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

Miniaturized piezoelectric/magnetostrictive contour-mode resonators have been shown to be effective magnetometers by exploiting the ΔE effect. With dimensions of ~100-200 μm across and <1 μm thick, they offer high spatial resolution, portability, low power consumption, and low cost. However, a thorough understanding of the magnetic material behavior in these devices has been lacking, hindering performance optimization. This manuscript reports on the strong, nonlinear correlation observed between the frequency response of these sensors and the stress-induced curvature of the resonator plate. The resonance frequency shift caused by DC magnetic fields drops off rapidly with increasing curvature: about two orders of magnitude separate the highest and lowest frequency shift in otherwise identical devices. Similarly, an inverse correlation with the quality factor was found, suggesting a magnetic loss mechanism. The mechanical and magnetic properties are theoretically analyzed using magnetoelastic finite-element and magnetic domain-phase models. The resulting model fits the measurements well and is generally consistent with additional results from magneto-optical domain imaging. Thus, the origin of the observed behavior is identified and broader implications for the design of nano-magnetoelastic devices are derived. By fabricating a magnetoelectric nano-plate resonator with low curvature, a record-high DC magnetic field sensitivity of 5 Hz/nT is achieved.