Fractional topological charges in two-dimensional magnets

Magnetic skyrmions and antiskyrmions are characterized by an integer topological charge $\mathcal{Q}=\ensuremath{\mp}1$, describing the winding of the magnetic orientation. Half-integer winding numbers, $\mathcal{Q}=\ifmmode\pm\else\textpm\fi{}\frac{1}{2}$, 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 $\mathcal{Q}=\ifmmode\pm\else\textpm\fi{}\frac{1}{6}$ or $\ifmmode\pm\else\textpm\fi{}\frac{1}{8}$ arise naturally when three or more magnetic domains meet. We also show that a single magnetic skyrmion with $\mathcal{Q}=\ensuremath{-}1$ can explode into four fractional defects, each carrying charge $\mathcal{Q}=\ensuremath{-}\frac{1}{4}$. Additionally, we investigate a point defect with a nonquantized fractional charge ($\mathcal{Q}\ensuremath{\ne}\frac{n}{m},n,m\ensuremath{\in}\mathbb{Z}$) 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.