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Magnetic skyrmion bundles and their current-driven dynamics

An Author Correction to this article was published on 03 September 2021

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Topological charge Q classifies non-trivial spin textures and determines many of their characteristics. Most abundant are topological textures with |Q| ≤ 1, such as (anti)skyrmions, (anti)merons or (anti)vortices. In this study we created and imaged in real space magnetic skyrmion bundles, that is, multi-Q three-dimensional skyrmionic textures. These textures consist of a circular spin spiral that ties together a discrete number of skyrmion tubes. We observed skyrmion bundles with integer Q values up to 55. We show here that electric currents drive the collective motion of these particle-like textures similar to skyrmions. Bundles with Q ≠ 0 exhibit a skyrmion Hall effect with a Hall angle of ~62°, whereas Q = 0 bundles, the so-called skyrmioniums, propagate collinearly with respect to the current flow, that is, with a skyrmion Hall angle of ~0°. The experimental observation of multi-Q spin textures adds another member to the family of magnetic topological textures, which may serve in future spintronic devices.

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Fig. 1: Schematics of a magnetic skyrmion bundle.
Fig. 2: Realization of magnetic skyrmion bundles with varying topological charges.
Fig. 3: Current-driven motions of a skyrmion bundle with Q = 18.
Fig. 4: Dependence of skyrmion bundle dynamics on the topological charge Q.
Fig. 5: Simulated skyrmion Hall effects of skyrmion bundles.

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Data availability

The data that support the plots provided in this paper and other findings of this study are available from the corresponding author upon reasonable request due to the huge volume (over 200 GB) of raw data in this study.

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H.D. acknowledges financial support from the National Key R&D Program of China (grant no. 2017YFA0303201), the Key Research Program of Frontier Sciences, CAS (grant no. QYZDB-SSW-SLH009), the Key Research Program of the Chinese Academy of Sciences (grant no. KJZD-SW-M01), the Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDB33030100) and the Equipment Development Project of the Chinese Academy of Sciences (grant no. YJKYYQ20180012). H.D., J.T. and L.K. acknowledge the financial support of the Natural Science Foundation of China (grant nos. 51622105, 11804343 and 11974021). A portion of this work was supported by the High Magnetic Field Laboratory of Anhui Province. J.Z. was supported by U.S. Department of Energy, Office of Science, Basic Energy Sciences (grant no. DE-SC0020221).

Author information

Authors and Affiliations



H.D. supervised the project. H.D. and J.T. conceived the experiments. W. Wei synthesized the FeGe single crystals. J.T. and Y.W. fabricated the FeGe microdevices and performed the TEM measurements. J.T. performed the simulations. H.D., J.T. and J.Z. prepared the manuscript. All authors discussed the results and contributed to the manuscript.

Corresponding author

Correspondence to Haifeng Du.

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The authors declare no competing interests.

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Peer review information Nature Nanotechnology thanks the anonymous reviewers for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Field and temperature dependence of magnetic phase diagram.

a, Magnetic phase diagram of a 150-nm thick FeGe plate. b, In-plane magnetization mappings of a skyrmion lattice with Q = 1 at T = 270 K and B ~ 200 mT. c, In-plane magnetization mappings of a skyrmion lattice with Q = 1 at T = 270 K and B ~ 200 mT. The scale bars in b and c are 100 nm. d, Transitions from helical domains at zero field and T = 260 K to the mixed skyrmions and spirals occur by increasing the negative field to B ~ 0 mT. The mixed state persists during a negative field cooling process at B ~ 70 mT. The zero-field mixed state at T = 95 K are finally achieved by decreasing the field to zero. The scale bars in d are 500 nm. SS, FM, PM, and SkL represent spin spirals, ferromagnetic state, paramagnetic state and skyrmion lattice, respectively. Defocus value in d is 1000 μm.

Extended Data Fig. 2 In-plane magnetic configurations of several typical magnetic skyrmion bundles with varying topological charges.

The magnetic contrasts were retrieved by TIE analysis. a, Skyrmion bundles with varying topological charge. at B ~ 100 mT. b, Skyrmion bundles with a negative topological charge Q = 1 - N at B ~ -100 mT. The scale bars are 100 nm.

Extended Data Fig. 3 FeGe microdevice for the in-situ Lorentz experiments.

a, Overall view of the FeGe microdevice obtained from scanning electron microscopy imaging. An FeGe thin plate was electronically connected to a microchip using the ion-beam-deposited platinum (PtCx) as the electrode. Ion-beam-deposited carbon with electrical resistance greater than that of FeGe by three orders was deposited on the FeGe thin plate as a protection layer. Two narrow FeGe regions of thickness ~90 nm were fabricated on the two sides of the 150-nm thick FeGe thin plate for high-resolution TEM measurements. b, An 80-ns pulsed current profile applied in the microdevice. c, A high-resolution TEM image of the FeGe thin plate with the inset showing the TEM diffraction, revealing that the FeGe thin plate is a (111) crystal plane.

