Calculation of intrinsic hysteresis loops of ferroelectric thin films

A general numerical scheme is applied to calculate the dielectric equation of state (mean polarisation versus applied field) and resulting hysteresis loop for ferroelectric films. The scheme is sufficiently general to apply to films in which the phase transition from the paraelectric state is either first or second order, and possible variation of the polarisation P near the surfaces is included. It is shown that by design of the film thickness and of the variation of P the hysteresis loop in a film of first-order material can be varied between forms which resemble those of the bulk material in various temperature intervals.