Enhanced harmonic generation accompanying Ferromagnetic resonance in thin permalloy elliptical disks

Large amplitude magnetization dynamics in elliptical permalloy nano-disks are studied via simulation of the Landau-Lifshitz equation. When the external magnetic field is applied in the plane of the disk two low-lying resonant modes exist. The higher frequency mode corresponds to the Kittel-like uniform ferromagnetic resonance mode and is consistent with previous experimental observations. The second mode with the lower frequency, termed the "cap mode", is localized near the two ends of the ellipse. At certain fields the ratio of the frequencies of these modes is equal to two or three and here one can efficiently generate the Kittel mode as the 2nd or 3rd harmonic of the "cap mode" when the magnitude of the input microwave field is of order 0.1 Oe, which can easily be achieved in practice. The nonlinear responses depend strongly on the equilibrium, field-dependent, behavior of the magnetization which is non-uniform and displays features not captured by the StonerWohlfarth model for an ellipsoid.