Derivation of the resonance frequency from the free energy of ferromagnets

The general form for the magnetic resonance frequency ω of anisotropic ferromagnets as derived from the free energy F by Smit and Beljers (ω/γ${)}^2$=(M sinθ${)}^{\mathrm{-}2}$(${\mathit{F}}_{\mathrm{\theta }\mathrm{\theta }}$ ${\mathit{F}}_{\mathrm{\phi }\mathrm{\phi }}$-${\mathit{F}}_{\mathrm{\theta }\mathrm{\phi }}^2$), although numerically correct, is physically not convenient, because the origin of the different terms in F is obscured by an angular-dependent mixing. This mixing is avoided by using the relation (ω/γ${)}^2$=1/${\mathit{M}}^2$ [${\mathit{F}}_{\mathrm{\theta }\mathrm{\theta }}$(${\mathit{F}}_{\mathrm{\phi }\mathrm{\phi }}$ /${\sin }^2$θ+cosθ/sinθ${\mathit{F}}_{\mathrm{\theta }}$)-(${\mathit{F}}_{\mathrm{\theta }\mathrm{\phi }}$/sinθ-cosθ/sinθ ${\mathit{F}}_{\mathrm{\phi }}$/sinθ${)}^2$]. .sp Explicit expressions will show the symmetry of each of the terms in F for all magnitudes and directions of H. In addition, an alternate method which uses only rectangular coordinates and which can easily be generalized for multisublattice systems is described.