Spin Waves in a Ferromagnetic Nanotube in The Presence of a Spin-Polarized Current

Dipole-exchange spin waves in a ferromagnetic nanotube in the presence of a spin-polarized electric current are investigated. The exchange interaction, the dipole-dipole magnetic interaction, the anisotropy effects, the dissipation effects and the influence of the spin-polarized current are taken into account. For above-described spin waves, an equation for the magnetic potential and a dispersion relation are obtained. It is shown that the presence of the spin-polarized current can strengthen or weaken the effective dissipation, or lead to a spin wave generation. The condition of such generation is obtained.