On the Theory of Ferromagnetic Resonance Absorption

The theory of ferromagnetic resonance absorption previously developed is extended to include the effect of the shape of the specimen and, in the case of a single crystal, the effect of crystal orientation. The resonance condition may be written ${\omega }_0=\gamma H_{\mathrm{eff}}$, where $H_{\mathrm{eff}}$ is equal to ${\mathrm{}\left(\mathrm{BH}\right)\mathrm{}}^{\frac{1}{2}}$ for a plane surface, $H+2\mathrm{}\pi M$ for a long circular cylinder, and $H$ for a sphere; the latter two values apply only to the situation in which the eddy current skin depth is large in comparison with the radius of the specimen. In the case of an uniaxial crystal with the axis parallel to the static magnetic field, the value of $H$ to be used in the resonance conditions is increased by $\frac{2K}{M}$, where $K$ is the anisotropy constant. The case of a cubic crystal is also considered. A detailed discussion of macroscopic eddy current effects is given, and it is shown that the usual eddy current losses do not introduce damping terms into the expression for the permeability, when properly interpreted.