Spin wave vortex as topological probe of magnetic texture

A vortex, a circulating flow around a void, is one of the basic topological phenomena in nature. Here we show that vortices generally emerge in spin wave travelling upon topologically nontrivial magnetic texture, due to the transverse precession of spin wave about the background magnetization. The winding number of each spin wave vortex is equivalent to sign of the local topological density of magnetic texture at the vortex core, and all winding numbers add up as twice the topological number of the magnetic texture. Based on the charts of spin wave vortices, the magnetization profile of the magnetic texture is reversely constructed, and a universal relation for the magnon topological Hall angle is theoretically proposed and numerically confirmed in vast types of magnetic textures. The simple connection between dynamic and static magnetizations, promotes spin wave vortex as a powerful tool to reveal the topology of the underlying magnetic texture.