Spin-wave excitations in ferromagnetic nanotubes

A microscopic theory for the spin-wave excitations in cylindrical ferromagnetic nanotubes is developed by extending earlier work on nanowires. It is applied to nickel nanorings of high length-to-diameter aspect ratio. A Green’s function method is employed, taking account of the long-range magnetic dipole–dipole interactions, the short-range exchange interactions, and the single-ion anisotropy, together with an external magnetic field applied either parallel or perpendicular to the cylinder axis. The frequencies, spatial distributions, and spectral intensities of the discrete spin-wave modes are calculated. The field dependence of the frequencies is compared numerically with experimental data.