Speed of domain walls in thin nanotubes: The transition from the linear to the magnonic regime

Abstract

Numerical simulations of domain wall propagation in thin nanotubes when an external magnetic field is applied along the nanotube axis have shown an unexpected behavior described as a transition from a linear to a magnonic regime. As the applied magnetic field increases, the initial regime of linear growth of the speed with the field is followed by a sudden change in slope accompanied by the emission of spin waves. In this work an analytical formula for the speed of the domain wall that explains this behavior is derived by means of an asymptotic study of the Landau Lifshitz Gilbert equation for thin nanotubes. We show that the dynamics can be reduced to a one dimensional hyperbolic reaction diffusion equation, namely, the damped double Sine Gordon equation, which shows the transition to the magnonic regime as the domain wall speed approaches the speed of spin waves. This equation has been previously found to describe domain wall propagation in weak ferromagnets with the mobility proportional to the Dzyaloshinskii-Moriya interaction constant, for Permalloy nanotubes the mobility is proportional to the nanotube radius.