Theory of ferroelectricity: The polarizability model

We consider ferroelectric compounds created by relative ionic displacements between two or more sublattices (‘‘displacive’’ phase transitions). For these ferroelectric materials the nonbonding p orbitals of oxygen (0^2-) or chalcogen (S^2-, etc.) ions play a central role, which is taken into account in the dynamical theory. It turns out that the fourth-order polarizability of the chalcogen ions is the main mechanism responsible for specific dynamical properties such as phonon dispersion curves and their anomalies (‘‘soft modes’’), Raman scattering, etc. The self-consistent phonon approximation is shown to give good results at all temperatures, particularly at T=0 (‘‘quantum limit’’) where this approximation is consistent with renormalized-group theory, and at very high temperatures (T≫T_c).