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.

• Received 8 August 1968

DOI:https://doi.org/10.1103/PhysRevLett.21.1256