Field and frequency dependent dielectric response in ferroelectrics from impedance spectroscopy measurements: The domain wall pinning element

We introduce an equivalent-circuit element $Z_{\rm DW}$ based on the theory of interface pinning in random systems, to analyze the contribution of domain wall motion to the impedance of a ferroelectric, as a function of amplitude $E_0$ and frequency $f$ of an applied ac electric field. We investigate capacitor stacks, containing ferroelectric 0.5(Ba$_{0.7}$Ca$_{0.3}$)TiO$_{3}$--0.5Ba(Zr$_{0.2}$Ti$_{0.8}$)O$_{3}$ (BCZT) thin films, epitaxially grown by pulsed laser deposition on Nb-doped SrTiO$_3$ single crystal substrates and covered with Au electrodes. Impedance spectra from $f=10$ Hz to $1$ MHz were collected at different $E_0$. Deconvolution of the spectra is achieved by fitting the measured impedance with an equivalent-circuit model of the capacitor stacks. We find that dielectric nonlinearity and logarithmic frequency dispersion are coupled in the BCZT thin films, and we report on the explicit functional form of the coupled dielectric response. From an extended data analysis, we quantify the coupling strength and obtain a schematic phase diagram of the different domain wall motion regimes.