Determination of effective magnetization and gyromagnetic ratio of yttrium iron garnet from multi-mode ferromagnetic resonance S21 spectra

We acquire ferromagnetic resonance (FMR) spectra for an out-of-plane magnetized yttrium iron garnet sample with a vector network analyzer at microwave frequencies ranging from 4.2 to 5.2 GHz. The applied static magnetic field varies from approximately 253.6 to 260.1 kA/m. Based on an empirical model for resonant features in the $S_{21}$ spectrum produced by the excitation of multiple modes and instrumental effects, we predict measured values of $S_{21}$ -parameters. For each of many microwave frequencies, for each of multiple modes, we determine the resonant field value of the applied magnetic field, an amplitude, and an FMR linewidth. Based on the frequency-dependent resonant field values produced by excitation of the main mode, we determine the effective magnetization and the gyromagnetic ratio of the sample.