Fractional Topological Charges in 2D Magnets

Abstract: Magnetic skyrmions and antiskyrmions are characterised by an integer topological charge $\mathcal Q =\mp 1$, describing the winding of the magnetic orientation. Half-integer winding numbers, $\mathcal Q=\pm \frac{1}{2}$, can be obtained for magnetic vortices (merons). Here, we discuss the physics of magnets with fractional topological charge which is neither integer nor half-integer. We argue that in ferromagnetic films with cubic anisotropy, textures with $\mathcal Q=\pm\frac{1}{6} $ or $\pm\frac{1}{8}$ arise naturally when three or more magnetic domains meet. We also show that a single magnetic skyrmion with $\mathcal Q =-1$ can explode into four fractional defects, each carrying charge $\mathcal Q=-\frac{1}{4}$. Additionally, we investigate a point defect with a non-quantised fractional charge ($\mathcal Q\neq \frac{n}{m}, n,m\in\mathbb{Z}$) which can move parallel to a magnetic domain wall. Only defects with fractional charge lead to an Aharonov-Bohm effect for magnons. We investigate the resulting forces on a fractional defect due to magnon currents.