Dipole-exchange spin waves in a periodically layered ferromagnetic nanotube

Abstract

Spin waves in a periodically layered ferromagnetic nanotube (nanotube magnetophotonic crystal) are investigated. External magnetic field is considered to be applied parallel to the nanotube symmetry axis. The linearized Landau-Lifshitz equation in magnetostatic approximation is used, taking into account the magnetic dipole-dipole interaction, theexchange interaction and the anisotropy effects. As a result, the local dispersion relation (for uniform nanotube sections), the radial wave number spectrum and the longitudinal quasi-wave number spectrum (for the entire nanotube) for spin waves in the above-described nanotube are found. From the radial wave number spectrum, limitations on the transverse-angular modes are defined. The longitudinal quasi-wave number spectrum in the "effective medium" limit is shown to have the same form as for a uniform nanotube (with averaged parameters).