  In the paper we consider size effects of phase transitions and polar
properties of the thin antiferroelectric films. We modified phenomenological
approach proposed by Kittel. The Euler-Lagrange equations were solved by direct
variational method. The free energy with renormalized coefficients depending on
the film thickness has been derived. The approximate analytical expression for
the coefficients dependence on film thickness, temperature, polarization
gradient coefficient and extrapolation lengths were obtained. We have shown how
the anti-ferroelectric double hysteresis loop transforms into the ferroelectric
single one under the film thickness decrease. Proposed theoretical
consideration explains the experimental results obtained in antiferroelectric
PbZrO_3 thin films.
