VARIATIONAL PHASE FIELD FORMULATIONS OF POLARIZATION AND PHASE TRANSITION IN FERROELECTRIC THIN FILMS

The electric field plays an important role in ferroelectric phase transition. There have been numerous phase field formulations attempting to account for electrostatic interactions subject to different boundary conditions. In this paper, we develop new variational forms of the phase field electrostatic energy and the relaxation dynamics of the polarization vector that involves a hybrid representation in both real and Fourier variables. The new formulations avoid ambiguities appearing in earlier studies and lead to much more effective ways to perform variational studies and numerical simulations. Computations of phase transition and polarization switching in a single domain by applying the new formulations are provided as illustrative examples.