Magnetoelectric effect in thin-film magnetostriction-piezoelectric structures grown on a substrate

The theory of the magnetoelectric effect in a thin magnetoelectric film-passive substrate structure is presented. Based on the simultaneous solution of the constitutive equations and the equations of motion for the film and substrate, the dispersion law has been derived for elastic waves propagating in the sample plane. It has been shown that the elastic vibrations in the substrate propagate in a near-surface layer if the velocity of propagation of elastic vibrations in the substrate is higher than that in the magnetoelectric film. In this case, the substrate thickness almost does not influence the magnitude of the effect.