Analytical Modelling of Magnetic DW Motion

The main analytical model for describing the motion of magnetic domain walls is the 1-D model formulated based on the profile of a Bloch wall. This model qualitatively describes the motion of magnetic domain wall in nanowires, while it may fail to match experimental and numerical results quantitatively. In recent years, the 1-D model has been further generalized by the introduction of terms such as spin transfer torques and spin orbit torques. It has also been used to describe the motion of different domain walls, including vortex walls. It seems that in many such attempts, formalisms are not followed accurately and the main assumptions of the model (such as the Bloch wall profile used in developing the model) are underestimated. In this paper, we first derive an analytical model to describe the motion of a tilting Bloch wall in perpendicularly magnetized materials using four collective coordinates. We then compare the energy landscape predicted by this model to that of micromagnetic simulations, highlighting the possibility of using such comparisons to develop corrections for the 1-D model.