Topological transport of deconfined hedgehogs in magnets*

We theoretically investigate the dynamics of magnetic hedgehogs, which are three-dimensional topological spin textures that exist in common magnets, focusing on their transport properties and connections to spintronics. We show that fictitious magnetic monopoles carried by hedgehog textures obey a topological conservation law, based on which a hydrodynamic theory is developed. In the high-temperature (paramagnet) regime, the topological stability of the hedgehog flows results in an algebraically decaying drag signal in nonlocal transport measurements. The bulk-edge correspondence between hedgehog number and skyrmion number, the fictitious electric charges arising from magnetic dynamics, and the analogy between the low-temperature bound states of hedgehogs and the quark confinement in quantum chromodynamics are also discussed. Our study points to a practical potential in utilizing hedgehog flows for long-range neutral signal propagation or manipulation of skyrmion textures in three-dimensional magnetic materials.