Soft phonon dispersion in BaTiO₃

Abstract

We treat a simple lattice dynamical model for the critical modes in BaTiO₃. The Ti-ions move in an anharmonic single particle potential formed by the frame of Ba- and O-ions that are bound more tightly to their equilibrium positions. The dipole interaction of displaced Ti-ions is enhanced by polarization effects due to all electronic polarizabilities and to an additional ionic polarizability of the oxygen ions. The transverse optical mode of this model is low lying and softening as temperature decreases until its frequency for zero wavevector vanishes. This leads to a ferroelectric instability. The dispersion of this critical mode for small wavevectors was found to be highly anisotropic. So long this prediction has not been tested experimentally.