Abrupt appearance of the domain pattern and fatigue of thin ferroelectric films

We study the domain structure in ferroelectric thin films with a passive (nonferroelectric) layer at the interface between the film and electrodes. An abrupt transition from a monodomain to a polydomain state has been found with the increase of the passive layer thickness d. The domain width changes very quickly at the transition (exponentially with d(-2)). The slope of the hysteresis loop is in agreement with experiment, assuming realistic parameters of the layer. The slope scales as lid, involving only the properties of the layer. We believe that specific properties of the domain structure in ferroelectrics with a passive layer can resolve the lone-standing paradox of the coercive field..