Micromagnetic calculations of ferromagnetic resonance in submicron ferromagnetic particles

Micromagnetic simulations of the ferromagnetic resonance (FMR) spectrum of submicron circular ferromagnetic particles show a number of well-defined absorption peaks as a function of the applied dc magnetic field. In addition to a single large peak due to the uniform mode of precession, smaller peaks are observed on both sides of the uniform mode peak, corresponding to nonuniform or spin-wave modes of precession. The positions of these peaks are a function of particle size. Simulations of the FMR spectrum with and without exchange interactions show that the primary contribution to the energy of the spin-wave modes with absorption peaks at magnetic fields smaller than the uniform mode peak is from exchange interactions, whereas the primary contribution to the energy of the spin-wave modes above the uniform resonance mode arises from dipolar interactions, although all spin-wave modes have some contributions from both types of interactions.