Possibility of Semicommensurate Phases When the Corresponding Purely Incommensurate Phases Are Forbidden

Abstract

The order parameters are assumed to number two, and denoted by Q and Q^*. The free energy function is denoted by Φ. Let the degree of anisotropy of Φ in its gradient-less part be 2α, where α is an integer ≥2. The Lifshitz term, i.e., Q^*∂_zQ−Q∂_zQ^* and a term expressed as a product of Q^α+Q^*α or Q^α−Q^*α with Q^*∂_zQ−Q∂_zQ^* are interrelated as follows: If one of them is allowed (or forbidden) to exist in Φ, the other is always forbidden (or often allowed). Even if the former term is forbidden and no purely incommensurate phase is possible, a semicommensurate phase is possible owing to the latter term. (The coefficient to term ∂_zQ∂_zQ^* is assumed to be positive.) On cooling, the prototypic phase can transform to the semicommensurate phase earlier than to the corresponding purely commensurate ferroic phase. A detailed explanation is given.