Ferroelectric thin film properties—Depolarization field and renormalization of a “bulk” free energy coefficients

We suggest an approach to calculate the physical properties of ferroelectric thin films. Our approach takes into account the depolarization field and spatial inhomogeneity of the order parameter inherent to thin films. In or approach, we consider the thin film to be short circuited with the perfectly conducting electrodes and monodomain. The solution of the corresponding Euler–Lagrange equation by the direct variational method shows that the initial free-energy functional of a thin film can be reduced to some effective functional which does not include spatial derivatives of the order parameter. The coefficients of this functional, however, are renormalized as compared to those of the initial free-energy functional. We present the detailed calculation of the spontaneous polarization, pyrocoefficient, and dielectric susceptibility. We analyze in detail the spatial profile of the depolarization field with special attention to its properties near size-driven phase transition in a film.