Phase-transition and dynamics of ferroelectric-paraelectric multilayer structure

A simple phenomenological model allowing description of multilayer structure composed of ferroelectric and non-ferroelectric (normal dielectric) layers is proposed. The short-range interaction term describing the strength of coupling of both materials at the interlayer interfaces is introduced. Within the model, the system undergoes ferroelectric phase transition at reduced temperature, depending on the ferroelectric layer thickness d either as 1/d(2) or 1/d, and on the relation between the dielectric layer thickness D and the polarization correlation length xi(A). In the para-phase, an infinite discrete set of dielectrically active polarization modes exists differing in the wave vectors normal to the layers. Ferroelectric instability then occurs due to the softening of the lowest-frequency one.