Date of Award
Master of Science (MS)
Mark A. Hoefer
Thomas J. Silva
Topological solitary waves have recently attracted attention from the applied mathematics and physics communities because of both their perceived robustness and technological applications, e.g. storage and logic. In the field of magnetism, topological structures include the one-dimensional domain wall and the two-dimensional magnetic skyrmion. Topology in these structures is the result of a quantized winding number, as the magnetization vector is restricted to the unit sphere. The winding number provides a notion of “topological protection”, meaning that topological wave structures cannot be continuously deformed into other structures with different winding numbers. This thesis presents two problems in magnetic solitary wave dynamics where topology plays an important role. First, transverse instabilities of elongated bound states of two precessing and translating domain walls, or bion filaments, are described. It is found that topological and non-topological domain wall pairs break into two-dimensional structures via "neck'' and "snake'' instabilities respectively. Next, the perimeter dynamics of two two-dimensional structures are described: the non-topological droplet and the topological dynamic skyrmion. A multiscale, differential geometry description is utilized to analytically obtain perimeter wave dynamics of both textures in the large-diameter limit. Energy dissipation is incorporated and an analytical expression for the textures' decay is found. Beyond this thesis, the averaged Lagrangian and differential geometry approaches have potential application in a variety of fields from optics to water waves.
Ruth, Maximilian Emil, "The Role of Topology in Magnetic Solitary Wave Dynamics" (2018). Applied Mathematics Graduate Theses & Dissertations. 104.