Structural Phase Transitions in Perovskite-Type Crystals

Abstract

We introduce a simple model Hamiltonian for the study of phase transitions in perovskite compounds $\mathrm{AB}{\mathrm{O}}_{3}$ involving rotations of $B{\mathrm{O}}_{6}$ octahedra. Depending on the relative magnitude of the anharmonic coefficients, we find a transition to the tetragonal or to the trigonal phase. We obtain the temperature dependence of the rotation angle below the transition temperature ${T}_{a}$, and of the soft-mode frequencies associated with the transition both above and below ${T}_{a}$. The coupling to an elastic deformation field is briefly discussed.