Crossover in a non-analytical behaviour of dielectric non-linearity in relaxor ferroelectric

The dielectric response of the relaxor ferroelectric (PMN) is found to be a non-analytical function of the ac field, with the absolute value of the non-linear component of the polarization given by . The dependence on the temperature, T , and frequency, , of the exponent manifests itself in the form of a crossover in from approximately 2 to 3 upon cooling, whose position depends upon the frequency of the applied ac field. From the comparison of with the linear complex dielectric permittivity, , of PMN, the following can be correlated: (i) in the regime of the quasi-static response, and starts deviating from 2 simultaneously with the onset of the frequency dispersion; and (ii) when the spectrum of relaxation times in PMN becomes flat. These findings can be understood in terms of the change in the type of the motion of the interphase boundaries of the microscopic polar regions existing in PMN, namely in the change of the scale on which the interphase boundaries can move.