Refined treatment of the model of linearly coupled anharmonic oscillators and its application to the temperature dependence of the zone-center soft-mode frequencies of KTaO3 and SrTiO3

Abstract

The temperature behavior of the zone-center soft modes of ${\mathrm{KTaO}}_3$ and ${\mathrm{SrTiO}}_3$ is remeasured betwen 5 and 300 K by the technique of hyper-Raman spectroscopy, the experimental errors of soft-mode frequency and damping constant being reduced to below ±1 ${\mathrm{cm}}^{\mathrm{-}1}$. The results are taken as a stimulus to a refined treatment of the prototype dynamical model of a ferroelectric crystal, i.e., a lattice of anharmonic oscillators randomly driven by a heat bath and coupled to each other by a dipolarlike intercell interaction. While the intercell coupling is described as previously in terms of a molecular-field approximation, the pseudoharmonic frequency of the anharmonic oscillator at each lattice site is calculated as exactly as possible within the framework of the statistical-linearization approach. The effective classical potential method is used to test a variety of local anharmonic-oscillator potentials. In the case of ${\mathrm{KTaO}}_3$ excellent fits to the experimental values of the soft-mode frequency ${\mathrm{\Omega }}_0$(T) are obtained on the basis of only three parameters characterizing globally the harmonic limit, the anharmonicity, and the dipolar interaction, respectively. In the case of ${\mathrm{SrTiO}}_3$ some uncertainty arises from the unknown dependence of these parameters on the octahedral rotation in the antiferrodistortive phase below 105 K. In both materials ${\mathrm{\Omega }}_0$(T) turns out to be too smooth for deducing details of the local anharmonic-oscillator potential like its anisotropy and the ratio of sextic and quartic anharmonicity parameters. On the other hand, local potentials of the multiple-well type with quartic anharmonicities and negative harmonic terms can definitely be excluded.