Parallel Pumping of Spin Waves for Ferromagnetic Nanowires and Nanotubes With Circular Cross Sections

Calculations are reported for the spin-wave instabilities in a ferromagnetic nanowire with circular cross section, as well as nanotubes, under conditions of parallel microwave pumping. The quantized spin waves are characterized by a one-dimensional wave vector along the nanowire and the external applied magnetic field is taken to be parallel to the longitudinal axis. In nanowires with lateral dimensions less than about 200 nm, the spatial quantization of the eigenmodes become predominant and our theory employs a microscopic (or Hamiltonian-based) dipole-exchange method analogous to that used recently for ultrathin films and nanowire stripes with rectangular cross section. Numerical applications are made to wires with different radii and comparisons are presented with nanowires having square cross sections. When our nanowire results are compared with those for macroscopic samples or for ultrathin films, it is found that the “butterfly curves” (threshold field vs. applied field) are significantly modified and show more structural features.