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


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.

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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

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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.