Extended Data Fig. 4 Current-induced motion of skyrmion aggregates and bundles.

a, Typical merging processes of two separated skyrmion aggregates (Q = -3 and -2, respectively) into one (Q = -5) when the distance between them decreases under the action of current pulses. b, Dynamics of two adjacent skyrmion bundles (Q = 1 and 2, respectively) under the action of current pulses, respectively. In the whole process, the two skyrmion bundles keep stable even when they get closer. c, The averaged merging probability (<p>) of two adjacent skyrmion aggregates (blue dots line) and bundles (black dots line) with respect to their distance, d, defined as the central distance of their two nearest skyrmions. p is counted as the “1” or “0” if the two adjacent skyrmion bundles (clusters) merge or not after a single current pulse. <p> is sampled over a number of current pulses marked beside the data points. The statistical events of magnetic aggregates comprise of wide groups, e.g., Q = -2 and Q = -3, Q = -2 and Q = -7, Q = -2 and Q = -2, Q = -1 and Q = -4, Q = -4 and Q = -10 etc. The statistical events of magnetic bundles are obtained from three groups, i.e. Q = 1 and Q = 2, Q = 0 and Q = 14, and Q = 1 and Q = 12. The distance d is rounded up the times of period of spin helix in FeGe (~ 70 nm). <p> increases as d decreases for the magnetic aggregates. In contrast, the surrounding spiral of each skyrmion bundle protects the internal skyrmions from breaking down, resulting in the high stability of nearby magnetic bundles against current. The current density j ~ 4.2 × 1010 A m-2 and B ~ 100 mT. The number and direction of current pulses is marked at the top of the corresponding panels. The numbers in a and b mark the topological charge. The pulse width is set to be 80 ns. The scale bar is 400 nm.

Extended Data Fig. 5 Q – dependent low critical current density jc1.

Small objects including skyrmionium, single skyrmion and low-Q skyrmion bundles have in general high values, suggesting that they are more easily pinned by localized defects.

Extended Data Fig. 6 Current-driven motion of the skyrmionium.

The current density is j ~ 4.2 × 1010 A m-2. The magnetic field is B ~ 100 mT. The scale bars in all panels are 400 nm.

Extended Data Fig. 7 Dependence of skyrmion Hall angle θH on the magnetic field.

Representative snapshots of the current-driven motion of a Q = 36 skyrmion bundle at B ~ 70 mT and a current density of j ~ 4.0 × 1010 A m-2in the –x direction. The Lorentz images were obtained under the out-of-focus conditions with the defocus value of -1000 μm. b, Trajectories of the bag at various external fields. c, Magnetic field B dependence of skyrmion Hall angle θH. The scale bars in panel a are 500 nm.

Extended Data Fig. 8 Current-driven motion of magnetic bundles with a, Q = 2, and b, Q = 5.

The current density is j ~ 4.2 × 1010 A m-2, and the magnetic field is B ~ 100 mT. The Lorentz images were obtained under the out-of-focus conditions with a defocus value of -1000 μm. The scale bars in all figures are 500 nm.

Supplementary information

Supplementary Information

Supplementary Figs. 1–3 and Notes 1 and 2.

Supplementary Video 1

Thickness-dependence of magnetic configurations in a 3D magnetic skyrmion bundle with Q = 5. The magnetic configurations are represented by the contours of mz = 0.

Supplementary Video 2

Current-driven motion of a skyrmion bundle with Q = 18 at j ≈ 4.0 × 1010 A m2 and B ≈ 100 mT.

Supplementary Video 3

Current-driven motion of a skyrmion bundle with Q = 18 at a reversed current j ≈ 4.0 × 1010 A m2 and B ≈ 100 mT.

Supplementary Video 4

Current-driven motion of a skyrmion bundle with Q = 55 at j ≈ 4.0 × 1010 A m2 and B ≈ 100 mT.

Supplementary Video 5

Comparison of the stability of skyrmion aggregates and bundles against current at j ≈ 4.2 × 1010 A m2 and B ≈ 100 mT.

Supplementary Video 6

Current-driven motion of a skyrmionium with Q = 0 at j ≈ 4.2 × 1010 A m2 and B ≈ 100 mT.

Supplementary Video 7

Current-driven motion of a skyrmion with Q = –1 at j ≈ 4.2 × 1010 A m2 and B ≈ 100 mT.

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Tang, J., Wu, Y., Wang, W. et al. Magnetic skyrmion bundles and their current-driven dynamics. Nat. Nanotechnol. 16, 1086–1091 (2021).

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