The effect of Dzyaloshinskii–Moriya interaction on field-driven domain wall dynamics analysed by a semi-analytical approach

Fast domain wall (DW) propagation through perpendicularly magnetized nanostrips with a Dzyaloshinskii-Moriya interaction (DMI) offers promising opportunities for the development of magnetic memory and logic devices. However, as the DW speed increases, the DW magnetization is also progressively affected which ultimately leads to an unstable DW and a drop in the velocity, i.e. the Walker breakdown. In this paper, we introduce a semi-analytical approach to describe and quantify changes to the internal degrees of freedom of the DW. By spatially averaging the Landau-Lifshitz-Gilbert equation, we derive equations of motion and identify seven DW variables in addition to the DW position. This contrasts analytical models where such variables are introduced in an ansatz for the DW shape. We apply this to a field driven DW motion and we study the effect of DMI in detail. Our method helps characterize the opposing and reinforcing effects of the different interactions involved, contributing to our understanding of the Walker breakdown.