- Email: [email protected]
Jahn-Teller distortion and magnetic structures in LaMnO3
1oarnaI
of
Magnetism and Magnetic Materials 177-181 (1998) 879-880
Journalof magnetism and magnetic materials
,~
ELSEVIER
Jahn-Teller distortion and magnetic structures in LaMnO3 H. Sawada ~'*, Y. Morikawa b, N. Hamada °, K.
Terakura b
~JRCqT-ATP, ]-1-4 Higashi, Tsukuba, Ibaraki 305, Japan bJRCA T-NAIR, 1-1-4 Higashi, Tsukuba, Ibaraki 305, Japan Science LbzicersiO' of To~'o, 2461 YamazaM, Noda, Chiba 278, Japan
Abstract
Structure optimization is performed for LaMnO3 with the first-principIes pseudopotential method based on the local density approximation (LDA), the generalized gradient approximation and the LDA + U approximation. The Jahn=Teller distortion is reproduced even by LDA, but the magnitude of the distortion is not quite Iarge compared with the experimental value for all the three approximations. For the hypothetical ferromagnetic state, the Jahn-Telier distortion still exists but the magnitude is much reduced. The unit-cell shape becomes nearly cubic. These features are qualitatively consistent with the related experimental observations. The present band calculation predict the ferromagnetic state to be lower in energy than the A-type antiferromagnetic state for the optimized structure, being inconsistent with the experimental observation..~- 1998 Elsevier Science B.V. All rights reserved. Keywor&v Band calculation; Correiated electron system; Jahn-Teller effect; Magnetic ordering
The purpose of this study is to see how the Jahn-Teller (JT) distortion of LaMnO3 is produced by the three different approximations of the electron-electron interaction, i.e., the local density approximation (LDA), the generalized gradient approximation (GGA), and the LDA + U method. We also studied how the JT distortion is affected by the magnetic ordering; in other words, the structure optimization is performed not only for A-type antiferromagnetic (AF) state but also for ferromagnetic (FM) state. For these purposes we used pseudopotential (PP) method with Vanderbih's ultrasoft PP to optimize the structure of LaMnO3 efficiently. The magnitude of the Jahn-Teller distortion becomes clearer by decomposing the lattice distortion into the normal modes 0-, and (23, which are shown in Fig. 1. We plot the 0-~ as a function of normalized unit ceil volume in Fig. 2. Let us first discuss the A-type AF ordering case. We readily note that the 0_3 distortion is considerably reduced in LDA. This is mostly caused by the underestimation of the lattice constants in LDA. Anyway, the fact that LDA can produce an appreciable JT distortion
*Corresponding author. Fax: +81 298 54 2788: e-mail: [email protected].
x
(a)
(b)
Fig. 1. (a) The normal mode 02 (0-2 > 0). (b) The normal mode 0-3 (03 > 0). in LaMnO3 is qualitatively different from the situation in KCuF3 [1]. In contrast to L D A , G G A overestimates the lattice constants as in many cases and the estimated (23 distortion becomes larger though still smaller than the experimental value. This figure seems to suggest that the (23 distortion depends sensitively on the volume and that for a given volume LDA and G G A give nearly the same 0_3. Experimentally, small doping of Sr changes the volume and 0_3 as shown in Fig. 2. In this case the slope of 0-3 against unit cell volume is about two times steeper than that for the calculated result. The difference in slope between theory and experiment may have two reasons.
0304-8853/98/$19,00 ~ I998 Elsevier Science B.V. AII rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 4 5 1-4
H, Sawada et al, / Journal of Magnetism and Magnetic Materials ] 77-18] (1998) 879-880
880
1.04
0.8
1.03 f
X
(LDA) •OAF AF (GGA) OAF (LDA+U) ,'kFM (LDA) • FM(GGA} '¢'FM (LDA+U) x Exp,
0.6 .'--. = o.a
x
g./
~
.
