Simulating Gadolinium-Induced Magnetic Field Variations for Temperature Sensing with Magneto-Mechanical Resonators

Small-size magneto-mechanical resonators (MMR) represent an emerging class of passive, wireless sensors that combine a sensing functionality with a tracking option. The operation principle is based on a resonating rotor oscillation whose frequency is defined by the magnetic flux density of a stator magnet. One general sensing mechanism is the coupling of an external parameter to this resonator frequency. In this study, we investigate an approach for encoding a temperature information as a shift in the natural oscillation frequency utilizing the temperature-dependent magnetic properties of gadolinium (Gd). We perform an isolated simulation study on the temperature scaling of the magnetic field generation for stators coated with Gd of varying thickness. Our results show that the magnetic phase transition of Gd at its Curie temperature leads to a pronounced change in the magnetic permeability enabling a significant magnetic shielding behavior only for lower temperatures. In the transition regime, we find a peak sensitivity reaching <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$45.8 ~\text{Hz} / \mathrm{K}$</tex> exceeding existing values from the literature by up to a factor of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\sim 20$</tex>. The findings of this work are an important step toward quantitative high-sensitivity temperature extraction with MMRs.