Magnetoelastic Coupling and Delta-E Effect in Magnetoelectric Torsion Mode Resonators

Abstract

Magnetoelectric resonators have been studied for the detection of small amplitude and low frequency magnetic fields via the delta-E effect, mainly in fundamental bending or bulk resonance modes. Here, we present an experimental and theoretical investigation of magnetoelectric thin-film cantilevers that can be operated in bending modes (BMs) and torsion modes (TMs) as a magnetic field sensor. A magnetoelastic macrospin model is combined with an electromechanical finite element model and a general description of the delta-E effect of all stiffness tensor components Cij is derived. Simulations confirm quantitatively that the delta-E effect of the C66 component has the promising potential of significantly increasing the magnetic sensitivity and the maximum normalized frequency change ∆fr. However, the electrical excitation of TMs remains challenging and is found to significantly diminish the gain in sensitivity. Experiments reveal the dependency of the sensitivity and ∆fr of TMs on the mode number, which differs fundamentally from BMs and is well explained by our model. Because the contribution of C11 to the TMs increases with the mode number, the first-order TM yields the highest magnetic sensitivity. Overall, general insights are gained for the design of high-sensitivity delta-E effect sensors, as well as for frequency tunable devices based on the delta-E effect.

Curvature and Stress Effects on the Performance of Contour‐Mode Resonant ΔE Effect Magnetometers

“…On the other hand, the Δ E effect [ 18,19 ] is the property of magnetic materials in which the Young's modulus changes nonlinearly as a function of magnetic field, which may be DC or AC. This can be utilized as a sensing mechanism by monitoring the magnetic field‐induced change in output signal from a driven resonator, caused by a shift in resonance frequency.…”

Modeling and Parallel Operation of Exchange-Biased Delta-E Effect Magnetometers for Sensor Arrays

“…The higher resonance frequencies permit miniaturization and render the devices robust against mechanical disturbances. The modulation occurs via the magnetoelastic delta-E effect [24][25][26], i.e., the magnetization induced change of the stiffness of the material, which leads to a detuning of the resonance frequency upon the application of a magnetic field. This detuning can be measured as a change of the electrical admittance of the sensor and causes a modulation of the current through the sensor [27].…”

“…This detuning can be measured as a change of the electrical admittance of the sensor and causes a modulation of the current through the sensor [27]. Although precursor steps towards the delta-E effect sensor concept were already made in the 1990s [28], it took another two decades until fully integrable delta-E effect sensors [29] were developed based on microelectromechanical magnetoelectric composite cantilevers [26,[30][31][32][33][34], plate resonators [35,36], or other designs [37], including macroscopic laminate structures [38,39]. MEMS cantilever sensors achieved LODs < 100 pT/ √ Hz in the frequency range from approximately 10-100 Hz [32].…”

Magnetoelectric Magnetic Field Sensors: A Review

“…Taking into account the requirements for the frequency range and dimensions, we should consider ME sensors based on the delta-E effect to be more promising for biomagnetic measurements. In [ 22 , 29 , 68 ], such sensors with high sensitivity and micro-design are described, which can find wide application in biomedicine.…”

“…In particular, the magnetostrictive component was replaced by a NdFeB magnet [ 20 ], then a miniature and highly sensitive MEMS structure [ 21 , 22 ], and NEMS and nanoresonator [ 23 , 24 , 25 ] for biomedicine were proposed, and a nonlinear regime and new components such as piezoelectric AlN and soft magnetic Ni [ 26 , 27 , 28 ] were used. In addition, new possibilities for developing sensors on the basis of the ΔE—effect have been discussed [ 29 , 30 ]. In this article, we look at these options in more detail.…”