Origin of Modulated Incommensurate Phases in Insulators

Abstract

We discuss the origin of incommensurate structural modulations as found in certain insulating crystals. The theory developed is based on the necessary existence of a second, independent, transformation mode which can have an energy-lowering interaction with the main mode of transformation only at nonzero wave vector, due to symmetry. The required subsidiary mode, of correct symmetry, has been directly observed, or strongly inferred, in four cases.