A collective coordinate approach to describe magnetic domain wall dynamics applied to nanowires with high perpendicular anisotropy

Several future spintronic devices are based on domain wall propagation through magnetic nanowires. Next to experiments and simulations, theoretical models are an indispensable tool to understand the magnetic domain wall mobility. In this paper, we extract the collective coordinates and derive the equations of motion that describe the domain wall dynamics directly from averaging the underlying micromagnetic equations. This way, five collective coordinates naturally emerge in the equations of motion: the domain wall displacement, the magnetization tilting, the domain wall width, effective demagnetizing factors and the domain wall asymmetry. While not predictive by itself, the approach enables a direct macroscopic interpretation of micromagnetic simulations, largely enhancing the complementarity between theory and simulations. We apply the method to study the field and current driven domain wall dynamics in nanowires with high perpendicular anisotropy. We suggest the existence of an intrinsic depinning threshold for such domain wall dynamics, even when taking into account non-adiabatic contributions to the spin-transfer torques. Furthermore, we show that the domain wall asymmetry has a resonant behaviour at high excitation strengths.