Improper ferroelectrics

Improper ferroelectrics are considered in the review from a unified point of view on the basis of the phenomenological Landau theory of phase transitions. In such ferroelectrics, in contrast to the ordinary ones, the order parameter of the phase transition is not the polarization but another physical quantitiy whose transformation properties are different from those of the polarization. Spontaneous polarization arises in the phase transition as a secondary effect. Therefore, the dielectric anomalies in the improper ferroelectrics are significantly different from the dielectric anomalies in the ordinary ferroelectrics. In particular, the temperature dependence of the permittivity does not obey the Curie-Weiss law, an electric field does not suppress the phase transition, etc. The dielectric anomalies are derived by analyzing a definite form of the thermodynamic potential with a two-component order parameter. Such an analysis turns out to be sufficient for the discussion of the available experimental data. The domain structure of the improper ferroelectrics also possesses specific properties: In particular, there exist domains which do not differ in their polarizations. Since the loss of stability in an improper ferroelectric phase transition occurs not with respect to polarization, the soft mode in the nonpolar phase is inactive in the infrared spectrum. Other distinctive features of the phonon spectrum in the phase-transition region are also considered. The experimental data on improper ferroelectrics are discussed. For the rare-earth molybdates, the theory is in quantitative agreeement with experiment. In certain other improper ferroelectrics the phase transitions are of first order and nowhere near to being of second order. The quantitative description of such transitions requires additional experimental data and further development of the theory.