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Transformation between meron and skyrmion topological spin textures in a chiral magnet

Naturevolume 564pages9598 (2018) | Download Citation


Crystal lattices with tetragonal or hexagonal structure often exhibit structural transitions in response to external stimuli1. Similar behaviour is anticipated for the lattice forms of topological spin textures, such as lattices composed of merons and antimerons or skyrmions and antiskyrmions (types of vortex related to the distribution of electron spins in a magnetic field), but has yet to be verified experimentally2,3. Here we report real-space observations of spin textures in a thin plate of the chiral-lattice magnet Co8Zn9Mn3, which exhibits in-plane magnetic anisotropy. The observations demonstrate the emergence of a two-dimensional square lattice of merons and antimerons from a helical state, and its transformation into a hexagonal lattice of skyrmions in the presence of a magnetic field at room temperature. Sequential observations with decreasing temperature reveal that the topologically protected skyrmions remain robust to changes in temperature, whereas the square lattice of merons and antimerons relaxes to non-topological in-plane spin helices, highlighting the different topological stabilities of merons, antimerons and skyrmions. Our results demonstrate the rich variety of topological spin textures and their lattice forms, and should stimulate further investigation of emergent electromagnetic properties.

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  1. 1.

    Kittle, C. Introduction to Solid State Physics Ch. 1 (John Wiley & Sons, New York, (2005).

  2. 2.

    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).

  3. 3.

    Yi, S. D., Onoda, S., Nagaosa, N. & Han, J. H. Skyrmions and anomalous Hall effect in a Dzyaloshinskii–Moriya spiral magnet. Phys. Rev. B 80, 054416 (2009).

  4. 4.

    Berdiyorov, G. R., Milošević, M. V. & Peeters, F. M. Vortex configurations and critical parameters in superconducting thin films containing antidote arrays: nonlinear Ginzburg−Landau theory. Phys. Rev. B 74, 174512 (2006).

  5. 5.

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

  6. 6.

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

  7. 7.

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

  8. 8.

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

  9. 9.

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

  10. 10.

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

  11. 11.

    Li, W. et al. Emergence of skyrmions from rich parent phases in the molybdenum nitrides. Phys. Rev. B 93, 060409(R) (2016).

  12. 12.

    Woo, S. et al. Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets. Nat. Mater. 15, 501–506 (2016).

  13. 13.

    Jiang, W. et al. Blowing magnetic skyrmion bubbles. Science 349, 283–286 (2015).

  14. 14.

    Sampaio, J., Cros, V., Rohart, S., Thiaville, A. & Fert, A. Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures. Nat. Nanotechnol. 8, 839–844 (2013).

  15. 15.

    Zheng, F. S. et al. Experimental observation of chiral magnetic bobbers in B20-type FeGe. Nat. Nanotechnol. 13, 451–455 (2018).

  16. 16.

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

  17. 17.

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

  18. 18.

    Vousden, M. et al. Skyrmions in thin films with easy-plane magnetocrystalline anisotropy. Appl. Phys. Lett. 108, 132406 (2016).

  19. 19.

    Shinjo, T., Okuno, T., Hassdorf, R., Shigeko, K. & Ono, T. Magnetic vortex core observation in circular dots of permalloy. Science 289, 930–932 (2000).

  20. 20.

    Phatak, C., Petford-Long, A. K. & Heinonen, O. Direct observation of unconventional topological spin structure in coupled magnetic discs. Phys. Rev. Lett. 108, 067205 (2012).

  21. 21.

    Wintz, S. et al. Topology and origin of effective spin meron pairs in ferromagnetic multilayer elements. Phys. Rev. Lett. 110, 177201 (2013).

  22. 22.

    Tan, A. et al. Topology of spin meron pairs in coupled Ni/Fe/Co/Cu (001) disks. Phys. Rev. B 94, 014433 (2016).

  23. 23.

    Ishizuka, K. & Allman, B. Phase measurement in electron microscopy using the transport of intensity equation. J. Electron Microsc. 54, 191–197 (2005).

  24. 24.

    Shibata, K. et al. Large anisotropic deformation of skyrmions in strained crystals. Nat. Nanotechnol. 10, 589–592 (2015).

  25. 25.

    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).

  26. 26.

    Nakajima, T. et al. Skyrmion lattice structural transition in MnSi. Sci. Adv. 3, e1602562 (2017).

  27. 27.

    Oike, H. et al. Interplay between topological and thermodynamic stability in a metastable magnetic skyrmion lattice. Nat. Phys. 12, 62–66 (2016).

  28. 28.

    Münzer, W. et al. Skyrmion lattice in the doped semiconductor Fe1−xCoxSi. Phys. Rev. B 81, 041203(R) (2010).

  29. 29.

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

  30. 30.

    Yu, X. Z. et al. Current−induced nucleation and annihilation of magnetic skyrmions at room temperature in a chiral magnet. Adv. Mater. 29, 1606178 (2017).

  31. 31.

    Beleggia, M. et al. Quantitative study of magnetic field distribution by electron holography and micromagnetic simulations. Appl. Phys. Lett. 83, 1435 (2003).

  32. 32.

    Morikawa, D. et al. Deformation of topologically-protected supercooled skyrmions in a thin plate of chiral magnet Co8Zn8Mn4. Nano Lett. 17, 1637–1641 (2017).

  33. 33.

