Magnetoelectric effects in compositionally-stepped multilayers of lead-free piezoelectric and magnetostrictive components

A theoretical model is provided for ME effect in compositionally-stepped multi-layers of piezoelectric and magnetostrictive components. We assume the piezoelectric and piezo-magnetic layers to be perfectly bonded together and the piezoelectric layers restrict the strain of the piezomagnetic layer in an applied magnetic field. Analytical expressions for ME voltage coefficients are derived by substituting the value of stress into open electric circuit condition. Using the layered structure based on the compositionally-stepped piezoelectric components leads to an enhanced magnetoelectric coupling for specific component thickness ratio due to an increase in flexural deformation as compared with the bilayer based on homogeneous piezoelectric layer. As an example, we consider the layered structure based on lead-free piezoelectric langasite bimorph and magnetostrictive permendur.