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Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet

Abstract

Magnetic skyrmions are topologically stable spin swirls with a particle-like character and are potentially suitable for the design of high-density information bits. Although most known skyrmion systems arise in non-centrosymmetric systems with a Dzyaloshinskii–Moriya interaction, centrosymmetric magnets with a triangular lattice can also give rise to skyrmion formation, with a geometrically frustrated lattice being considered essential in this case. Until now, it remains an open question if skyrmions can also exist in the absence of both geometrically frustrated lattice and inversion symmetry breaking. Here we discover a square skyrmion lattice state with 1.9 nm diameter skyrmions in the centrosymmetric tetragonal magnet GdRu2Si2 without a geometrically frustrated lattice by means of resonant X-ray scattering and Lorentz transmission electron microscopy experiments. A plausible origin of the observed skyrmion formation is four-spin interactions mediated by itinerant electrons in the presence of easy-axis anisotropy. Our results suggest that rare-earth intermetallics with highly symmetric crystal lattices may ubiquitously host nanometric skyrmions of exotic origins.

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Fig. 1: Crystal structure, magnetic structure and magnetic phase diagram of GdRu2Si2.
Fig. 2: RXS results for GdRu2Si2.
Fig. 3: Polarization analysis of RXS profiles in phase I and phase II.
Fig. 4: Real-space imaging of a square SkL in phase II by L-TEM.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

References

  1. Nagaosa, N. & Tokura, Y. Emergent electromagnetism in solids. Phys. Scripta T146, 014020 (2012).

    Article  Google Scholar 

  2. Rößler, U. K., Bogdanov, A. N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797–801 (2006).

    Article  Google Scholar 

  3. Rößler, U. K., Leonov, A. A. & Bogdanov, A. N. Chiral skyrmionic matter in non-centrosymmetric magnets. J. Phys. Conf. Ser. 303, 012105 (2011).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  8. Kanazawa, N., Seki, S. & Tokura, Y. Noncentrosymmetric magnets hosting magnetic skyrmions. Adv. Mater. 29, 1603227 (2017).

    Article  Google Scholar 

  9. Mühlbauer, S. et al. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  11. Seki, S., Yu, X. Z., Ishiwata, S. & Tokura, Y. Observation of skyrmions in a multiferroic material. Science 336, 198–201 (2012).

    Article  CAS  Google Scholar 

  12. Tokunaga, Y. et al. A new class of chiral materials hosting magnetic skyrmions beyond room temperature. Nat. Commun. 6, 7638 (2015).

    Article  CAS  Google Scholar 

  13. Karube, K. et al. Robust metastable skyrmions and their triangular–square lattice structural transition in a high-temperature chiral magnet. Nat. Mater. 15, 1237–1242 (2016).

    Article  CAS  Google Scholar 

  14. Kakihana, M. et al. Giant Hall resistivity and magnetoresistance in cubic chiral antiferromagnet EuPtSi. J. Phys. Soc. Jpn 87, 023701 (2018).

    Article  Google Scholar 

  15. Tanigaki, T. et al. Real-space observation of short-period cubic lattice of skyrmions in MnGe. Nano Lett. 15, 5438–5442 (2015).

    Article  CAS  Google Scholar 

  16. Kézsmárki, I. et al. Néel-type skyrmion lattice with confined orientation in the polar magnetic semiconductor GaV4S8. Nat. Mater. 14, 1116–1122 (2015).

    Article  Google Scholar 

  17. Kurumaji, T. et al. Néel-type skyrmion lattice in the tetragonal polar magnet VOSe2O5. Phys. Rev. Lett. 119, 237201 (2017).

    Article  Google Scholar 

  18. Nayak, A. K. et al. Magnetic antiskyrmions above room temperature in tetragonal Heusler materials. Nature 548, 561–566 (2017).

    Article  CAS  Google Scholar 

  19. Batista, C. D., Lin, S. Z., Hayami, S. & Kamiya, Y. Frustration and chiral orderings in correlated electron systems. Rep. Prog. Phys. 79, 084504 (2016).

    Article  Google Scholar 

  20. Okubo, T., Chung, S. & Kawamura, H. Multiple-q states and the skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields. Phys. Rev. Lett. 108, 017206 (2012).

    Article  Google Scholar 

  21. Leonov, A. O. & Mostovoy, M. Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet. Nat. Commun. 6, 8275 (2015).

    Article  CAS  Google Scholar 

  22. Lin, S. Z., Saxena, A. & Batista, C. D. Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy. Phys. Rev. B 91, 224407 (2015).

    Article  Google Scholar 

  23. Ozawa, R. et al. Vortex crystals with chiral stripes in itinerant magnets. J. Phys. Soc. Jpn 85, 103703 (2016).

    Article  Google Scholar 

  24. Ozawa, R., Hayami, S. & Motome, Y. Zero-field skyrmions with a high topological number in itinerant magnets. Phys. Rev. Lett. 118, 147205 (2017).

    Article  Google Scholar 

  25. Hayami, S., Ozawa, R. & Motome, Y. Effective bilinear–biquadratic model for noncoplanar ordering in itinerant magnets. Phys. Rev. B 95, 224424 (2017).

