Simulation of hysteresis curves of crystalline ferroelectrics using the controlling electric field parameters

We propose a description of switching in crystalline ferroelectrics taking into account the action of a varying external electric field, based on the equations of relaxation processes. We suppose that the probability of switching of domains depends not only on the instantaneous value of the controlling field, but also on the rate of its variation. The time dependence of the controlling field is defined by an arbitrary periodic function. The equations of the domain switching processes in a ferroelectric are derived and the exact analytic solutions to these equations are obtained. Numerical analysis of the interrelation between the frequency of the sinusoidal external field and the shape of the hysteresis curves is carried out on the basis of the resultant solutions. It is shown that the inclusion of the dependence of relaxation time on the rate of the controlling field variation makes it possible to sufficiently improve the agreement between the results of simulation of the ferroelectric hysteresis curves and the experimental data.