Phase transitions and soft modes in ferroelectric superlattices

Abstract

A theory of periodic ferroelectric multilayers is presented. The multilayer system consists of two alternating ferroelectrics with different transition temperatures. The system is described by a Ginzburg-Landau functional with space-dependent coefficients. In particular, the authors consider the case of a ferroelectric phase transition of first order. Expressions for static properties such as transition temperature, supercooling temperature and polarisation profile are derived. Immediately below the transition temperature there are unpolarised domains within the stronger ferroelectric layers. Their existence is due to the possible phase coexistence of the ordered and disordered phases in the corresponding bulk material. In order to describe the soft-mode dynamics they use phenomenological equations of motion and study the spectrum of transverse optical modes. The lowest bands are almost dispersion-free and the corresponding modes are confined to those layers which have the lower bulk soft-mode frequency. Because the bulk soft modes of the two layers soften at different temperatures the localisation of the modes in one or the other layer depends upon the temperature. This temperature dependence of the mode form can be seen in the lineshape of the polarisation correlation function if the soft-mode damping of the two layers is different. Furthermore, interface modes are shown to exist. Their energy lies below the continuum, confined by the two bulk soft-mode frequencies. These modes result from the special form of the inhomogeneous polarisation profile in a superlattice in contrast to the Fuchs-Kliever interface modes, which have their origin in the long-range dipolar interaction. The number of these bound states depends on the temperature.