On inhomogeneous polarized states near the phase transition point in a thin ferroelectric film

It is shown in terms of the phenomenological Landau theory of phase transitions that a phase transition to an inhomogeneous polar phase preceding in temperature a phase transition to a homogeneous polar state is possible. As a result of solving a boundary eigenvalue problem for the polarization equilibrium equation and electrostatics equations, wave vector $k _\perp$ characterizing the inhomogeneous phase has been determined and the temperature boundaries of its existence in the dependence on the film thickness and its surface properties have been found.