Stability of a ferroelectric phase with electrical domains in multilayers

Multilayer BaTiO3-SrTiO3 and PbTiO3-SrTiO3 structures with different electrical domain states are studied using a Landau-Ginzburg-Devonshire free energy. Polarizations in the layers are computed for multi-domain and single-domain states where the paraelectric-to-ferroelectric volumetric layer ratio is varied. It is shown that the ferroelectric layers with electrical domains are thermodynamically more stable than the single-domain ferroelectric state. High domain wall energies result in the stabilization of the paraelectric state in the ferroelectric layers for large depolarizing fields. It is concluded that the stability of single-domain state ferroelectric layers correspond to a very small paraelectric-to-ferroelectric ratio after which multi-domain ferroelectric state is favored.