Landau Expansion for Ferroelectrics: Which Variable to Use?

The problem of the choice of the order parameter of the Landau expansion of proper ferroelectrics is discussed. The expansion with respect to the (i) electric displacement, (ii) polarization, (iii) ferroelectric contribution to the polarization, (iv) “order” parameter within the pseudo-proper approach, and (v) soft-mode displacements within the weak-ferroelectric approach are compared. The following conclusions concerning applicability of these expansions are made. The description in terms of the electric displacement is only of historical interest. This approach may lead to essentially wrong conclusions while it has no advantage over approach (ii) in terms of the simplicity of the framework. Approaches (ii) to (v) provide progressively more reliable descriptions of properties of ferroelectrics, although they are progressively more complex as well. Depending on the situation addressed, approaches (ii) to (iv) may lead to erroneous results or may be unable to describe a certain effect. In case the depolarizing energy comes into play approach (ii) may fail while (iii)–(v) still work well. In materials with anomalously small Curie Weiss constants (“weak ferroelectrics” with anomalously small effective charge of the soft mode) the full description is provided by approach (v), while a partial description is possible within (ii) to (iv).