Domain formation and elastic long-range interaction in ferroelectric perovskites

On the basis of a Ginzburg-Landau model for ferroelectric perovskites, we calculate an effective free energy for a polarization field by eliminating elastic fields which are coherently induced by inhomogeneous configurations of polarizations. We obtain elastic long-range interaction between polarization fields on an adiabatic approximation. Computer simulations of a two-dimensional time-dependent Ginzburg-Landau (TDGL) model are performed by taking into account those long-range interactions. Charge-neutral 90° twins and its time evolution in the tetragonal phase are obtained with appropriate parameters of a phenomenological free energy. Resultant domain patterns are in agreement with experimental observations of tetragonal ${\mathrm{BaTiO}}_3$ ceramics. It is shown that anisotropic long-range interaction between polarization fields caused by elastic effects plays a major role in determining both the domain morphology and domain growth law in ferroelectric perovskites.