Size dependence of domain patterns in a constrained ferroelectric system

We have simulated the size dependence of domain patterns in a two-dimensional (square shaped) constrained ferroelectric system by means of a time-dependent Ginzburg-Landau model. The theory incorporates elastic strain in the form of an effective long-range nonlocal interaction of the polarization. A nonferroelectric layer is introduced in the free energy that enforces a decaying polarization at the surface. The results show that the number of domains decreases on decreasing the system size. We also found two critical sizes. The first one signifies a transition from a multi-domain to a single-domain state and the second indicates the disappearance of ferroelectricity.