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 the critical temperature, as well as pressure and temperature 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.