Resonant magnetoelectric response of cantilevers with magnetostrictive and piezoelectric layers on opposite sides of the substrate

A theory is derived for the bending-mode magnetoelectric coefficients at resonance for magnetostrictive and piezoelectric layers on opposite sides of a substrate. Results are given for the transverse ME coefficient in the Metglas-Si-AlN system with magnetic field excitation parallel and electric polarization perpendicular to the cantilever. The center-substrate layer sequence is found to produce about 50 % enhancement of the magnetoelectric effect compared to magnetoelectric bilayers on one side of a substrate. Up to about 10 % additional enhancement of the ME effect is predicted if the magnetostrictive and piezoelectric layers are separated from the substrate by spacer layers with lower Youngs modulus. Lowest order bending mode resonance frequencies are given.