Analysis of the non linear domain wall response in ferroelectric thin films

In ferroelectric materials, domain wall displacement plays a key role in the dielectric properties measured with respect to the driving field amplitude and frequency. The low to medium field dielectric response in many ferroic systems can be often described by classical Rayleigh model, which is rate-independent i.e., it depends only on the strength of ac signal. However experiments show that the nonlinear parameters are frequency dependent. Thus a more general approach, which can describe both purely nonlinear, rate independent, and frequency dependent mechanisms is sought. Here, we show that a coupled power law and Rayleigh-type responses describe well nonlinear and dispersive complex dielectric permittivity in Pb(ZrTi)O-3 thin films over a broad frequency (0.01-100 kHz) and field amplitude range.