    Bogdanov, A. & Hubert, A. Thermodynamically stable magnetic vortex states in magnetic crystals. J. Magn. Magn. Mater. 138, 255–269 (1994).

  34. 34.

    Hubert, A. & Schäfer, R. Magnetic Domains Chs. 2, 3 (Springer, Berlin, 1998).

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We thank M. Ishida, Á. Butykai, D. Morikawa, T-H. Arima and M. V. Mostovoy for experimental support and discussions. N.N. was supported by JSPS KAKENHI (grant numbers JP26103006 and JP18H03676) and JST CREST (grant number JPMJCR1874), Japan.

Reviewer information

Nature thanks S. Woo and the other anonymous reviewers for their contribution to the peer review of this work.

Author information


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

    • X. Z. Yu
    • , W. Koshibae
    • , K. Shibata
    • , Y. Taguchi
    • , N. Nagaosa
    •  & Y. Tokura
  2. Department of Advanced Materials Science, University of Tokyo, Kashiwa, Japan

    • Y. Tokunaga
  3. Department of Applied Physics, University of Tokyo, Tokyo, Japan

    • N. Nagaosa
    •  & Y. Tokura


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Y. Tokura conceived the project. X.Z.Y. performed Lorentz TEM and analysed the experimental data. W.K. and N.N. performed the theoretical analyses. Y. Tokunaga and Y. Taguchi synthesized the Co-Zn-Mn alloys. K.S. simulated the Lorentz TEM images. All authors discussed the data and collaborated on the manuscript.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to X. Z. Yu.

Extended data figures and tables

  1. Extended Data Fig. 1 The crystal structure, magnetic configurations and magnetic phase diagrams of the (001) thin plate of Co8Zn9Mn3.

    a, b, Schematics of the crystal structure with space group P4132 (a) and P4332 (b). Coloured arrows indicate the crystal axes. c, Magnetic phase diagram (approximate) of the hex-SkL30 and sq-ML observed over field-increasing runs from low (less than 10 mT) field cooling for a (001) thin plate of Co8Zn9Mn3. The phase determination was based on the continuous magnetic-field scans at fixed temperatures in intervals of ΔT = 5 K. The arrow indicates the field-increasing run for the Lorentz TEM images shown in Fig. 2a–c. FM, field-magnetized ferromagnetic structure. d, e, Periodic stripe domains with a single wavevector along the [100] axis at 95 K (d), the helical structure with possible multi-domains composed of helices with in-plane wavevectors (area B) and with out-of-plane wavevectors (dark regions; area A) at 295 K (e), respectively. f, A hex-SkL realized under 65 mT at 300 K. Colours in df (see colour wheel) depict the direction (white arrows) of the local in-plane magnetization; black shows the out-of-plane magnetization.

  2. Extended Data Fig. 2 The approximate in-plane magnetization textures and simulated defocused Lorentz TEM images.

    a, d, h, sq-ML. b, e, i, sq-SkL. c, f, j, hex-SkL. The parameters for the simulations are shown in Extended Data Table 1. The colour bar indicates the normalized component of the out-of-plane magnetization mz.

  3. Extended Data Fig. 3 Magnetic phase diagrams and several over-focused Lorentz TEM images observed in the (001) thin plate of Co8Zn9Mn3 with varying temperature T and external magnetic field B.

    a, Phase diagram of the magnetic structure observed after 60-mT field cooling with increasing B (red dashed arrows), decreasing (black arrow) B and then increasing T (blue dashed arrow). b, Phase diagram of the magnetic structure observed after field cooling with various cooling fields (indicated by red dashed arrows). H + M shows the mixed structure of helices (dominant) and merons (minor). The open circles specify the (TB) points that we measured. The dark blue region shows the helical phase. cf, Over-focused Lorentz TEM images observed for different T and B, indicated by black solid circles in a (c, d) and yellow solid circles in b (e, f).

  4. Extended Data Fig. 4 Various periodic arrays of the topological spin textures observed in the (001) thin plate of Co8Zn9Mn3 with varying external magnetic field.

    a, b, d, e, g, h, Lorentz TEM images (a, d and g; insets show the corresponding fast Fourier transforms) and their magnetization maps (b, e and h) for the sq-ML (a, b), hex-SkL (d, e) and skyrmion chains (g, h) observed at 295 K and various fields. c, f, i, Magnified magnetization textures in the boxed areas in b, e and h.

  5. Extended Data Fig 5 Spontaneous magnetic structures in thin plates of Co-Zn-Mn with various Mn compositions.

    ah, Defocused Lorentz TEM images observed in the thin plates of Co-Zn-Mn at zero field and 95 K. il, Electron-phase images obtained from analysing Lorentz TEM images in ah with the transport-of-intensity equation.

  6. Extended Data Fig. 6 Exotic topological spin textures in thin plates of Co-Zn-Mn with various Mn compositions.

    ac, Over-focused Lorentz TEM images of skyrmion chains observed in Co8Zn9Mn3 (a), bound skyrmions in Co8Zn10Mn2 (b; such as that indicated by the yellow arrow) and bubble-like domains in CoZn (c; such as that indicated by the white arrow).

  7. Extended Data Table 1 Parameters for Fresnel image simulations

Supplementary information

  1. Video 1

    An in-situ Lorentz TEM video showing transitions of magnetic configurations from the helical structure to a hexagonal lattice of skyrmion, via a square lattice of meron and antimeron in a (001) thin plate of Co8Zn9Mn3 with an increasing run of the magnetic bias field.

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