Ferroelectric phase transitions in cubic perovskites

Abstract

In low-temperature phase, due to the pseudo Jahn-Teller effect in unit cells, atoms are coherently localized in one of eight trigonal wells of the adiabatic potential energy surface. With temperature, nuclear motion delocalizes over symmetry-equivalent wells. Depending on the size of potential barriers, the two limiting cases are considered: (a) shallow wells, and (b) deep wells. They correspond to two different mechanisms of delocalization. When potential barriers are shallow compared to kTC, the delocalization is due to over-the-barrier activation of Arrhenius type. Alternatively, when the over-the-barrier activation is thermally inaccessible, the delocalization is due to tunnelling. Temperature dependence of spontaneous polarization is treated in terms of the mean-field approximation. Using experimental data for BaTiO3, numerical values of the corresponding parameters are estimated. The qualitative description is followed by a numeric evaluation of the temperature sequence of ferroelectric phase transitions for the two cases of shallow and deep wells. The theory agrees with the experimental data.