Computation of Magnetization Normal Oscillation Modes in Complex Micromagnetic Systems

The small oscillation modes in complex micromagnetic systems around an equilibrium are analyzed in the frequency domain by using a formulation which naturally preserves the main physical properties of the problem. The Landau-Lifshitz-Gilbert (LLG) equation is linearized around a stable equilibrium configuration. The linear equation is recast as a generalized eigenvalue problem for suitable self-adjoint operators connected to the micromagnetic effective field. The spectral properties of the eigenvalue problem are studied in the lossless limit and in the presence of small dissipative effects. It is shown that the discrete approximation of the eigenvalue problem obtained either by finite difference or finite element methods has a structure which preserves relevant properties of the continuum formulation. Finally, the normal oscillation modes and frequencies are numerically computed for different micromagnetic systems in order to show the generality of the approach.