Identification of defect distribution at ferroelectric domain walls from evolution of nonlinear dielectric response during the aging process

The motion of ferroelectric domain walls greatly contributes to the macroscopic dielectric and piezoelectric response of ferroelectric materials. The domain-wall motion through the ferroelectric material is, however, hindered by pinning on crystal defects, which substantially reduces these contributions. Here, using thermodynamic models based on the Landau-Ginzburg-Devonshire theory, we find a relation between the microscopic reversible motion of nonferroelastic 180 degrees domain walls interacting with a periodic array of pinning centers and the nonlinear macroscopic permittivity. We show that the reversible motion of domain walls can be split into two basic modes: first, the bending of a domain wall between pinning centers, and, second, the uniform movement of the domain-wall plane. We show that their respective contributions may change when the distribution of pinning centers is rearranged during the material aging. We demonstrate that it is possible to indicate which mechanism of the domain-wall motion is affected during material aging. This allows one to judge whether the defects only homogeneously accumulate at domain walls or prefer to align in certain directions inside the domain-wall plane. We suggest that this information can be obtained using simple macroscopic dielectric measurements and a proper analysis of the nonlinear response. Our results may therefore serve as a simple and useful tool to obtain details on domain-wall pinning in an aging process.