Fractional Topological Charges in 2D Magnets

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 ($\mathcal{Q}\mathrm{\ne }\frac{n}{m},n,m\in \mathbb{Z}$) 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.