Alternative theoretical approach of the exact ferromagnetic resonance frequency for common sample shapes by considering the phenomenological damping parameter - A tribute to C. Kittel and T.L. Gilbert

Abstract

In order to establish an expression for the ferromagnetic resonance frequency of specimen with general shape, the Landau-Lifschitz-Gilbert differential equation was solved by considering demagnetisation effects and damping. By beginning the approach of calculation in a three dimensional space the sample was regarded as a uniformly magnetised ferro- or ferrimagnetic conventional ellipsoid. The condition for calculation must be a one-domain state which can be obtained by introducing a marked uniaxial anisotropy field and/or by applying an external magnetic saturation field. This can now be put on the level with a macro-spin precessing about its preferred direction. As a result, a more exact solution for the ferromagnetic resonance frequency was achieved which takes the phenomenological damping parameter as well as the demagnetisation factors into account. Applying it to certain sample shapes (plane, spherical or cylindrical) the uniaxial anisotropy field, the saturation magnetisation and especially the damping parameter show a different impact on the resonance frequency value. It could be shown that a plane sample (film) is more influenced by the damping parameter.