Static magnetoelectric and magnetoelastic response of composite cantilevers: Theory of short vs. open circuit operation and layer sequence effects

The static bending-mode transverse magnetoelectric effect and the magnetic field-induced bending response of composite cantilevers with thin magnetostrictive (MS), piezoelectric (PE), and substrate (Sub) layers is investigated for the PE layer subjected to open and short circuit conditions. Analytic theories are presented for strain-coupled three layer composites of PE, MS, and Sub layers in all layer sequences. We use constitutive equations with linear coupling of stress, strain, H, E, and D fields and present results for the open and short circuit magnetoelectric and bending responses for arbitrary layer thickness ratios for the FeCoBSi-AlN-Si materials system. Besides a rich sequence dependent behavior the theory predicts great and systematic differences between the open and short circuit magnetoelectric response yielding maxima at similar MS and PE layer thicknesses in the open circuit and near vanishing PE layer thicknesses in the short circuit cases. In contrast, the open vs. short circuit bending response differences are pronounced but much smaller. Layer sequence systematics and implications for static H-field sensors will be discussed