  Recent electron spin resonance experiments on CaWO$_4$:Gd$^{3+}$ and on other
magnetic impurities have demonstrated that sustained Rabi oscillations can be
created by driving a magnetic moment with a microwave field frequency slightly
larger than the Larmor frequency and tuned to the Floquet resonance together
with another microwave field (image drive). These observations are confirmed by
the new experimental results reported in this paper. We investigate several
mechanisms of decoherence and dissipation by using a combination of numerical
and analytical techniques. The first microscopic model describes a magnetic
moment in external magnetic fields, interacting with a bath of two-level
systems acting as a source of decoherence and dissipation. The second model
describes a collection of the identical, interacting magnetics moments, all
subject to the same magnetic fields. In this case, the many-body interactions
causes a decay of the Rabi oscillations. In addition, we also study the effect
of the inhomogeneity of the microwave radiation on the decay of the Rabi
oscillations. Our simulation results show that the dynamics of a magnetic
moment subject to the two microwave fields with different frequencies and in
contact with an environment is highly nontrivial. We show that under
appropriate conditions, and in particular at the Floquet resonance, the
magnetization exhibits sustained Rabi oscillations, in some cases with
additional beatings. Although these two microscopic models separately describe
the experimental data well, a simulation study that simultaneously accounts for
both types of interactions is currently prohibitively costly. To gain further
insight into the microscopic dynamics of these two different models, we study
the time dependence of the bath and system energy and of the correlations of
the spins, data that is not readily accessible experimentally.
