Dynamics of interacting clusters and dielectric response of relaxor ferroelectrics

TL;DR

This paper presents a model for the dielectric response of relaxor ferroelectrics based on polar cluster dynamics, explaining the Vogel-Fulcher behavior of permittivity maxima through cluster reorientation frequencies.

Contribution

The study introduces a comprehensive polarization dynamics model that accounts for cluster interactions and distribution of reorientation frequencies in relaxor ferroelectrics.

Findings

The dielectric constant shape aligns with experimental data for PST.

Vogel-Fulcher dependence arises from cluster reorientation frequency temperature dependence.

The model links polar cluster behavior to relaxor dielectric properties.

Abstract

The dielectric response in relaxor ferroelectrics is analyzed in the framework a model for the polarization dynamics in the presence of polar clusters. We associate the origin of polar clusters with the atoms displaced from their centro-symmerical positions even above $T_c$. Their collective hopping in multi-well potentials induced by disorder is analogous with the situation in glasses. The theory explicitly takes into account the distribution of cluster reorientation frequencies and the effect of cluster-cluster interactions in highly polarizable crystals, which we describe in terms of the local field distribution function. The dielectric constant is obtained from an integral master equation for the polarization dynamics in the presence of a time dependent electric field. The theory is applied for the analysis of the shape of the frequency dependent permittivity in the typical relaxor ferrolectrics $PST$ as a function of temperature. The comparison of the theory with experiment shows that in contrast to earlier assumptions, the observed Vogel-Fulcher dependence of the permittivity maximum is a consequence of the Vogel-Fulcher temperature dependence of the cluster reorientation frequency.