A ferromagnetic gyroscope (FG) is a ferromagnet whose angular momentum is dominated by electron spin polarization and that will precess under the action of an external torque, such as that due to a magnetic field. Here we model and analyze FG dynamics and sensitivity, focusing on practical schemes for experimental realization. In the case of a freely floating FG, we model the transition from dynamics dominated by libration in relatively high externally applied magnetic fields, to those dominated by precession at relatively low applied fields. Measurement of the libration frequency enables in situ measurement of the magnetic field and a technique to reduce the field below the threshold for which precession dominates the FG dynamics. We note that evidence of gyroscopic behavior is present even at magnetic fields much larger than the threshold field below which precession dominates. We also model the dynamics of an FG levitated above a type-I superconductor via the Meissner effect, and find that for FGs with dimensions larger than about 100 nm the observed precession frequency is reduced compared to that of a freely floating FG. This is akin to negative feedback that arises from the distortion of the field from the FG by the superconductor. Finally we assess the sensitivity of an FG levitated above a type-I superconductor to exotic spin-dependent interactions under practical experimental conditions, demonstrating the potential of FGs for tests of fundamental physics.
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