  We investigate the fluctuation properties in the eigenfrequency spectra of
flat cylindrical microwave cavities that are homogeneously filled with
magnetized ferrite. These studies are motivated by experiments in which only
small pieces of ferrite were embedded in the cavity and magnetized with an
external static magnetic field to induce partial time-reversal (T ) invariance
violation. We use two different shapes of the cavity, one exhibiting an
integrable wave dynamics, the other one a chaotic one. We demonstrate that in
the frequency region where only transverse-magnetic modes exist, the
magnetization of the ferrites has no effect on the wave dynamics and does not
induce T -invariance violation whereas it is fully violated above the cutoff
frequency of the first transverse-electric mode. Above all, independently of
the shape of the resonator, it induces a chaotic wave dynamics in that
frequency range in the sense that for both resonator geometries the spectral
properties coincide with those of quantum systems with a chaotic classical
dynamics and same invariance properties under application of the generalized T
operator associated with the resonator geometry.
