Theory of surface modes in ferroelectrics

A theoretical investigation is made of the possible occurrence of surface modes in semi-infinite ferroelectric materials. Three different approaches are used: (1) a microscopic pseudo-spin theory based on the Ising model in a transverse field, (2) a macroscopic Landau theory in which surface effects can be introduced phenomenologically, and (3) a polariton model appropriate to the very long wavelength region. Existence conditions and dispersion relations are deduced for the localised surface modes, which are predicted by all three methods. The results are illustrated by means of numerical examples. Methods (1) and (2) are found to give rise to similar results in certain limits, and the authors are able to establish a formal relationship between the two approaches. The applicability of the theoretical models to real ferroelectrics is discussed, and some experimental techniques by which the surface modes might be detected are suggested.