On the Theory of Ferromagnetic Resonance Absorption

TLDR

Ferromagnetic resonance absorption theory incorporates crystal anisotropy, with uniaxial crystals requiring an H increase of 2K/M and cubic crystals also examined. The study extends this theory to account for specimen shape and crystal orientation effects. The resonance condition ω₀=γH_eff is expressed with H_eff equal to (BH)¹ᐟ² for a plane surface, H+2πM for a long circular cylinder, and H for a sphere, the latter two applying only when the eddy‑current skin depth exceeds the specimen radius. The analysis shows that macroscopic eddy‑current losses do not introduce damping terms into the permeability expression when properly interpreted.

Abstract

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 ${\ensuremath{\omega}}_{0}=\ensuremath{\gamma}{H}_{\mathrm{eff}}$, where ${H}_{\mathrm{eff}}$ is equal to ${(\mathrm{BH})}^{\frac{1}{2}}$ for a plane surface, $H+2\ensuremath{\pi}M$ 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.