Microwave Resonance Relations in Anisotropic Single Crystal Ferrites

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Abstract
The ferromagnetic resonance relations in magnetically anisotropic single crystal ferrites are reexamined. Detailed analyses are presented for spherical specimens. Generalized nomograms are shown which relate the resonance frequency to static field H, anisotropy parameter K/M, and the static field orientation. The nature of the susceptibility tensor is discussed. Below magnetic saturation, multidomain structure is expected. Under these conditions, with H applied in a [110] direction, a simple multidomain arrangement is suggested by crystal geometry. Ferromagnetic resonance can be used to investigate this structure. The analysis is similar to that employed by Smit and Beljers who investigated like effects in uniaxial crystals. The domains are lamellar in form, separated by 180° walls, and lie perpendicular to H. Corresponding to the two nearby easy directions of magnetization, the domains are of two varieties which alternate in sequence. Two resonance frequencies are found for a given H, depending on whether the microwave magnetic field is perpendicular or parallel to H. Nomograms are given relating these resonance frequencies to H, K/M, and saturation magnetization M. The nature of the magnetization curve for these simple structures is also discussed. The predictions of these analyses are compared with the results of recent experiments.