Excitations in vortex-state permalloy dots

Thin submicron magnetic cylinders can have a vortex ground state, and dynamic magnon normal mode excitations of this ground state exhibit a rich spectrum consisting of the subgigahertz gyrotropic mode as well as other higher frequency modes. The frequencies and structure of the normal modes are obtained analytically within the basis of the vortex-magnon interaction, including both exchange and the magnetostatic interaction to obtain the structures and frequencies of these modes. It is remarked that the modes can be classified according to an azimuthal integer eigenvalue, m corresponding to the number of azimuthal nodes, with the gyrotropic mode belonging to the vertical bar m vertical bar=1 class. In this paper the higher frequency vertical bar m vertical bar=1 modes are also investigated. Analytic calculation shows that the mode frequency is an approximately linear function of root L/R (where L is the cylinder thickness and R is the cylinder radius) for small values of the aspect ratio, with deviations from linearity as the aspect ratio increases. Time-resolved Kerr microscopy imaging of the dynamic magnetic structure (excited by an in-plane pulse) in single permalloy cylinders of radii from 250 to 1000 nm indicates that the calculated frequencies are close to the measured frequencies. Finally, the azimuthal node is also observed, showing that the high frequency vertical bar m vertical bar=1 mode is indeed excited and observed.