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Real-space observation of a two-dimensional skyrmion crystal


Crystal order is not restricted to the periodic atomic array, but can also be found in electronic systems such as the Wigner crystal1 or in the form of orbital order2, stripe order3 and magnetic order. In the case of magnetic order, spins align parallel to each other in ferromagnets and antiparallel in antiferromagnets. In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23. Among them is the unusual, topologically stable skyrmion spin texture, in which the spins point in all the directions wrapping a sphere4,5,6,7. The skyrmion configuration in a magnetic solid is anticipated to produce unconventional spin–electronic phenomena such as the topological Hall effect24,25,26. The crystallization of skyrmions as driven by thermal fluctuations has recently been confirmed in a narrow region of the temperature/magnetic field (TB) phase diagram in neutron scattering studies of the three-dimensional helical magnets MnSi (ref. 17) and Fe1−xCo x Si (ref. 22). Here we report real-space imaging of a two-dimensional skyrmion lattice in a thin film of Fe0.5Co0.5Si using Lorentz transmission electron microscopy. With a magnetic field of 50–70 mT applied normal to the film, we observe skyrmions in the form of a hexagonal arrangement of swirling spin textures, with a lattice spacing of 90 nm. The related TB phase diagram is found to be in good agreement with Monte Carlo simulations. In this two-dimensional case, the skyrmion crystal seems very stable and appears over a wide range of the phase diagram, including near zero temperature. Such a controlled nanometre-scale spin topology in a thin film may be useful in observing unconventional magneto-transport effects.

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Figure 1: Topological spin textures in the helical magnet Fe 0.5 Co 0.5 Si.
Figure 2: Variations of spin texture with magnetic field and temperature in Fe 0.5 Co 0.5 Si.
Figure 3: Phase diagrams of magnetic structure and spin textures in a thin film of Fe 0.5 Co 0.5 Si.

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We would like to thank K. Ishizuka, K. Kimoto, T. Asaka, T. Hara and W. Z. Zhang for discussions. This work was partly supported by the Nanotechnology Network Project (no. ADE21005) and Grants-in-Aid for Scientific Research (numbers 16076205, 17105002, 19019004, 19048008, 19048015, 20046004, 20340086, 21244053 and 22014003) from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and also by the Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program). J.H.H. is supported by grants from the Korea Research Foundation (KRF-2008-521-C00085 and KRF-2008-314-C00101).

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Y.T. contributed to the planning of the study and the writing of the paper. X.Z.Y. and Y.M. performed the Lorentz TEM observations and wrote the experimental section of the paper. Y.O. and N.K. grew the sample crystal and contributed to the assignment of the Lorentz TEM images. J.H.P., J.H.H. and N.N. did the calculations and wrote a significant part of the discussion.

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Correspondence to X. Z. Yu or Y. Tokura.

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The authors declare no competing financial interests.

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

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