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

• Main Authors: Benjamin Spetzler, Elizaveta V. Golubeva, Ron-Marco Friedrich, Sebastian Zabel, Christine Kirchhof, Dirk Meyners, Jeffrey McCord, Franz Faupel
• Format: Article
• Language: English
• Published: MDPI AG 2021-03-01
• Series: Sensors
• Subjects: delta-E effect; magnetoelectric; magnetoelastic; resonator; torsion mode; bending mode
• Online Access: https://www.mdpi.com/1424-8220/21/6/2022

<b> </b>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 <i>C</i><em>_ij</em><i> </i>is derived. Simulations confirm quantitatively that the delta-E effect of the <i>C</i>₆₆ component has the promising potential of significantly increasing the magnetic sensitivity and the maximum normalized frequency change ∆<em>f</em>_r. 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 ∆<em>f</em>_r of TMs on the mode number, which differs fundamentally from BMs and is well explained by our model. Because the contribution of <i>C</i>₁₁ 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.