We introduce an equivalent-circuit element based on the theory of interface pinning in random systems to analyze the contribution of
domain wall motion below the coercive field to the impedance of a ferroelectric, as a function of amplitude E0 and frequency f of an
applied ac electric field. We demonstrate our model on a bulk PbZrxTi1xO3 (PZT) reference sample and then investigate capacitor
stacks, containing ferroelectric 0:5(Ba0:7Ca0:3)TiO3–0:5Ba(Zr0:2Ti0:8)O3 (BCZT) thin films, epitaxially grown by pulsed laser deposition
on Nb-doped SrTiO3 single crystal substrates and covered with Au electrodes. Impedance spectra from f ¼ 10 Hz to 1 MHz were collected at different E0. Deconvolution of the spectra is achieved by fitting the measured impedance with an equivalent-circuit model of
the capacitor stacks, and we extract for E0 ¼ 2:5 kV/cm, a frequency-dependent permittivity of ε0
r(f) ¼ 458 þ 7:3 ln 1Hz ð Þ =2πf for the
BCZT films from the obtained fit parameters. From an extended Rayleigh analysis, we obtain a coupling strength of 0.187 cm/kV
between dielectric nonlinearity and dielectric dispersion in the BCZT films and identify different domain-wall-motion regimes. Finally,
we construct a schematic diagram of the different domain-wall-motion regimes and discuss the corresponding domain-wall dynamics.
Our approach can be utilized to replace purely phenomenological constant phase elements (CPEs) in modeling the impedance response
of ferroelectrics and extracting material properties.