Transitions from Artificially Incommensurately Undulated Prototypic Phases to Ferroic Phases. II. In the Presence of a Lifshitz Term

Abstract

This paper complements a previous one [J. Phys. Soc. Jpn. 63 (1994) 1018]. Let Φ denote the free energy function. Let the order parameters be two real variables Q α and Q β . The previous paper studied cases where Φ contains term ∂ z ( Q 2 α - Q 2 β ) or ∂ z ( Q α Q β ). These cases contrast with a case where Φ contains term Q β ∂ z Q α - Q α ∂ z Q β . The present paper investigates the latter case. Let \(\hat{h}\) and U denote the wavenumber and amplitude of prototype undulation, respectively. Let h denote the wavenumber of undulation of the order parameters in the ferroic phase. In the present case, unlike in the previous cases, h separates from \(\hat{h}\). The expression of dependence of h on U and the expression of dependence of the transition temperature on both U and \(\hat{h}\) are deduced. The former expression presents the criterion for judging whether ∣ h ∣ increases or decreases with increasing U .