Elastic properties of magnetostrictive thin films using bending and torsion resonances of a bimorph

In recent years the delta-E effect has been used for detecting low frequency and low amplitude magnetic fields. Delta-E effect sensors utilize a forced mechanical resonator that is detuned by the delta-E effect upon application of a magnetic field. Typical frequencies of operation are from several kHz to the upper MHz regime. Different models have been used to describe the delta-E effect in those devices, but the frequency dependency has mainly been neglected. With this work we present a simple description of the delta-E effect as a function of the differential magnetic susceptibility χ of the magnetic material. We derive an analytical expression for χ that permits describing the frequency dependency of the delta-E effect of the Young’s modulus and the magnetic sensitivity. Calculations are compared with measurements on soft-magnetic (Fe90Co10)78Si12B10 thin films. We show that the frequency of operation can have a strong influence on the delta-E effect and the magnetic sensitivity of delta-E effect sensors. Overall, the delta-E effect reduces with increasing frequency and results in a stiffening of the Young’s modulus above the ferromagnetic resonance frequency. The details depend on the Gilbert damping. Whereas for large Gilbert damping the sensitivity continuously decreases with frequency, typical damping values result in an amplification close to the ferromagnetic resonance frequency.

Section: The Delta-e Effectsupporting

confidence: 90%

Frequency Dependency of the Delta-E Effect and the Sensitivity of Delta-E Effect Magnetic Field Sensors

Spetzler

Голубева

Müller

et al. 2019

“…This concept was realized with bulk acoustic shear waves in amorphous ribbons [ 38 ] and recently with surface acoustic shear waves in magnetic thin film devices [ 10 , 39 , 40 , 41 , 42 ]. Only very few studies investigate torsion modes in beam structures [ 43 , 44 ], either with electrostatically actuated cantilevers [ 43 ] or double-clamped beams [ 44 ]. Both studies are limited to specific configurations of the magnetic system and consider neither the full tensor relations of the mechanics and the delta-E effect nor higher resonance modes.…”

Section: Introductionmentioning

confidence: 99%

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

Spetzler

Голубева

Friedrich

et al. 2021

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.

“…Due to the different layer stack of the delay-line region with the MS layer, the wave velocity and the wavelength decrease, before returning to its original velocity and wavelength at the receiver IDT. Applying a magnetic field changes the effective mechanical stiffness of the MS material via the delta-E effect [ 12 , 13 , 14 , 15 ]. This results in a change of the wave velocity and thereby in a magnetic field dependent phase change

as illustrated in Figure 1 .…”

Section: Introductionmentioning

confidence: 99%

“…Besides other SAW sensors [ 5 , 6 , 7 , 16 , 17 , 18 ], the delta-E effect is used for magnetic-field sensing with magnetoelectric composite resonators operating in bending or bulk modes [ 19 , 20 , 21 , 22 ]. In contrast to such sensors, the sensitivity of Love-wave magnetic-field sensors is expected to benefit from shear-resonance, as the elastic modulus change of the magnetostrictive material was reported to be largest for shear stress [ 14 ]. A focus of current research is to maximize the sensitivity, which is essential to overcome thermal phase noise, thus allowing measurements of small amplitude magnetic fields.…”

Section: Introductionmentioning

confidence: 99%

Multi-Mode Love-Wave SAW Magnetic-Field Sensors

Schmalz

Kittmann

Durdaut

et al. 2020

A surface-acoustic-wave (SAW) magnetic-field sensor utilizing fundamental, first- and second-order Love-wave modes is investigated. A 4.5 μ m SiO2 guiding layer on an ST-cut quartz substrate is coated with a 200 n m (Fe90Co10)78Si12B10 magnetostrictive layer in a delay-line configuration. Love-waves are excited and detected by two interdigital transducers (IDT). The delta-E effect in the magnetostrictive layer causes a phase change with applied magnetic field. A sensitivity of 1250 ° / m T is measured for the fundamental Love mode at 263 M Hz . For the first-order Love mode a value of 45 ° / m T is obtained at 352 M Hz . This result is compared to finite-element-method (FEM) simulations using one-dimensional (1D) and two-and-a-half-dimensional (2.5 D) models. The FEM simulations confirm the large drop in sensitivity as the first-order mode is close to cut-off. For multi-mode operation, we identify as a suitable geometry a guiding layer to wavelength ratio of h GL / λ ≈ 1.5 for an IDT pitch of p = 12 μ m . For this layer configuration, the first three modes are sufficiently far away from cut-off and show good sensitivity.