Study of the evolution of 180° domain pattern microstructure using measurements of nonlinear permittivity

In this work, we study theoretically and experimentally the linear and nonlinear dielectric response in a system where the extrinsic permittivity is controlled by bending movements of pinned 180° domain walls. We calculated the linear and nonlinear extrinsic contribution to permittivity and discovered a quadratic relationship between them, which is a feature quite different from that of the lattice contribution derived from Landau theory. We show that, from measured values of linear and nonlinear permittivity, it is possible to determine the configuration of the 180° domain pattern and the concentration of the pinning centers in the ferroelectric. Therefore, our results can be used as a simple and useful tool for getting a deeper insight into the configuration of the domain pattern and the quality of the ferro-electric thin films, which is demonstrated on data obtained from [111] oriented PZT (45/55) thin film.