Structural Phase Transitions in Perovskite-Type Crystals

We introduce a simple model Hamiltonian for the study of phase transitions in perovskite compounds ABO₃ involving rotations of BO₆ 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 Tₐ, and of the soft-mode frequencies associated with the transition both above and below Tₐ. The coupling to an elastic deformation field is briefly discussed.