The influence of the Jahn–Teller effect on phonons in LaMnO3

Physica B 276}278 (2000) 772}773

The in#uence of the Jahn}Teller e!ect on phonons in LaMnO  A.E. Nikiforov, S.E. Popov*, S.Yu. Shashkin Ural State University, Lenin av. 51, Ekaterinburg, 620083 Russia

Abstract A model of the low-temperature orthorombic phase (O) of LaMnO was constructed using pair potentials with  explicitly allowing for the many-body Jahn}Teller contribution to the crystal energy. The analysis of the structure, elastic constants and phonon frequencies is based on the comparison of the structural phases that obtained with including and `switching-o!a Jahn}Teller contribution to the energy and dynamical matrix of the crystal.  2000 Elsevier Science B.V. All rights reserved. Keywords: Jahn}Teller e!ect; Elastic constants; Lattice Dynamics; Crystal structures

1. Introduction Upon the microscopic description of the structures of ionic crystals, the shell model [1], which takes into account both short-range repulsion of the ionic shells related to the Pauli principle and the long-range Coulomb interaction, proved to be e!ective. In this work, the model of pair potentials explicitly including the Jahn} Teller contribution to the energy and dynamical matrix of the crystal was used to describe structural, elastic, and dielectric properties of crystalline LaMnO . In order to  "nd the parameters of the potentials for di!erent pairs in the lanthanum manganite, we used the procedure used in Ref. [2]. We assume that the short-range characteristics for the pairs in the LaMnO crystal do not di!er strongly  from those in MnO, NiO, SrO and La NiO crystals [2].   The main idea of our study was the comparison of the structure parameters, elastic constants and phonon frequencies in the structures obtained with included and with `switched-o!a (< "0) JT contribution.  2. The in6uence of the JT contribution on crystal structure and phonon frequencies of LaMnO3 The O and O* structural phases both belong to the space group Pnma (D), but "rst one has non-zero  * Corresponding author. Fax: 7-3432-615978. E-mail address: [email protected] (S.E. Popov)

Q crystal distortion. Also the second one has  pseudocubic lattice parameters (a+c+b/(2). When analyzing the results, it is useful to establish the relation of the local distortions of oxygen octahedra with parameters of the structure. For the Q , Q local distortions   we have Q "(2(< a#< c),  V X

(1)

X. Q "( Wb!( (c#a)   

(2)

The magnitudes of the structure parameters were found by minimizing crystal energy calculated as in Ref. [2]. Table 1 gives the theoretical values of these structure parameters allowing for the JT contribution and without such contribution (< "0). Simulation of the crystal  structure with the `switching-o!a linear JT interaction leads to the appearance of the pseudocubic phase (b/(+a+c) that can be identi"ed with the O* phase of lanthanum manganite. We calculated the adiabatic potential depending on the value of Q distortion. The  height of the barrier between two minima proved to be 0.04 eV, which agrees well with the transition temperature [3]. The many-sublattice structure of the crystal leads to the substantial e!ect of internal displacement of the sublattices on the macroscopic characteristics of the crystal. Thus, for the crystal with < "0, the elastic constants  must obey certain relationships, in particular, C !C "0, C !C "0, in view of the small    

0921-4526/00/$ - see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 6 6 1 - 0

A.E. Nikiforov et al. / Physica B 276}278 (2000) 772}773

773

Table 1 Values of the structural parameters of LaMnO (all parameters are given in As , < in eV/As )  

a b c Q  Q 

¹"14 K [4]

¹"121 K [4]

¹"300 K [4]

¹"798 K [3]

"< ""0 

"< ""1.29 

5.739 7.672 5.532 0.27 !0.09

5.739 7.679 5.530 0.27 !0.09

5.736 7.699 5.536 0.26 !0.08

5.583 7.889 5.581 0.05 !0.001

5.769 8.185 5.792 !0.001 !0.003

5.929 8.117 5.845 0.258 !0.06

Table 2 Calculated elastic constants (GPa) of LaMnO  "< " (eV/As ) 

C 

C 

C 

C 

C 

C 

C 

C 

C 

0.0 1.29

170 57

43 62

82 35

250 172

90 119

209 179

71 69

80 66

69 67

PDOS the di!erence both in the number of main peaks and in the gap width could be seen (Fig. 1). 3. Conclusions

Fig. 1. Calculated phonon density of states (solid line !"< ""1.29 eV/As ; dotted line !"< ""0 eV/As . C C

`degree of orthorombicitya of such a crystal. It is seen that these relationships do not ful"ll (Table 2). Thus, without allowing for the displacement of sublattices that accompany uniform deformation, we have C !C "   !29 GPa C !C "3 Gpa.   The phonon density of states (PDOS) calculated with < "0 has about 12 main peaks and the gap between  14.5 and 17.2 THz (Fig. 1). But for the crystal with < O0 

We have performed the simulation of the crystal structure of the low doped LaMnO with explicitly allowing  many-body Jahn}Teller contribution to the crystal energy. We have shown that the Q deformation is  completely caused by the cooperative JT e!ect. The gaint anisotropy of the elastic constants in O phase is predicted. The substantial dependence of the frequencies on the JT contribution to the dynamical matrix of the crystal is shown. References [1] C.R.A. Catlow, W.C. Macrodt, in: Computer Simulation of Solid, Springer, Berlin, 1982. [2] A.E. Nikiforov et al., Z. Phys. Chem. 201 (1997) 597. [3] J. Rodriguez-Carvajal et al., Phys. Rev. B 57 (1998) R3189.