A multi-scale approach for magnetisation dynamics: Unraveling exotic magnetic states of matter

Crystallographic lattice defects strongly influence dynamical properties of magnetic materials at both microscopic and macroscopic length scales. A multi-scale approach to magnetisation dynamics, which is presented in this paper, accurately captures such effects. The method is illustrated using examples of systems with localized, non-trivial topological properties, e.g. in the form of skyrmions and chiral domain walls that interact with lattice dislocations. Technical aspects of the methodology involve multi-scale magnetisation dynamics that connects atomistic and continuum descriptions. The technique is capable of solving the Landau-Lifshitz-Gilbert equations efficiently in two regions of a magnetic material --- the mesoscopic and the atomistic regions, which are coupled in a seamless way. It is demonstrated that this methodology allows simulating realistically-sized magnetic skyrmions interacting with material defects and novel physical effects, uncovered using this theoretical methodology, are described.