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

抄録

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(Q²_α -Q²_β ) or ∂ _z(Q_α Q_β ). These cases contrast with a case where {Φ} contains term Q_β ∂ _zQ_α -Q_α ∂ _zQ_β . The present paper investigates the latter case. Let ĥ 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 ĥ. The expression of dependence of h on U and the expression of dependence of the transition temperature on both U and ĥ are deduced. The former expression presents the criterion for judging whether | h| increases or decreases with increasing U.