Tuning skyrmion helicity for racetrack memory and quantum computing applications

Three distinct topological degrees of freedom are used to define all topological spin textures based on out-of-plane and in-plane spin configurations: the topological charge, representing the number of times the magnetization vector m wraps around the unit sphere; the vorticity, which quantifies the angular integration of the magnetic moment along the circumferential direction of a domain wall; and the helicity, defining the swirling direction of in-plane magnetization.