Azimuthal spin-wave modes in rolled-up permalloy microtubes: Tuneable mode frequency, mode patterns, and mode splitting

We investigated rolled-up permalloy microtubes using microwave absorption spectroscopy. The resonance frequencies of the tubes are tuneable by the external magnetic field. Up to four resonant azimuthal modes have been found and were attributed to constructive spin-wave interference in axial and perpendicular magnetization geometry. We show that the degeneracy of the mode can be lifted by applying a magnetic field in specified directions. The resonances of the system are described analytically. Thereby, an effective layer thickness and a demagnetization field are used to account for the multilayer structure and the curved surface, respectively. This modeling approach is supported by micromagnetic simulations.