Spin-wave instabilities of ferromagnetic nanowire stripes under parallel pumping.

A microscopic (or Hamiltonian-based) theory is presented for the spin-wave instability thresholds in ferromagnetic nanowires under conditions of parallel pumping with a microwave field. A dipole-exchange Hamiltonian is employed in which the external magnetic field is either longitudinal or transverse to the length of the nanowire. This contrasts with most previous work on nonlinear spin waves which concentrate on situations where a macroscopic (or continuum) theory is appropriate. In nanowire stripes with lateral dimensions of order 100 nm or less, the quantization of the eigenmodes becomes modified due to strong spatial confinement and edge effects, making it appropriate to employ a microscopic dipole-exchange approach analogous to that used recently for ultrathin films. Numerical applications are presented for the dependence of the threshold microwave field amplitude for instability on the static applied field (the analog of the butterfly curves). The cases of longitudinal and transverse applied fields are found to lead to distinctly different behaviors, which are illustrated using EuS and permalloy as materials with different ratios of dipolar to exchange interactions. Structural effects due to the discrete spin-wave branches lead to structural aspects of the butterfly curves that are significantly modified compared with those for ultrathin films due to the edge modes in the nanowires.