Dispersive Frequency Shifts in the EPR spectra of the Single-Molecule Magnet Fe$_8$

High-frequency electron paramagnetic resonance (EPR) has been used to study single-molecule magnets (SMMs) for more than a decade. We observe dispersive effects in a cylindrical cavity when a single crystal of the Fe$_8$ SMM is tuned to resonance with millimeter-wave radiation. The reflected power from the cavity is measured as a function of the radiation frequency at magnetic fields from 0 to 1.5 Tesla and temperatures between 2.0 and 20.0 K. Although the sample/cavity filling factor is small, $\sim$0.1\%, we observe a substantial sample-induced frequency shift of the cavity resonance when the field brings a dipole- allowed transition near resonance with the applied radiation. At 2.0 K, the resonant frequency of the cavity ($\sim$117.5 GHz) exhibits a shift on the order of 10 MHz (comparable to the width of the cavity resonance). At the same time, we observe a reduction in both the cavity Q and the amount of power absorbed by the cavity. The data allows us to gain both dispersive and absorptive information about the material.