Magnetic Torque-Force Characterization of Permalloy Microspheres

We collected torque and force measurements from permalloy microspheres (diameter 40-60 um) mounted on silicon-nitride micro-oscillators to characterize the magnetic moments of the microspheres. The oscillator with the microsphere was held in vacuum and fixed above a permanent magnet, providing different microsphere moment orientations. Each sample was excited in an alternating magnetic field generated using an anti-Helmholtz configuration. Resonant frequency, damping, and force data were taken across various Helmholtz coil positions vertically about the sample-oscillator alignment, changing the AC magnetic field strength at positions outside of the center. At each position, frequency sweeping was repeated for differing permanent magnet angles, allowing for a range of torque variation. Data was collected using a traditional 1310 nm fiber optic interferometer. Our reported measurements, which have resolved microsphere moments as small as 5.1 × 10^-9 J/T, also delineate competing force-torque effects within our system.