Electrodynamic improvements to the theory of magnetostatic modes in ferrimagnetic spheres and their applications to saturation magnetization measurements

Electrodynamic theory applied to the analysis of TE_n0p mode resonances in ferrimagnetic spheres placed either in metallic cavities or in the free space is compared with Walker-Fletcher's theory of so-called magnetostatic modes. The influence of the diameter of the sample, its permittivity and the permittivity of the surrounding media on the resonance frequencies of a few modes is analyzed. It is shown that the dominant resonances are essentially related either to negative values of the diagonal component of the permeability tensor or, for clockwise circularly polarized magnetic fields, to negative effective permeability. The electrodynamic theory is used to determine the saturation magnetization (M_s) from measured TE_n01 frequency differences. Measurements on different samples confirmed that M_s can be determined using an electrodynamic approach with uncertainties of the order of 2% regardless of sample sizes or metal enclosures if the anisotropy field is negligible compared to the static internal magnetic bias.