Phase-field model for epitaxial ferroelectric and magnetic nanocomposite thin films

A phase-field model was developed for studying the magnetoelectric coupling effect in epitaxial ferroelectric and magnetic nanocomposite thin films. The model can simultaneously take into account the ferroelectric and magnetic domain structures, the electrostrictive and magnetostrictive effects, substrate constraint, as well as the long-range interactions such as magnetic, electric, and elastic interactions. As an example, the magnetic-field-induced electric polarization in $BaTiO3–CoFe2O4$ nanocomposite film was analyzed. The effects of the film thickness, morphology of the nanocomposite, and substrate constraint on the degree of magnetoelectric coupling were discussed.