Investigation of domain structure in ferroelectric thin films by means of the Ising model

The domain structure in thin ferroelectric films was investigated in the framework of the modified Ising model with short-range exchange and long-range dipole-dipole interactions. The depolarizing field was also taken into account for the study of size effects in thin films. This field is the dominant factor influencing on the existence of phase transitions in the films. We used Monte Carlo method with the standard Metropolis algorithm to generate configurations on three-dimensional cubic lattices. The domains sizes were calculated in the longitudinal and transverse directions relatively to the spontaneous polarization direction. Temperature dependences of the domain sizes are obtained for different values of interaction constants. It was proved that the introduction of the depolarizing field leads to the appearance of a dead layer on the film boundaries. The dead layer thickness increases with increasing temperature. At a certain temperature (not equal to the Curie temperature), the dead layer is destroyed. The temperature dependences of the dielectric susceptibility at different film thicknesses have been calculated. It was shown that these dependencies have two maxima. The first maximum corresponds to a phase transition, the second one exists only for only thin films and corresponds to the destruction of the dead layer.