Published: March 20, 2018

The Role of Topology in Magnetic Solitary Wave Dynamics

 Topological solitary waves have recently attracted attention from applied mathematics and physics communities for both technological applications and novel phenomena. In the field of ferromagnetism, topological structures include the one-dimensional topological bion and the two-dimensional skyrmion. The topology 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 the topological waves cannot be continuously deformed into a state with a different winding number. This talk presents two problems in magnetic solitary wave dynamics where topology plays an important role. First, the transverse instability--which has a “snaking” or “pinching” instability depending on its topology--of a dynamically precessing and moving soliton filament known as the bion stripe is described. Next, the transverse perimeter dynamics of two circular solitons are described: the non-topological droplet and the topological skyrmion. A multiscale, differential geometry description for the soliton filament is utilized to analytically obtain the motion of modulations about the perimeter of both textures in the presence of dissipation in the large-diameter limit.  Interestingly, large-amplitude modulations of this nonlinear problem are described by a linear partial differential equation, solvable via Fourier series.