Domain proximity and ferroelectric transition in ferro-paraelectric superlattices

We investigate the ferroelectric phase transition and the domain formation in a periodic multilayer structure consisting of alternate ferroelectric (FE) and paraelectric (PE) layers of nanometric thickness. The principle result of this study is that the polarization domains formed in the different FE layers interact with each other through the PE layers via an inhomogeneous depolarizing electric field emerging from the domains of the neighboring FE layers. We call this a proximity effect. Based on electrostatic equations coupled with those obtained by the minimization of the Ginzburg-Landau functional for a ferroelectric, we calculated the renormalization of T c as a function of the FE/PE superlattice modulation period. We can describe quantitatively the recent experiments on the thickness dependence of the ferroelectric transition in KNbO3 -KTaO3 strained-layer superlattices.