Monte Carlo simulation of ferroelectric domain structure and applied field response in two dimensions

A two-dimensional, lattice-Monte Carlo approach, based upon the energy minimization of an ensemble of electric dipoles, was developed to simulate ferroelectric domain behavior. The model utilizes a Hamiltonian for the total energy based upon electrostatic terms involving dipole-dipole interactions, local polarization gradients, and the influence of applied electric fields. The impact of boundary conditions on the domain configurations obtained was also examined. In general, the model exhibits domain structure characteristics consistent with those observed in a tetragonally distorted ferroelectric. The model was also extended to enable the simulation of ferroelectric hysteresis behavior. Simulated hysteresis loops were found to be very similar in appearance to those observed experimentally in actual materials. This qualitative agreement between the simulated hysteresis loop characteristics and real ferroelectric behavior was also confirmed in simulations run over a range of simulation temperatures and applied field frequencies.