Field evolution of the magnetic normal modes in elongated permalloy nanometricrings

Abstract

The eigenmode spectrum of elongated permalloy rings with relatively wide arms isinvestigated by combined Brillouin light scattering and ferromagnetic resonancemeasurements as a function of the applied field intensity, encompassing both vortex andonion ground states. To reproduce the frequencies and the spatial profiles of themeasured modes we performed micromagnetic simulations which solve the discretizedLandau–Lifshitz–Gilbert equation in the time domain and calculate locally theFourier transform. This allowed us to correlate the field dependence of differentmodes to their localization inside different portions of the rings. With the ringsin the vortex ground state, in addition to radial, fundamental, and azimuthalmodes, a localized mode, existing in the element portions where the internalfield assumes its minima, has been measured and identified. This latter mode,whose frequency decreases for increasing field intensity, becomes soft near thetransition from vortex to onion state and determines the change in symmetryof the magnetic ground state. After the transition, it is replaced by two edgemodes, localized on the internal and external boundary of the rings, respectively.