  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.
