Walker Breakdown in Magnon-Induced Ferromagnetic Domain Wall Motion

Abstract

We derive for the first time the collective coordinate equations for magnon-driven domain wall motion in ferromagnets from the Landau-Lifshitz-Gilbert equation. By performing a consistent calculation to second order we are able to include the damping torque and obtain the dynamic equation for the tilt angle. Our results show that the magnonic spin-transfer torque does not induce Walker breakdown. The spin-wave amplitude is examined for the special case of a microwave source and the spatial topology of the applied magnetic field is found to determine the frequency dependence of the amplitude and the domain wall velocity. This highlights the importance of implementing more realistic sources in numerical models to be able to study the frequency dependence we expect to observe in experiments. The established equations are supported by a simple one-dimensional numerical implementation of the Landau-Lifshitz-Gilbert equation.