Theory of the nonlinear susceptibility of relaxor ferroelectrics

Abstract

The theory of the nonlinear dielectric response to an external dc electric field is developed in the random-field-theory framework. The equations describing the dependence of the order parameter and the dielectric susceptibility (both linear and nonlinear) on the temperature, dc electric field, frequency, parameters of the host lattice and random-field sources are obtained. The numerical solution of these equations for several random-field-source concentrations and other parameters has shown that in the dipole-glass phase the dc electric field always decreases the dielectric response, while in the mixed ferroelectric-glass phase the dc field can either decrease or increase this response. Approximation of the numerical results for the nonlinear part of the susceptibility leads to with ( is the dimensionless dc-field value). It was shown that, for all of the cases considered, remains finite and has a maximum ( is the dipole-glass freezing temperature). The absence of critical divergency of the nonlinear susceptibility both in theory and experiment proves that, unlike conventional spin glass, the dipole-glass state in relaxors is a metastable state with long (up to infinite) relaxation times. A comparison of the theoretical results obtained with available experimental data for PMN and PMN-10PT is carried out. The calculated temperature and dc-field dependences of the nonlinear susceptibility are in agreement with observed data.