~
1.02 ,HAF
o~
1.01
o.-o FM
1,00
t
I
•
•
t
0.99 0.2
0,97
z& o.o
-4..0
i
I
Exp. [
i I i 0.0 (V-V~,'V,~ (%)
-2,0
I
LDA
I
GGA
I
2.0
4.0
Fig. 2. The normal mode Qs obtained by LDA, GGA and LDA + U are plotted as a function of cell volume. Circles and triangles correspond to the AF and FM LaMnO3, respectively. Open and closed symbols are calculated in LDA and GGA, respectively.Closed and open diamonds denote the (~3 obtained in LDA + U for the AF and FM LaMnO3, respectively.Experimental results for the Sr doping in LaMnO3 are plotted by crosses [4].
One is that the carrier doping will reduce the JT distortion and second is that the present calculation underestimates the JT distortion. The full structure optimization for the FM ordering modifies the lattice constants appreciably and reduces the JT distortion. Experimentally, the doped FM state may not have any static JT distortion, while the present calculation predicts the presence of small static JT distortion in the hypothetical FM state of undoped LaMnO> We must note again that doping will efficiently destroy static cooperative JT distortion
E23. Fig. 3 shows the ratios of lattice constants of the orthorhombic cell (Pbnm), b/a and (c/x/2)/a, for the AF and FM LaMnO3. For the AF LaMnO3 the calculated resuits agree with the experiment within about 1%. We should note that the lengths of a, b, and c/,,//2 become closer to each other in the FM state. Experiments for Lal-xSrxMnO3 indicate that b decreases, a slightly decreases and c increases by increasing the Sr concentration x, causing the phase transition from AF to FM and from the orthorhombic to rhombohedral structure [3]. The experimental behavior is consistent with the calculated results. Tabte 1 shows the total energy difference between the AF and FM spin orderings. Though the AF phase is more stable than the FM phase for the experimental structure, the energy ordering is reversed after the structure optimization. The failure in prediction of the stable magnetic structure for the optimized structure may be due to the underestimation of the Jahn-Teller distortion and, therefore, the underestimation of the orbital ordering in the AF LaMnO> The fundamental problem may be overestimation of the p-d hybridization.
Fig. 3. The ratios of lattice constants of the orthorhombic cell (Pbnm),b/a and (c/v/2-)/a, obtained by experiment [51, LDA and GGA. Closed and open circles denote the ratios for the AF and FM LaMnO> respectively. Table 1 The total energy difference(meV/f.u.) between the AF and FM LaMnO3, that is EAr -- EF~a.The 'Exp.' and 'Opt.' correspond to the energy differences for the experimental and optimized structures, respectively
Exp. Opt.
LDA
GGA
- 19.4 56.5
-- 15.2 62.6
LDA + U --0.1
In summary, the present calculation reproduces the JT distortion by about 40-75%, depending on the approximations of the electron-electron interaction. However, the calculated JT distortion shows linear dependence on the calculated cell volume, The lattice becomes nearly cubic (a ~-b ~-c/x/~) and the JT distortion is significantly suppressed in the hypothetical FM state of LaMnO> The A-type AF has lower energy than FM state for the experimental structure. However, the FM states become more stable than the A-type AF states for the optimized structure, being inconsistent with the experiment. The present work is partly supported by the New Energy and Industrial Technology Development Organization (NEDO) and also by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan.
References
I1] A.I. Liechtenstein,V.I. Anisimov,J. Zaanen, Phys. Rev. B 52 (1995) R5467. [21 A.J. Millis, Phys. Rev. B 53 (1996) 8434. 131 A. Urushibara et al., Phys. Rev. B 51 (1995) 14103. [47 H. Kawano, R. Kajimoto, M. Kubota, H. Yoshizawa, Phys. Rev. B 53 (1996) R14709. [5] J.B.A.A. Etemans, B.V. Laar, K.R.V.D. Veen, B.O. Loopstra, J. Solid State Chem. 3 (1971) 238.
of
Magnetism and Magnetic Materials 177-181 (1998) 879-880
Journalof magnetism and magnetic materials
,~
ELSEVIER
Jahn-Teller distortion and magnetic structures in LaMnO3 H. Sawada ~'*, Y. Morikawa b, N. Hamada °, K.
