Off-center Ti model of barium titanate

It has recently been shown by NMR techniques that in the high-temperature cubic phase of BaTiO3 the Ti ions are not confined to the high-symmetry cubic sites, but rather occupy one of the eight off-center positions along the [111] directions. The off-center Ti picture is in apparent contrast with most soft-mode-type theoretical descriptions of this classical perovskite ferroelectric. Here we apply the Girshberg-Yacoby off-center cation model of perovskite ferroelectrics assuming that the symmetrized occupation operators or "pseudospins" for the Ti off-center sites are linearly coupled to the normal coordinates for TO lattice vibrations. In the adiabatic limit, the coupling is eliminated by transforming to displaced phonon coordinates, and after excluding the self-interaction terms an effective Ti-Ti interaction is obtained. Using the Langevin equations of motion and the soft-spin formalism for the Ti pseudospin degrees of freedom with T-1u symmetry, the dynamic response of the coupled system is derived. The results are shown to be in qualitative agreement with the experimental data of Vogt [Phys. Rev. B, 26, 5904 (1982)] obtained by hyper-Raman scattering. The nature of the phase transition, which is of a mixed displacive and order-disorder type, is discussed.