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

Abstract

Resonant bending-mode magnetoelectric (ME) coefficients of magnetostrictive-piezoelectric multilayer cantilevers are calculated analytically using a model developed for arbitrary multilayers on a substrate. Without quality factor effects the ME coefficient maxima in the four-dimensional parameter space of layer numbers, layer sequences, piezoelectric volume fractions, and substrate thicknesses are found to be essentially constant for nonzero substrate thickness. Global maxima occur for bilayers without substrates. Vanishing magnetoelectric response regions result from voltage cancellation in piezoelectric layers or absence of bending-mode excitation. They are determined by the neutral plane position in the multilayer stack. With Q-factor effects dominated by viscous air damping ME coefficients strongly increase with cantilever thickness primarily due to increasing resonance frequencies. The results yield a layer specific prediction of ME coefficients, resonance frequencies, and Q-factors in arbitrary multilayers and thus distinction of linear-coupling and Q-factor effects from exchange interaction, interface, or nonlinear ME effects

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

“…Recently near bulk piezoelectric properties were achieved for 10nm AlN. 42 The open circuit results 36,37 and corresponding neutral plane behavior are briefly reiterated here. Minima regions producing primary and secondary maxima of the ME response are observed only in the layer sequences with functional materials at the central layer.…”

“…Low frequencies required for biomagnetic applications in medical diagnostic and imaging techniques (Magnetoencephalography, Magnetocardiography) have focused research on cantilever sensors using the resonance enhanced bending-mode magnetoelectric effect. [9][10][11]21,23 In recent papers [36][37][38] we investigated the static and resonant bending mode magnetoelectric effect in multilayer cantilevers of arbitrary layer number and different sequences on a substrate identifying optimized device geometries in a large multidimensional parameter space.…”

Effect of excitation mode on the magnetic field detection limit of magnetoelectric composite cantilevers

“…for free-free modes. Equations (15) and (16) are derived from the results for dQ dH using Eqs. (6) and (8) and additional calculation of dH dz at the cantilever tip x = a for the bound-free and free-free mode cases.…”

“…[9][10][11][12][13] The results have encouraged investigations to enable the detection of weak low frequency biomagnetic fields with room temperature sensors. 14 This has involved research to increase the effect size of the ME response, e.g., materials, effects of device geometry and operation modes, [15][16][17][18] resonance-enhancement and loss mechanisms, 13 and investigation of noise effects and their behavior including the Johnson-Nyquist noise [19][20][21][22][23] from dielectric losses in piezoelectric materials 24 in ME cantilevers and electronics, noise in magnetostrictive (MS) materials, and thermal vibration noise. 23,[25][26][27][28] Different operation modes investigated for low frequency biomagnetic field sensing 14 include (1) direct detection, where magnetic fields oscillating at the cantilever resonance directly excite magnetostrictivepiezoelectric strain coupling and resonance-enhanced signals; (2) modulation techniques, [29][30][31] where signal fields are detected as sidebands to a carrier as a result of frequency mixing in non-linear functional materials; and (3) the ΔE effect, 32,33 where the field dependence of the elastic modulus in magnetostrictive materials is used.…”

Size-dependent effects on electromechanical response of multilayer piezoelectric nano-cylinder under electro-elastic waves

“…Dai et al obtained the analytical solution of stresses in multilayer piezoelectric hollow structures [6]. Using a model of arbitrary multilayers on a substrate, Krantz and Gerken calculated the resonant bending-mode magnetoelectric (ME) coefficients of magnetostrictive-piezoelectric multilayer cantilevers, and it was found that ME coefficients strongly increase with cantilever thickness primarily due to increasing resonance frequencies [7]. An improved 1-D stress model for a single layer transformer in vacuum was used to model the multilayered transformer mounted on a printed circuit board, and a square pulse signal was amplified [8].…”