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Derivation of the resonance frequency from the free energy of ferromagnets

1988; American Physical Society; Volume: 38; Issue: 4 Linguagem: Inglês

10.1103/physrevb.38.2237

1095-3795

L. Baselgia, M. Warden, F. Waldner, Stuart L. Hutton, John E. Drumheller, Yi He, P. E. Wigen, M. Maryško,

Magnetic Properties and Applications

The general form for the magnetic resonance frequency \ensuremath{\omega} of anisotropic ferromagnets as derived from the free energy F by Smit and Beljers (\ensuremath{\omega}/\ensuremath{\gamma}${)}^{2}$=(M sin\ensuremath{\theta}${)}^{\mathrm{\ensuremath{-}}2}$(${\mathit{F}}_{\mathrm{\ensuremath{\theta}}\mathrm{\ensuremath{\theta}}}$${\mathit{F}}_{\mathrm{\ensuremath{\varphi}}\mathrm{\ensuremath{\varphi}}}$-${\mathit{F}}_{\mathrm{\ensuremath{\theta}}\mathrm{\ensuremath{\varphi}}}^{2}$), although numerically correct, is physically not convenient, because the origin of the different terms in F is obscured by an angular-dependent mixing. This mixing is avoided by using the relation (\ensuremath{\omega}/\ensuremath{\gamma}${)}^{2}$=1/${\mathit{M}}^{2}$ [${\mathit{F}}_{\mathrm{\ensuremath{\theta}}\mathrm{\ensuremath{\theta}}}$(${\mathit{F}}_{\mathrm{\ensuremath{\varphi}}\mathrm{\ensuremath{\varphi}}}$ /${\mathrm{sin}}^{2}$\ensuremath{\theta}+cos\ensuremath{\theta}/sin\ensuremath{\theta}${\mathit{F}}_{\mathrm{\ensuremath{\theta}}}$)-(${\mathit{F}}_{\mathrm{\ensuremath{\theta}}\mathrm{\ensuremath{\varphi}}}$/sin\ensuremath{\theta}-cos\ensuremath{\theta}/sin\ensuremath{\theta} ${\mathit{F}}_{\mathrm{\ensuremath{\varphi}}}$/sin\ensuremath{\theta}${)}^{2}$]. .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.