Terakura b
~JRCqT-ATP, ]-1-4 Higashi, Tsukuba, Ibaraki 305, Japan bJRCA T-NAIR, 1-1-4 Higashi, Tsukuba, Ibaraki 305, Japan Science LbzicersiO' of To~'o, 2461 YamazaM, Noda, Chiba 278, Japan
Abstract
Structure optimization is performed for LaMnO3 with the first-principIes pseudopotential method based on the local density approximation (LDA), the generalized gradient approximation and the LDA + U approximation. The Jahn=Teller distortion is reproduced even by LDA, but the magnitude of the distortion is not quite Iarge compared with the experimental value for all the three approximations. For the hypothetical ferromagnetic state, the Jahn-Telier distortion still exists but the magnitude is much reduced. The unit-cell shape becomes nearly cubic. These features are qualitatively consistent with the related experimental observations. The present band calculation predict the ferromagnetic state to be lower in energy than the A-type antiferromagnetic state for the optimized structure, being inconsistent with the experimental observation..~- 1998 Elsevier Science B.V. All rights reserved. Keywor&v Band calculation; Correiated electron system; Jahn-Teller effect; Magnetic ordering
The purpose of this study is to see how the Jahn-Teller (JT) distortion of LaMnO3 is produced by the three different approximations of the electron-electron interaction, i.e., the local density approximation (LDA), the generalized gradient approximation (GGA), and the LDA + U method. We also studied how the JT distortion is affected by the magnetic ordering; in other words, the structure optimization is performed not only for A-type antiferromagnetic (AF) state but also for ferromagnetic (FM) state. For these purposes we used pseudopotential (PP) method with Vanderbih's ultrasoft PP to optimize the structure of LaMnO3 efficiently. The magnitude of the Jahn-Teller distortion becomes clearer by decomposing the lattice distortion into the normal modes 0-, and (23, which are shown in Fig. 1. We plot the 0-~ as a function of normalized unit ceil volume in Fig. 2. Let us first discuss the A-type AF ordering case. We readily note that the 0_3 distortion is considerably reduced in LDA. This is mostly caused by the underestimation of the lattice constants in LDA. Anyway, the fact that LDA can produce an appreciable JT distortion
*Corresponding author. Fax: +81 298 54 2788: e-mail: [email protected].
x
(a)
(b)
Fig. 1. (a) The normal mode 02 (0-2 > 0). (b) The normal mode 0-3 (03 > 0). in LaMnO3 is qualitatively different from the situation in KCuF3 [1]. In contrast to L D A , G G A overestimates the lattice constants as in many cases and the estimated (23 distortion becomes larger though still smaller than the experimental value. This figure seems to suggest that the (23 distortion depends sensitively on the volume and that for a given volume LDA and G G A give nearly the same 0_3. Experimentally, small doping of Sr changes the volume and 0_3 as shown in Fig. 2. In this case the slope of 0-3 against unit cell volume is about two times steeper than that for the calculated result. The difference in slope between theory and experiment may have two reasons.
0304-8853/98/$19,00 ~ I998 Elsevier Science B.V. AII rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 4 5 1-4
H, Sawada et al, / Journal of Magnetism and Magnetic Materials ] 77-18] (1998) 879-880
880
1.04
0.8
1.03 f
X
(LDA) •OAF AF (GGA) OAF (LDA+U) ,'kFM (LDA) • FM(GGA} '¢'FM (LDA+U) x Exp,
0.6 .'--. = o.a
x
g./
~
.
