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Topological domain walls in helimagnets

Abstract

Domain walls naturally arise whenever a symmetry is spontaneously broken. They interconnect regions with different realizations of the broken symmetry, promoting structure formation from cosmological length scales to the atomic level1,2. In ferroelectric and ferromagnetic materials, domain walls with unique functionalities emerge, holding great promise for nanoelectronics and spintronics applications3,4,5. These walls are usually of Ising, Bloch or Néel type and separate homogeneously ordered domains. Here we demonstrate that a wide variety of new domain walls occurs in the presence of spatially modulated domain states. Using magnetic force microscopy and micromagnetic simulations, we show three fundamental classes of domain walls to arise in the near-room-temperature helimagnet iron germanium. In contrast to conventional ferroics, the domain walls exhibit a well-defined inner structure, which—analogous to cholesteric liquid crystals—consists of topological disclination and dislocation defects. Similar to the magnetic skyrmions that form in the same material6,7, the domain walls can carry a finite topological charge, permitting an efficient coupling to spin currents and contributions to a topological Hall effect. Our study establishes a new family of magnetic nano-objects with non-trivial topology, opening the door to innovative device concepts based on helimagnetic domain walls.

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Fig. 1: Helimagnetic order and defect structures.
Fig. 2: Helimagnetic domain walls in FeGe.
Fig. 3: Micromagnetic domain wall simulations.
Fig. 4: Magnetic edge dislocation with non-zero skyrmion charge.

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Acknowledgements

We thank M. Fiebig for direct financial support. The work at ETH was supported by the Swiss National Science Foundation through grants 200021-149192 and 200021-137520. L.K. and M.G. were supported by SFB 1143 'Correlated Magnetism: From Frustration To Topology' and DFG grant GA 1072/5-1. J.M. and A.R. were supported by SFB 1238 (Kontrolle und Dynamik von Quantenmaterialien). J.M. also acknowledges support from the Deutsche Telekom Stiftung and Bonn-Cologne Graduate School of Physics and Astronomy BCGS. N.K. acknowledges funding through the JSPS Grant-in-Aids for Scientific Research (S) no. 24224009 and for Young Scientists (Start-up) no. 26886005. D.M. thanks the Research Council of Norway (FRINATEK project no. 263228) and the Norwegian University of Science and Technology (NTNU) for financial support.

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P.S. conducted the MFM experiments supervised by D.M.; J.M. performed the two-dimensional micromagnetic simulations supervised by M.G. and A.R.; N.K. grew the FeGe single crystals under supervision of Y.T.; P.S., J.M., L.K., M.G. and D.M. classified the domain walls; M.G. and L.K. defined the skyrmion charge of edge dislocations; P.S., J.M., L.K., M.G. and D.M. wrote the paper; M.G. and D.M. supervised the work. All authors discussed the results and contributed to their interpretation.

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Correspondence to M. Garst or D. Meier.

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The authors declare no competing interests.

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Supplementary Materials

Supplementary Text, Supplementary References 36–40, Supplementary Figures S0–S17

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Schoenherr, P., Müller, J., Köhler, L. et al. Topological domain walls in helimagnets. Nature Phys 14, 465–468 (2018). https://doi.org/10.1038/s41567-018-0056-5

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