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Topological domain walls in helimagnets

Nature Physics volume 14, pages 465–468 (2018)Cite this article

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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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References

  1. Chuang, I., Durrer, R., Turok, N. & Yurke, B. Cosmology in the laboratory: defect dynamics in liquid crystals. Science 251, 1336–1342 (1991).

    Article  ADS  Google Scholar 

  2. del Campo, A. & Zurek, W. H. Universality of phase transition dynamics: topological defects from symmetry breaking. Inter. J. Mod. Phys. A 29, 1430018 (2014).

    Article  Google Scholar 

  3. Catalan, G., Seidel, J., Ramesh, R. & Scott, J. F. Domain wall nanoelectronics. Rev. Mod. Phys. 84, 119–156 (2012).

    Article  ADS  Google Scholar 

  4. Parkin, S. S. P., Hayashi, M. & Thomas, L. Magnetic domain-wall racetrack memory. Science 320, 190–194 (2012).

    Article  ADS  Google Scholar 

  5. Salje, E. & Zhang, H. Domain boundary engineering. Phase Transit. 82, 452–469 (2009).

    Article  Google Scholar 

  6. Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010).

    Article  ADS  Google Scholar 

  7. Yu, X. Z. et al. Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe. Nat. Mater 10, 106–109 2011).

    Article  ADS  Google Scholar 

  8. Bak, P. & Jensen, M. H. Theory of helical magnetic structures and phase transitions in MnSi and FeGe. J. Phys. C 13, L881–L885 (1980).

    Article  Google Scholar 

  9. de Gennes, P. G. & Prost, J. The Physics of Liquid Crystals. (Clarendon: Oxford, 1993.

    Google Scholar 

  10. Hubert, A. & Schäfer, R. Magnetic Domains: The Analysis of Magnetic Microstructures. (Springer: Berlin, Heidelberg, 2009.

    Google Scholar 

  11. Kléman, M. Magnetic singularities in helimagnet crystals. Philos. Mag. 22, 739–749 (1970). 178.

    Article  ADS  Google Scholar 

  12. Seul, M., Monar, L. R., O’Gorman, L. & Wolfe, R. Morphology and local structure in labyrinthine stripe domain phase. Science 254, 1616–1618 (1991).

    Article  ADS  Google Scholar 

  13. Uchida, M. et al. Topological spin textures in the helimagnet FeGe. Phys. Rev. B 77, 184402 (2008).

    Article  ADS  Google Scholar 

  14. Li, F., Nattermann, T. & Pokrovsky, V. L. Vortex domain walls in helical magnets. Phys. Rev. Lett. 108, 107203 (2012).

    Article  ADS  Google Scholar 

  15. Lebech, B., Bernhard, J. & Freltoft, T. Magnetic structures of cubic FeGe studied by small-angle neutron scattering. J. Phys. Condens. Matter 1, 6105 (1989).

    Article  ADS  Google Scholar 

  16. Rybakov, F. N., Borisov, A. B., Blügel, S. & Kiselev, N. S. New spiral state and skyrmion lattice in 3D model of chiral magnets. New J. Phys. 18, 045002 (2016).

    Article  ADS  Google Scholar 

  17. Yagil, A. et al. Stray field signatures of Néel textured skyrmions in Ir/Fe/Co/Pt multilayer films. Preprint at https://arxiv.org/abs/1705.07608 (2017).

  18. Bouligand, Y. in Dislocations in Solids (ed. Nabarro, F. R. N.) Ch. 23 (North-Holland Publishing Company, New York, NY, 1983).

  19. Bouligand, Y. Recherches sur les textures des états mésomorphes. 3. Les plages à éventails dans les cholestériques. J. Phys. Fr. 34, 603–614 (1973).

    Article  Google Scholar 

  20. Bouligand, Y. Recherches sur les textures des états mésomorphes. 4. La texture à plans et la morphogenèse des principales textures dans les cholestériques. J. Phys. Fr. 34, 1011–1020 (1973).

