Finite element computations of resonant modes for small magnetic particles

The oscillations of a chain of ferromagnetic nanoparticles around a saturated spatially uniform equilibrium are analyzed by solving the linearized Landau–Lifshitz–Gilbert LLG equation. The linearized LLG equation is recast in the form of a generalized eigenvalue problem for suitable self-adjoint operators connected to the micromagnetic effective field, which accounts for exchange, magnetostatic, anisotropy, and Zeeman interactions. The generalized eigenvalue problem is solved numerically by the finite element method, which allows one to treat accurately complex geometries and preserves the structural properties of the continuum problem. The natural frequencies and the spatial distribution of the mode amplitudes are computed for chains composed of several nanoparticles sphere and ellipsoid . The effects of the interaction between the nanoparticles and the limit of validity of the point dipole approximation are discussed.