Calculations of three-dimensional magnetic excitations in permalloy nanostructures with vortex state

Dynamic susceptibility spectra of the vortex state in nanorings and nanodots are studied using three-dimensional micromagnetic simulations. Spatial maps of the susceptibility have enabled identification of various resonance modes. For an exciting field along the x axis, several resonance peaks appear for a thin dot, including a core mode, whereas only one main resonance peak is detected for a ring corresponding to a volume mode with uniform magnetization perpendicular to the exciting field (x direction). A low-frequency resonance peak related to a surface mode and a high-frequency resonance peak viewed as an edge mode are additionally observed for a thick ring. These three resonance modes (surface, volume and edge modes) which correspond to low, intermediate and high-frequency resonance peaks, respectively, are also captured for an exciting field along the y axis. In addition, a mixed edge and volume mode is revealed at a higher frequency.