] [18] [19] [20]
S. Jin, et al., Science 264 (1994) 413. A.P. Ramirez, J. Phys. Condens. Matter 9 (1997) 8171. S.A. Wolf, et al., Science 294 (2001) 1488. W.E. Pickett, J.S. Moodera, Phys. Today 54 (5) (2001) 39. R.A. de Groot, F.M. Mueller, P.G. van Engen, K.H.J. Buschow, Phys. Rev. Lett. 50 (1983) 2024. W.E. Pickett, D.J. Singh, Phys. Rev. B 53 (1996) 1146. G.M. Muller, et al., Nature Mater. 8 (2009) 56. K. Schwarz, J. Phys. F 16 (1986) L211. S.M. Watts, S. Wirth, S. von Molnar, A. Barry, J.M.D. Coey, Phys. Rev. B 61 (2000) 9621. J.B.A.A. Elemans, B.V. Laar, K.R.V.D. Veen, B.O. Loopstra, J. Solid State Chem. 3 (1971) 238. T. Hashimoto, S. Ishibashi, K. Terakura, Phys. Rev. B 82 (2010) 045124. R. Mahendiran, A.K. Raychaudhuri, A. Chainani, D.D. Sarma, S.B. Roy, Appl. Phys. Lett. 66 (1995) 233. T. Arima, Y. Tokura, J.B. Torrance, Phys. Rev. B 48 (1993) 17006. T. Saitoh, et al., Phys. Rev. B 51 (1995) 13942. B.C. Hauback, H. Fjellvag, N. Sakai, J. Solid State Chem. 124 (1996) 43. J.H. Jung, et al., Phys. Rev. B 55 (1997) 15489. K. Tobe, T. Kimura, Y. Okimoto, Y. Tokura, Phys. Rev. B 64 (2001) 184421. N.N. Kovaleva, et al., Phys. Rev. B 81 (2010) 235130. I. Loa, et al., Phys. Rev. Lett. 87 (2001) 125501. P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864;
1480
[21] [22] [23] [24]
S. Gong, B.-G. Liu / Physics Letters A 375 (2011) 1477–1480
W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133. J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. F. Tran, P. Blaha, Phys. Rev. Lett. 102 (2009) 226401. P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Proper-
ties, Karlheinz Schwarz, Techn. Universitat Wien, Austria, ISBN 3-9501031-1-2, 2001. [25] A.H. MacDonald, W.E. Pickett, D.D. Koelling, J. Phys. C 13 (1980) 2675; J. Kunes, P. Novak, R. Schmid, P. Blaha, K. Schwarz, Phys. Rev. B 64 (2001) 153102. [26] D.J. Singh, Phys. Rev. B 82 (2010) 205102.