Dipole-exchange spin waves in a periodically layered ferromagnetic nanotube

Spin waves in a periodically layered ferromagnetic nanotube (nanotube magnetophotonic crystal) are investigated. An external magnetic field is considered to be applied parallel to the nanotube symmetry axis. A linearized Landau-Lifshitz equation in the magnetostatic approximation is used with taking account of the magnetic dipole-dipole interaction, the exchange 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) are found for spin waves in the above-described nanotube. Limitations on the transverse-angular modes are determined from the radial wave number spectrum. 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).