    Article  Google Scholar 

  21. Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotech. 8, 899–911 (2013).

    Article  ADS  Google Scholar 

  22. Garst, M. in Topological Structures in Ferroic Materials (ed. Seidel, J.) Ch. 2 (Springer, Berlin, Heidelberg, 2016).

  23. Neubauer, A. et al. Topological Hall effect in the A phase of MnSi. Phys. Rev. Lett. 102, 186602 (2009).

    Article  ADS  Google Scholar 

  24. Schulz, T. et al. Emergent electrodynamics of skyrmions in a chiral magnet. Nat. Phys. 8, 301–304 (2012).

    Article  Google Scholar 

  25. Schütte, C. & Garst, M. Magnon-skyrmion scattering in chiral magnets. Phys. Rev. B 90, 094423 (2014).

    Article  ADS  Google Scholar 

  26. Mochizuki, M. et al. Thermally driven ratchet motion of a skyrmion microcrystal and topological magnon Hall effect. Nat. Mater 13, 241–246 (2014).

    Article  ADS  Google Scholar 

  27. Bauer, A. et al. Symmetry breaking, slow relaxation dynamics, and topological defects at the field-induced helix reorientation in MnSi. Phys. Rev. B 95, 024429 (2017).

    Article  ADS  Google Scholar 

  28. Dussaux, A. et al. Local dynamics of topological magnetic defects in the itinerant helimagnet FeGe. Nat. Commun. 7, 12430 (2016).

    Article  ADS  Google Scholar 

  29. Janoschek, M. et al. Fluctuation-induced first-order phase transition in Dzyaloshinskii–Moriya helimagnets. Phys. Rev. B 87, 134407 (2013).

    Article  ADS  Google Scholar 

  30. Wilhelm, H. et al. Precursor phenomena at the magnetic ordering of the cubic helimagnet FeGe. Phys. Rev. Lett. 107, 127203 (2011).

    Article  ADS  Google Scholar 

  31. Pfleiderer, C., Julian, S. R. & Lonzarich, G. G. Non-Fermi-liquid nature of the normal state of itinerant-electron ferromagnets. Nature 414, 427–430 (2001).

    Article  ADS  Google Scholar 

  32. Ritz, R. et al. Formation of a topological non-Fermi liquid in MnSi. Nature 497, 231–234 (2013).

    Article  ADS  Google Scholar 

  33. Pedrazzini, P. et al. Metallic state in cubic FeGe beyond its quantum phase transition. Phys. Rev. Lett. 98, 047204 (2007).

    Article  ADS  Google Scholar 

  34. Fert, A., Cros, V. & Sampaio, J. Skyrmions on the track. Nat. Nanotech. 8, 152–156 (2013).

    Article  ADS  Google Scholar 

  35. Wiesendanger, R. Nanoscale magnetic skyrmions in metallic films and multilayers: a new twist for spintronics. Nat. Rev. Mater. 1, 16044 (2016).

    Article  ADS  Google Scholar 

Download references

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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Authors and Affiliations

  1. Department of Materials, ETH Zurich, Zürich, Switzerland

    P. Schoenherr & D. Meier

  2. Institut für Theoretische Physik, Universität zu Köln, Köln, Germany

    J. Müller, A. Rosch & M. Garst

  3. Institut für Theoretische Physik, Technische Universität Dresden, Dresden, Germany

    L. Köhler & M. Garst

  4. Department of Applied Physics, University of Tokyo, Tokyo, Japan

    N. Kanazawa & Y. Tokura

  5. RIKEN Center for Emergent Matter Science (CEMS), Wako, Japan

    Y. Tokura

  6. Department of Materials Science and Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway

    D. Meier

  7. Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology (NTNU), Trondheim, Norway

    D. Meier

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  1. P. Schoenherr
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Contributions

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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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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