Transitions to Simultaneously Incommensurateand Ferroelectric Phases When the Numberof (Proper) Order Parameters Is One

Abstract

Transitions from prototypic phases to simultaneously incommensurate and ferroelectric phases are possible even when the number of (proper) order parameters is one. A case is investigated where the prototype point group is mmm and the (proper) order parameter belongs to the zero-wavenumber irreducible representation, B 2 u . A subsidiary order parameter, which is not soft like the proper one but moderately hard, is taken into account; it belongs to B 1 u . The B 2 u and B 1 u order parameters can be identified with polarization components P y and P z respectively. The free energy function contains term P y ( P z ∂ z P y - P y ∂ z P z ). This term can generate a phase incommensurate in the z direction and ferroelectric in the y direction. Sufficient conditions are found out for this ferroelectric incommensurate phase to outrival other ferroic phases in succeeding the prototypic phase.