~
1.02 ,HAF
o~
1.01
o.-o FM
1,00
t
I
•
•
t
0.99 0.2
0,97
z& o.o
-4..0
i
I
Exp. [
i I i 0.0 (V-V~,'V,~ (%)
-2,0
I
LDA
I
GGA
I
2.0
4.0
Fig. 2. The normal mode Qs obtained by LDA, GGA and LDA + U are plotted as a function of cell volume. Circles and triangles correspond to the AF and FM LaMnO3, respectively. Open and closed symbols are calculated in LDA and GGA, respectively.Closed and open diamonds denote the (~3 obtained in LDA + U for the AF and FM LaMnO3, respectively.Experimental results for the Sr doping in LaMnO3 are plotted by crosses [4].
One is that the carrier doping will reduce the JT distortion and second is that the present calculation underestimates the JT distortion. The full structure optimization for the FM ordering modifies the lattice constants appreciably and reduces the JT distortion. Experimentally, the doped FM state may not have any static JT distortion, while the present calculation predicts the presence of small static JT distortion in the hypothetical FM state of undoped LaMnO> We must note again that doping will efficiently destroy static cooperative JT distortion
E23. Fig. 3 shows the ratios of lattice constants of the orthorhombic cell (Pbnm), b/a and (c/x/2)/a, for the AF and FM LaMnO3. For the AF LaMnO3 the calculated resuits agree with the experiment within about 1%. We should note that the lengths of a, b, and c/,,//2 become closer to each other in the FM state. Experiments for Lal-xSrxMnO3 indicate that b decreases, a slightly decreases and c increases by increasing the Sr concentration x, causing the phase transition from AF to FM and from the orthorhombic to rhombohedral structure [3]. The experimental behavior is consistent with the calculated results. Tabte 1 shows the total energy difference between the AF and FM spin orderings. Though the AF phase is more stable than the FM phase for the experimental structure, the energy ordering is reversed after the structure optimization. The failure in prediction of the stable magnetic structure for the optimized structure may be due to the underestimation of the Jahn-Teller distortion and, therefore, the underestimation of the orbital ordering in the AF LaMnO> The fundamental problem may be overestimation of the p-d hybridization.
Fig. 3. The ratios of lattice constants of the orthorhombic cell (Pbnm),b/a and (c/v/2-)/a, obtained by experiment [51, LDA and GGA. Closed and open circles denote the ratios for the AF and FM LaMnO> respectively. Table 1 The total energy difference(meV/f.u.) between the AF and FM LaMnO3, that is EAr -- EF~a.The 'Exp.' and 'Opt.' correspond to the energy differences for the experimental and optimized structures, respectively
Exp. Opt.
LDA
GGA
- 19.4 56.5
-- 15.2 62.6
LDA + U --0.1
In summary, the present calculation reproduces the JT distortion by about 40-75%, depending on the approximations of the electron-electron interaction. However, the calculated JT distortion shows linear dependence on the calculated cell volume, The lattice becomes nearly cubic (a ~-b ~-c/x/~) and the JT distortion is significantly suppressed in the hypothetical FM state of LaMnO> The A-type AF has lower energy than FM state for the experimental structure. However, the FM states become more stable than the A-type AF states for the optimized structure, being inconsistent with the experiment. The present work is partly supported by the New Energy and Industrial Technology Development Organization (NEDO) and also by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan.
References
I1] A.I. Liechtenstein,V.I. Anisimov,J. Zaanen, Phys. Rev. B 52 (1995) R5467. [21 A.J. Millis, Phys. Rev. B 53 (1996) 8434. 131 A. Urushibara et al., Phys. Rev. B 51 (1995) 14103. [47 H. Kawano, R. Kajimoto, M. Kubota, H. Yoshizawa, Phys. Rev. B 53 (1996) R14709. [5] J.B.A.A. Etemans, B.V. Laar, K.R.V.D. Veen, B.O. Loopstra, J. Solid State Chem. 3 (1971) 238.