Theory of magnetoelectric effect in multilayer nanocomposites on a substrate: Static bending-mode response

Magnetoelectric (ME) coefficients for bending excitation in static magnetic fields and the bending response of multilayer composites with alternating magnetostrictive (MS) and piezoelectric (PE) layers on a substrate are investigated systematically. Theory and closed-form analytic solutions for the static magnetoelectric and the bending response coefficients are presented. Results of systematic variation of layer numbers, layer sequences, PE volume fractions, substrate thicknesses, and four different material systems (employing FeCoBSi, Terfenol-D, AlN, PZT, and Si) are given for a fixed total composite thickness of 5μm. Among more than 105 structures investigated the greatest static ME coefficient of 62.3 V/cmOe is predicted for all odd layer number FeCoBSi-AlN multilayer composites on a Si substrate at vanishing substrate thickness and a PE material fraction of 38%. Varying the substrate thickness from 0μm to 20μm and the PE fraction from 0% to 100%, broad parameter regions of high ME coefficients are found for odd and large layer number nanocomposites. These regions are further enhanced to narrow maxima at vanishing substrate thickness, which correspond to structures of vanishing static bending response. For bilayers and even layer number cases broad maxima of the ME coefficient are observed at nonzero substrates and bending response. The optimal layer sequence and PE fraction depend on the material system. Bending response maxima occur at zero Si substrate thickness and nonzero PE fractions for bilayers. For multilayers nonzero Si substrates and zero PE fractions are found to be optimal. Structures of even ME layer numbers of PE-MS...Sub layer sequence display regions of vanishing bending response with large ME coefficients, i.e., produced by longitudinal excitation.