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

Abstract

The magnetoelectric effect in layered composite cantilevers consisting of strain coupled layers of magnetostrictive (MS), piezoelectric (PE), and substrate materials is investigated for magnetic field excitation at bending resonance. Analytic theories are derived for the transverse magnetoelectric (ME) response in short and open circuit operation for three different layer sequences and results presented and discussed for the FeCoBSi-AlN-Si and the FeCoBSi-PZT-Si composite systems. Response optimized PE-MS layer thickness ratios are found to greatly change with operation mode shifting from near equal MS and PE layer thicknesses in the open circuit mode to near vanishing PE layer thicknesses in short circuit operation for all layer sequences. In addition the substrate layer thickness is found to differently affect the open and short circuit ME response producing shifts and reversal between ME response maxima depending on layer sequence. The observed rich ME response behavior for different layer thicknesses, sequences, operating modes, and PE materials can be explained by common neutral plane effects and different elastic compliance effects in short and open circuit operation.

Signal-to-Noise Ratio in Cantilever Magnetoelectric Sensors

“…In the first bending mode a magnetic field causes highest elastic deformations in the cantilever at the clamped end and due to the elastic coupling to the piezoelectric layer highest induced electric potentials are localized in the same area. It has been shown that the output signal can be enhanced by using magnetic flux concentrators [3]- [5], preventing air damping [6] and the use of optimized layer thicknesses and sequences [7], [8]. Furthermore, we have shown that the use of pick-up regions can further increase the electric potential [9].…”

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

“…In the following, we present a theory of the resonant magnetoelectric response and the noise density from thermal vibration, Johnson-Nyquist, and electronics noise yielding the magnetic field detection limit of ME cantilevers excited to arbitrary bound-free and free-free bending modes. As opposed to the theory for the ME-response for the first bound-free mode given earlier, 17 arbitrary higher bending modes, the differing solutions for free-free modes, mode-dependent thermal vibration noise, and the above noise sources are included here, predicting the detection limit parameterized to cantilever and layer dimensions and permitting the investigation of scaling behavior. A systematic comparison of the results of the thermal vibration noise limited magnetic field detection limit of the first three bound-free and free-free modes is given, whereby cantilever size scaling to a constant resonance frequency is used.…”

“…The ME response theory involves the constitutive equations for functional material effects and the Euler-Bernoulli beam theory covering cantilever dynamics for the calculation of the magnetic field-excited strain-induced piezoelectric charge at resonance and was given previously for the first bound-free bending mode. 17 The strain in the x-direction is related to stress and external fields by the following linear constitutive equations:…”

“…and was derived previously for the first bound-free mode 17 of a cantilever of length a and width b. Normalization by the quality factor Q f excludes details of line shape and damping effects affecting the resonance enhancement. These loss mechanism details and line shape effects are not considered here, the resonance enhancement of the dQ/dH term diverging at the ka values of Table I is normalized, and a constant Q f = 1000 is used throughout this work.…”

“…[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.…”