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Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet


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.


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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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Authors and Affiliations



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 Information

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).

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