Experimental studies in magnetically induced transverse force-frequency effect in thin quartz microresonators

In this work, the transverse force-frequency sensitivity of magnetostrictive Metglas^® (Fe₈₅B₅Si₁₀) thin film coated AT-cut thickness shear mode quartz thin plate microresonator (500 μm × 500 μm × 19 μm) is experimentally measured and modeled in Lagrangian formulation by coupling magnetostrictive deformation equations with the basic plate equations from the theory of small deformation. The quartz plate resonator is fabricated by micromachining techniques and released into fixed-free structure using focused ion beam milling. Application of a magnetic field results in the out-of-plane bending of the structure due to elastic coupling between the magnetostrictive Metglas^® and quartz resonator layers. As a result of the transverse loading and out-of-plane bending, the admittance characteristics of the resonator shifts, and these shifts are recorded in real time utilizing a network analyzer. The sensitivity is experimentally measured to be 162.3 mdeg/Oe for phase, corresponding to a frequency sensitivity of Δf/H = 11 Hz/Oe. The equivalent force-frequency sensitivity can then be calculated as 2.36 μN/Hz using the developed model. The coupled domain analysis fits well with the experimental data. Further reduction of quartz thickness and optimization of the thickness ratio of the magnetostrictive to quartz layers offers the possibility of exploiting the stress sensitivity of plate microresonators as sensitive magnetic field sensors capable of low nanoTesla to picoTesla level magnetic flux densities