Emergent electrodynamics of skyrmions in a chiral magnet

Abstract

An experiment demonstrates that the motion of so-called skyrmions—topologically quantized magnetic whirls—causes an emergent electric field that inherits the topological quantization of the skyrmions and is directly visible in the Hall effect. When an electron moves in a smoothly varying non-collinear magnetic structure, its spin orientation adapts constantly, thereby inducing forces that act both on the magnetic structure and on the electron. These forces may be described by electric and magnetic fields of an emergent electrodynamics1,2,3,4. The topologically quantized winding number of so-called skyrmions—a type of magnetic whirl discovered recently in chiral magnets5,6,7—has been predicted to induce exactly one quantum of emergent magnetic flux per skyrmion. A moving skyrmion is therefore expected to induce an emergent electric field following Faraday’s law of induction, which inherits this topological quantization8. Here we report Hall-effect measurements that establish quantitatively the predicted emergent electrodynamics. We obtain quantitative evidence for the depinning of skyrmions from impurities (at current densities of only 106 A m−2) and their subsequent motion. The combination of exceptionally small current densities and simple transport measurements offers fundamental insights into the connection between the emergent and real electrodynamics of skyrmions in chiral magnets, and might, in the long term, be important for applications.