$1/E^2$' law: solution of the unsolved problem in the physics of ferroelectrics

An unusual frequency dependence of a coercive field observed in polycrystalline ferroelectric films of Pb(Zr$_{1-x}$Ti$_{x}$)O$_{3}$ solid solutions in a wide frequency range has been explained within the model of surface sources emitting thin ferroelectric domains with reversed polarization. This model makes it possible to interpret experimental data as the manifestation of the coercivity paradox in polycrystalline films and predicts the existence of the limiting frequency for switching of domains in agreement with the experiment. The proposed mechanism of polarization switching explains the observed temperature dependence of the activation field $E_{a}\propto T^{-1/2}$. Furthermore, it predicts an increase in the activation energy for the nucleation of domains with an increase in the size of the source, indicating that the coercive field increases with the degradation of small.