Domains in Multiferroic Films

The theory and modeling of equilibrium self-assembling nanostructures based on concept of elastic domains in multiphase epitaxial films successfully explained the morpholgies of CoFe$_{2}$O$_{4}$-PbTiO$_{3}$ films grown on differently oriented substrates. It is shown that it is possible to design the different nanostructure architectures: cobalt ferrite rods in lead titanate matrix and vise versa as well as differently oriented laminar structures. The elastic interactions between the phases determine the mutual change of order parameters: magnetization and polarization, that allow one to estimate the magneto-electric coupling through the study of constrained polarization and magnetization.