A Second Type of Prototypic to Ferroelectro-Incommensurate Transitions When the Number of Proper Order Parameters is One

Abstract

This paper proposes a second type of transitions from prototypic phases to simultaneously incommensurate and ferroelectric phases when the number of proper order parameters, N p , equals one. This type differs from the first type in the following respects: In the second type, the number of subsidiary order parameters equals two ( not one), the gradient-linear term is second degree ( not third degree) with respect to the order parameters, and the transition can be second order ( not must be first order). The \bar4 m 2- A 2 - E case, where A 2 is the irreducible representation for the proper order parameter and E for the subsidiary order parameters, is investigated as exemplifying the second type. Although the reverse case, i.e., the \bar4 m 2- E - A 2 case has N p ≠1, it is also investigated for the sake of comparison.