First - principles model Hamiltonians for ferroelectric phase transitions

Abstract

A model-based approach to the first-principles study of ferroelectric phase transitions is described. Formal relationships of the various possible models to the full crystal Hamiltonian and connections to phenomenological models in the literature are examined. Specific considerations for application to the perovskite ferroelectrics BaTiO₃ and PbTiO₃, including the incorporation of long-range interactions, are discussed. Approaches to the computation of the nonlinear spontaneous polarization are compared and related to Berry's phase arguments and the quantum adiabatic theorem.