Dynamics of nonlinear dielectric susceptibility of ferroelectrics near the morphotropic phase boundary

Abstract

The dynamics of the nonlinear (NL) dielectric susceptibility of ferroelectrics (FE) near the morphotropic phase boundary (MPB) is theoretically investigated based on the Landau–Devonshire free energy approach and the concept of FE soft modes. To do so, the NL dielectric susceptibility elements of FE material in the tetragonal phase are expressed as functions of optical phonon modes. These are the E modes with normal characteristic frequency and the A modes with . On the one hand, the tetragonal E modes appear to exhibit a double soft-mode character, i.e. the mode softens either when the thermodynamic temperature T approaches the transition temperature Tc or when the free energy parameter β1 approaches β2. On the other hand, the A modes exhibit single soft-mode character when T approaches Tc. Within this formulation, the dynamics of first-, second- and third-order NL susceptibility elements are investigated. The origin of the anomalous behavior of certain NL elements at the MPB appears to be a manifestation of FE mode-softening. This approach provides a simple yet powerful technique to understand the dynamics of the NL dielectric susceptibility elements of FE material near the MPB.