The Tilting Mode: A New Degree of Freedom for Magneto-Mechanical Resonator Sensors

Abstract

Magneto-mechanical resonators (MMRs) are an emerging class of passive, wireless sensors. Their torsional oscillation mode has recently been established for sensing and tracking applications. In this work, we report the identification and characterization of a second mechanical mode, the tilting mode, that provides sensitivity along an axis inaccessible to the torsional mode, opening up a new degree of freedom for tracking and sensing with a single MMR sensor. We derive an analytical model predicting the tilting frequency as a function of the geometric and magnetic parameters of the resonator, compare the tilting mode frequency to that of the torsional mode, and obtain a characteristic frequency ratio between the torsional and the tilting mode in the small angle approximation. Experimental characterization using three-axis excitation and detection confirms the mode's existence and its directional selectivity. Notably, the three-axis frequency response shows no observable cross-coupling between the torsional and the tilting mode. We further show that the tilting mode frequency follows the predicted dependence on magnet distance, confirming the analytical model and the mode's applicability for sensing, analogous to that of the torsional mode.