Light scattering in displacive incommensurate structures: a Landau theory approach

This paper is concerned with the derivation of selection rules for light scattering by soft modes in displacive incommensurate structures, when the latter result from the condensation of a single pair of non-degenerate modes at q0 and -q0, the high-temperature phase being centrosymmetric. The analysis is based on a direct second-order high-temperature Raman process involving the soft modes which condense at the transition temperature Ti. Special attention is given to the case of the pseudo-acoustic phason. It is shown that its integrated intensity is proportional to (Ti-T) near Ti, and that its selection rules are similar to those obtained in Brillouin scattering. It is further shown that the latter are somewhat relaxed by the acoustic phonon-phason coupling. The method is finally extended to light scattering by hard phonons at q0 and -q0.