Order-parameter symmetries for improper ferroelectric nonferroelastic transitions

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Abstract
The possibility of improper ferroelectric nonferroelastic transitions and the symmetry of their order parameter are theoretically investigated on the basis of Landau's symmetry criteria for second-order phase transitions. Crystallographic restrictions lead to the examination of 103 different paraelectric space groups for which results are given, in table form, at all the relevant high-symmetry points of their respective Brillouin zone. It is found that the considered transitions are associated with irreducible representations corresponding to nine points only of the boundaries of the different Brillouin zones. The allowed space-symmetry changes are indicated, and the related free-energy expansions are constructed. Three forms of thermodynamic potentials are encountered, associated, respectively, with a two-component order parameter quadratically coupled to the polarization, with a two-component order parameter whose third power is coupled to the polarization, and with a three-component order parameter whose third power is coupled to the polarization. Available experimental data are discussed in the light of these theoretical results.