Effects of an external magnetic field on spin waves in finite-length ferromagnetic nanotubes

Abstract

A theoretical study is reported for the effects of an external magnetic field on the spin-wave dynamics of finite-length nanotubes, where the end effects are important as well as radial variations. By using a microscopic (or Hamiltonian-based) formalism, the frequencies and spatial amplitudes of the dipole-exchange spin waves are calculated for two orientations of the applied magnetic field. When the magnitude of this field is varied there is a switching between different magnetic ordering states and a modification to the spin-wave modes. For a longitudinal field (along the nanotube axis) there is competition between the bottleneck (or bamboo) state and a twisted bottleneck state with vortex components at the ends, having either the same or opposite chirality. For a transverse field the equilibrium spin orientations are tilted relative to the nanotube axis and vary with respect to their position in the finite-length nanotube. The resulting effect on the spin waves is studied as the transverse field is increased from a low value: initially the field inhibits the vortex states and eventually it produces an overall spin reorientation. Numerical calculations are presented for permalloy and nickel nanotubes with realistic dimensions and magnetic field values.