    Article  Google Scholar 

  26. Heinze, S. et al. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat. Phys. 7, 713–718 (2011).

    Article  CAS  Google Scholar 

  27. Takagi, R. et al. Multiple-q noncollinear magnetism in an itinerant hexagonal magnet. Sci. Adv. 4, eaau3402 (2018).

    Article  CAS  Google Scholar 

  28. Martin, I. & Batista, C. D. Itinerant electron-driven chiral magnetic ordering and spontaneous quantum Hall effect in triangular lattice models. Phys. Rev. Lett. 101, 156402 (2008).

    Article  Google Scholar 

  29. Kurumaji, T. et al. Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet. Science 365, 914–918 (2019).

    Article  CAS  Google Scholar 

  30. Hirschberger, M. et al. Skyrmion phase and competing magnetic orders on a breathing kagomé lattice. Nat. Commun. 10, 5831 (2019).

    Article  CAS  Google Scholar 

  31. Ślaski, M., Szytuła, A., Leciejewicz, J. & Zygmunt, A. Magnetic properties of RERu2Si2 (RE = Pr, Nd, Gd, Tb, Dy, Er) intermetallics. J. Mag. Mag. Mater. 46, 114 (1984).

    Article  Google Scholar 

  32. Garnier, A. et al. Anisotropic metamagnetism in GdRu2Si2. J. Magn. Magn. Mater. 140, 899–9000 (1995).

    Article  Google Scholar 

  33. Devishvili, A. Magnetic Properties of Gd 3+ Based Systems. PhD Thesis, Univ. Vienna (2010).

  34. Samanta, T., Das, I. & Banerjee, S. Comparative studies of magnetocaloric effect and magnetotransport behavior in GdRu2Si2 compound. J. Appl. Phys. 104, 123901 (2008).

    Article  Google Scholar 

  35. Adams, T. et al. Long-range crystalline nature of the skyrmion lattice in MnSi. Phys. Rev. Lett. 107, 217206 (2011).

    Article  CAS  Google Scholar 

  36. Blume, M. in Resonant Anomalous X-Ray Scattering (eds Materlik, G., Sparks, C. J. and Fischer, K.) 495–512 (Elsevier, 1994).

  37. Marcus, G. G. et al. Multi-q mesoscale magnetism in CeAuSb2. Phys. Rev. Lett. 120, 097201 (2018).

    Article  CAS  Google Scholar 

  38. Yu, X. Z. et al. Transformation between meron and skyrmion topological spin textures in a chiral magnet. Nature 564, 95–98 (2018).

    Article  CAS  Google Scholar 

  39. Nakajima, T. et al. Skyrmion lattice structural transition in MnSi. Sci. Adv. 3, 1602562 (2017).

    Article  Google Scholar 

  40. Yu, X. Z. et al. Aggregation and collapse dynamics of skyrmions in a non-equilibrium state. Nat. Phys. 14, 832–836 (2018).

    Article  CAS  Google Scholar 

  41. Ishizuka, K. & Allman, B. Phase measurement of atomic resolution image using transport of intensity equation. J. Electron Microsc. 54, 191–197 (2005).

    CAS  Google Scholar 

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Acknowledgements

We would like to thank T. Kurumaji, N. Nagaosa, R. Arita, K. Ishizaka, T. Hanaguri, Y. Motome, S. Hayami, Y. Yasui, C. J. Butler, T. Koretsune, T. Nomoto, Y. Ohigashi and A. Kikkawa for enlightening discussions and experimental help. RXS measurements were performed under the approval of the Proposal no. 2018G570 at the Institute of Material Structure Science, High Energy Accelerator Research Organization (KEK). This work was partly supported by Grants-In-Aid for Scientific Research (A) (grant nos 18H03685 (S.S.) and 19H00660 (X.Y.)), and Grant-in-Aid for Scientific Research on Innovative Area, ‘Nano Spin Conversion Science’ (Grant no. 17H05186) from JSPS, and PRESTO (grant no. JPMJPR18L5) and CREST (grant no. JPMJCR1874) from JST, and Asahi Glass Foundation. M.H. was supported as a Humboldt/JSPS International Research Fellow (18F18804). R.T. was supported by the Murata Science Foundation.

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Contributions

N.D.K., S.S., T.A. and Y.T. conceived the project. N.D.K. grew single crystals and characterized the magnetic and transport properties with the assistance of R.T. and M.H. T.N., S.G. and N.D.K. carried out the RXS measurements with the assistance of K.S., Y.Y., H.S. and H.N. X.Y. performed the L-TEM observations and L.P. and K.N. prepared the TEM samples. N.D.K. and S.S. wrote the manuscript. All the authors discussed the results and commented on the manuscript.

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Correspondence to Nguyen Duy Khanh or Shinichiro Seki.

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Supplementary Figs. 1–8, Notes I–VIII and refs. 1–7.

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Khanh, N.D., Nakajima, T., Yu, X. et al. Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet. Nat. Nanotechnol. 15, 444–449 (2020). https://doi.org/10.1038/s41565-020-0684-7

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