Theory of the quantum paraelectric-ferroelectric transition

A realistic theory of the quantum paraelectric-ferroelectric transition is presented, involving parameters determined from band calculations and a renormalization group treatment of critical fluctuations. The effects of reduced dimensionality and deviations from cubic symmetry are determined. Expressions for the pressure dependence of Tc as well as p and T dependence of the specific heat are derived, and evaluated for realistic materials parameters for the systems BaTiO₃ and PbTiO₃. In these materials the ferroelectric soft mode dispersion apparently exhibits a very strong cubic anisotropy, which affects results in an important, albeit quantitative, manner. A change in order parameter orientation from (100) to (111) is predicted as quantum criticality is approached.