Abstract
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.
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Acknowledgements
We wish to thank P. Böni, H. Hagn, N. Nagaosa, T. Nattermann, S. Mayr, M. Opel, B. Russ, B. Spivak, G. Stölzl and V. M. Vinokur for helpful discussions and support. R.R., A.B., M.W. and C.F. acknowledge financial support through the TUM Graduate School. K.E. acknowledges financial support through the Deutsche Telekom Stiftung and the Bonn Cologne Graduate School. Financial support through Deutsche Forschungsgemeinschaft TRR80, SFB608 and FOR960 is gratefully acknowledged.
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T.S., R.R. M.H., M.W. and C.P. developed the experimental set-up; T.S. and R.R. performed the experiments; T.S., R.R. and C.P. analysed the experimental data; C.F. wrote the software for analysing the data; A.B. grew the single-crystal samples and characterized them; K.E., M.G. and A.R. developed the theoretical interpretation; C.P. supervised the experimental work; C.P. and A.R. proposed this study and wrote the manuscript; all authors discussed the data and commented on the manuscript.
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Schulz, T., Ritz, R., Bauer, A. et al. Emergent electrodynamics of skyrmions in a chiral magnet. Nature Phys 8, 301–304 (2012). https://doi.org/10.1038/nphys2231
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DOI: https://doi.org/10.1038/nphys2231
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