Article | Published:

Aggregation and collapse dynamics of skyrmions in a non-equilibrium state

Abstract

Magnetic skyrmions have attracted attention because of their emergent electromagnetic properties. In particular, non-equilibrium-state skyrmions, which are protected by topology and hence can exist over a wider temperature–magnetic-field region, show promise for possible practical applications, but their dynamics remain elusive. Here, we report the observation of a magnetic-field-induced dynamical transition from the metastable hexagonal-lattice skyrmion crystal (SkX) at a zero bias-field to an amorphous state via the densely vacancy-populated SkX. With decreasing field, on the other hand, the aggregate transforms from ‘random particles’ to ‘microcrystals’ of skyrmions in a non-equilibrium state, in analogy to colloidal crystallization, and subsequently undergoes a topologically distinct phase separation between the SkX and helical/conical domains accompanied by topological defects. These observations directly demonstrate the aggregation and collapse dynamics of metastable skyrmions and may provide a route to other nontrivial topological phenomena such as the zero-magnetic-field topological Hall effect.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

References

  1. 1.

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

  2. 2.

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

  3. 3.

    Kanazawa, N. et al. Large topological Hall effect in a short-period helimagnet MnGe. Phys. Rev. Lett. 106, 156603 (2011).

  4. 4.

    Moutafis, C., Komineas, S. & Bland, J. A. C. Dynamics and switching processes for magnetic bubbles in nanoelements. Phys. Rev. B 79, 224429 (2009).

  5. 5.

    Jonietz, F. et al. Spin transfer torques in MnSi at ultralow current densities. Science 330, 1648–1651 (2011).

  6. 6.

    Yu, X. Z. et al. Skyrmion flow near room temperature in an ultralow current density. Nat. Commun. 3, 988 (2012).

  7. 7.

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

  8. 8.

    Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2011).

  9. 9.

    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).

  10. 10.

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

  11. 11.

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

  12. 12.

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

  13. 13.

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

  14. 14.

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

  15. 15.

    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).

  16. 16.

    Bolle, O. et al. Room-temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures. Nat. Nanotech. 11, 449–454 (2016).

  17. 17.

    Moreau-Luchaire, C. et al. Additive interfacial chiral interaction in multilayers for stabilization of small individual skyrmions at room temperature. Nat. Nanotech. 11, 444–448 (2016).

  18. 18.

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

  19. 19.

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

  20. 20.

    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).

  21. 21.

    Romming, N., Kubetzka, A., Hanneken, C., Bergmann, K. & Wiesendanger, R. Field-dependent size and shape of single magnetic skyrmions. Phys. Rev. Lett. 114, 177203 (2015).

  22. 22.

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

  23. 23.

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

  24. 24.

    Shibata, K. et al. Temperature and magnetic field dependence of the internal and lattice structures of skyrmions by off-axis electron holography. Phys. Rev. Lett. 118, 087202 (2017).

  25. 25.

    Savage, J. R. & Dinsmore, A. D. Experimental evidence for two-step nucleation in colloidal crystallization. Phys. Rev. Lett. 102, 198302 (2009).

  26. 26.

    Elías, R. G. & Verga, A. Magnetization structure of a Bloch point singularity. Eur. Phys. J. 82, 159–166 (2011).

  27. 27.

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

Download references

Acknowledgements

The authors thank W. Koshibae and H. Oike for helpful discussions. This work was supported in part by JSPS Grant-in-Aid for Scientific Research(S) no. 24224009.

Author information

Y.T. conceived the project and wrote the draft. X.Y. designed the experiments, performed Lorentz TEM measurements, analysed Lorentz TEM data and wrote the draft. D.M. and N.K. prepared FeGe samples. T.Y. and K.S. performed LLG simulations. All authors discussed the data and commented on the manuscript.

Competing interests

The authors declare no competing interests.

Correspondence to Xiuzhen Yu.

Supplementary information

  1. Supplementary Information

    Supplementary information, Supplementary Figures 1–9, Supplementary References 1–2

  2. Supplementary Movie 1

    In situ Lorentz TEM movie shows the recrystallization of skyrmion aggregates

  3. Supplementary Movie 2

    Micromagnetic simulations for metastable skyrmions in a micromagnet (1,024 nm × 1,024 nm × 128 nm in size) with decreasing the bias field

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Further reading

Fig. 1: Skyrmion crystal (SkX) formation and annihilation in the thermal-equilibrium state in a (110) FeGe thin plate.
Fig. 2: SkX formation at zero-bias field in the FeGe plate.
Fig. 3: Shape and size changes of quenched skyrmions and their aggregation form with the increase of B after the 100 mT field-cooling.
Fig. 4: Collective transformations of random skyrmion aggregates with decreasing bias magnetic field B.