Cavity Perturbation Technique: The Effects of Crystal Size on the EPR Spectra of Fe$_{8}$ Single-molecule Magnets*

The Cavity Perturbation Technique (CPT) is a contact-free technique that measures the change of the characteristics of a cavity resonator upon the introduction of the sample. In this experiment, we study the effect of crystal size with regards to the CPT transmission spectra for a single crystal of the Fe$_{8}$ single-molecule magnets. It is interesting to study the interaction between these two resonance systems, i. e. a cavity and a crystal of Fe8. We want to know whether it is a quantum mechanical or a classical interaction. The frequency shift and suppression of the cavity Q value increase linearly with increasing sample size. These observations are in agreement with the theoretical expectation for a classical coupling between the Fe$_{8}$ crystal and the cavity. From cavity perturbation theory, these phenomena may be explained by the following classical formula: $\Delta \omega $/$\omega \quad =-\beta \chi $, where $\omega $ is the complex frequency, $\beta $ is the filling factor that depends on the sample volume and the resonant mode of the cavity, and $\chi $ is the complex susceptibility.