Microscopic theory of dipole-exchange spin-wave excitations in ferromagnetic nanowires

Abstract

A microscopic theory is developed for the spin-wave excitations in ferromagnetic nanowires. Both the long-range magnetic dipole-dipole interactions and the Heisenberg-exchange interactions between nearest neighbors are included in the Hamiltonian, as well as effects of an applied magnetic field, which may be directed parallel or perpendicular to the wire axis. Our formalism can be applied to ferromagnetic nanowires of arbitrary cross section to deduce both the energy spectrum of the discrete dipole-exchange spin-wave modes and the relative intensities as a function of position. The long-range dipole sums in the wire geometry are evaluated numerically and spin-wave calculations are presented for nanowires with approximately circular cross section. When the applied field is perpendicular to the wire axis, there is a canting of the net spin orientation away from the axis, and the magnetization is spatially nonuniform due to the dipolar interactions. We find that typically there are two phases and two distinct regimes of spin-wave behavior, corresponding to the applied field being less than or greater than a critical value.