Domain wall motion in magnetic nanowires: an asymptotic approach

Arseni Goussev, Ross G. Lund, J. M. Robbins, Valeriy Slastikov, Charles Sonnenberg

Abstract

We develop a systematic asymptotic description for domain wall motion in one-dimensional magnetic nanowires under the influence of small applied magnetic fields and currents and small material anisotropy. The magnetization dynamics, as governed by the Landau–Lifshitz–Gilbert equation, is investigated via a perturbation expansion. We compute leading-order behaviour, propagation velocities and first-order corrections of both travelling waves and oscillatory solutions, and find bifurcations between these two types of solutions. This treatment provides a sound mathematical foundation for numerous results in the literature obtained through more ad hoc arguments.

  • Received May 11, 2013.
  • Accepted September 20, 2013.
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