Spatial topology not only classifies static magnetic textures by magnetization, but also categorizes dynamic spin waves by flow. Here we establish the topological connections between the order and flow in the same magnetic system, and further propose to use the vortices developing in spin waves to probe the essential information of the background magnetic texture. Particularly, the cores of these spin-wave vortices indicate texture magnetization along a specific direction, the windings reveal the texture topology, and their chart yields a unified relation for the topological magnon Hall angle. The geometric relations established purely upon the transverse precession of spin waves about the texture magnetization provide an integrated description of the static and dynamic magnetic phenomena. By utilizing topological defects in excitations to acquire the key features of the background medium, the vortex acts as a powerful toolkit to explore and exploit the functionalities embedded in complex structures.

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• Disclinations & dislocations
• Hall effect
• Magnetic texture
• Skyrmions
• Spin waves
• Vortex dynamics
• Vortices in superfluids
• Topology