Magnon modes in permalloy nanorings

Submicron permalloy rings can have a vortex ground state as a result of the competing effects arising from the exchange and magnetostatic interactions. The dynamic properties of this state are investigated by analytical calculations of the structure and frequencies of the magnon normal modes in the presence of the vortex-magnon interaction. For thin rings of thickness, L=60nm and inner and outer radii, Ri and Ro=200 nm, respectively it is shown that the magnon node frequencies in the 10 GHz range for rings of radii of a few hundred nanometers. Moreover, the frequencies are slowly increasing functions of Ro for fixed Ro.