Ferromagnetic Resonance in Multilayer Perpendicular Films

Ferromagnetic resonance measurements can provide valuable information about thin-film structures, including recording media. This paper develops analytic expressions for the behavior of continuous-coupled multilayer perpendicular films and compares these with micromagnetic simulations. A frequency-domain equation is derived for small excitation, where the in-plane variables are expressed as complex quantities. The corresponding micromagnetic simulations implement the standard Landau-Lifshitz-Gilbert equation and are driven with an in-plane linear sinusoidal excitation. A four-layer graded medium is used as an illustrative example. The medium includes a relatively soft, lossy, weakly coupled cap. The analytic result reveals four resonant modes with the lowest mode at 16.40 GHz with zero external dc field. The simulation matches the analytic frequency and damping factor well but only for very low levels of excitation.