Polarization Reversal Kinetics with Conducting Domain Walls: Application to Lithium Niobate Crystals

We model the ferroelectric polarization reversal taking into account conduction of domain walls. The capacitor geometry is considered as applied to lithium niobate. We show that the field dependence of the domain nucleation rate obeys the law $$\exp(-E_{n}/E)$$ , where $$E$$ is the applied field and $$E_{n}\approx 10^{2}$$ kV/mm is the characteristic field controlling the domain nucleation process. For the critical domains, the longitudinal size $$l_{c}^{*}$$ strongly exceeds the transversal size $$l^{*}_{a}\approx 1$$ nm. Our kinetic model includes not only random nucleation events but also the subsequent elementary events of the lateral growth obeying the Merz law $$\exp(-E_{l}/E)$$ with the field $$E_{l}=E_{n}/3\sqrt{3}$$ controlled by the crystal symmetry. Numerical simulations show distinct stages of the domain nucleation, lateral growth, and coalescence. In accordance with experiment, the polarization switching time obeys the law $$\exp(E_{*}/E)$$ with $$E_{*}=(E_{n}+2E_{l})/3$$ , while the hysteresis loops show a standard behavior with the coercive field $$E_{c}=(3-5)$$ kV/mm weakly dependent on the field ramping period.