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Stable singular fractional skyrmion spin texture from the quantum Kelvin–Helmholtz instability

Nature Physics volume 21, pages 1398–1403 (2025)Cite this article

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Abstract

Topological defects give rise to non-trivial excitations—such as solitons, vortices and skyrmions—characterized by integer-valued topological charges. However, their classification becomes difficult when singularities are present in the order parameter field, complicating the computation of these charges. Although exotic nonlinear excitations have been theoretically proposed in the superfluid 3He-A phase and spinor Bose–Einstein condensates, they have not been experimentally observed and their stability has not been investigated. Here we demonstrate the presence of a singular skyrmion that goes beyond the framework of topology in a ferromagnetic superfluid. These skyrmions emerge from anomalous symmetry-breaking associated with an eccentric spin singularity and carry half the elementary charge—a feature that distinguishes them from conventional skyrmions and merons. We realize the universal regime of the quantum Kelvin–Helmholtz instability, and we identify the unconventional fractional skyrmions produced by emission from a magnetic domain wall and the spontaneous splitting of an integer skyrmion with spin singularities. The singular skyrmions are stable even after 2 s of hold time. Our results confirm the universality between classical and quantum Kelvin–Helmholtz instabilities and broaden our understanding of complex nonlinear dynamics for a non-trivial texture in topological quantum systems.

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Fig. 1: EFSs from the quantum KHI.
Fig. 2: The quantum KHI.
Fig. 3: Nonlinear dynamics after the KHI.
Fig. 4: Eccentric fractional skyrmion.
Fig. 5: The birth and death of the EFS.

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Acknowledgements

We acknowledge discussions with G. E. Volovik, W. J. Kwon, M. O. Borgh and Y. Shin. J.-y.C. acknowledges grants from the National Research Foundation of Korea (NRF) (Project Nos. RS-2023-00207974, RS-2023-00218998, RS-2023-00256050, RS-2023-NR119928 and 2023M3K5A1094812). W.Y. and S.K.K. acknowledge support from the Brain Pool Plus Program through the NRF funded by the Ministry of Science and ICT (Grant No. 2020H1D3A2A03099291) and the NRF (Grant No. 2021R1C1C1006273). H.T. acknowledges suppors from the JST, Japan (PRESTO Grant No. JPMJPR23O5) and JSPS (KAKENHI Grants No. JP18KK0391 and JP20H01842).

Author information

Authors and Affiliations

  1. Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, South Korea

    SeungJung Huh, Wooyoung Yun, Gabin Yun, Samgyu Hwang, Kiryang Kwon, Junhyeok Hur, Seungho Lee, Se Kwon Kim & Jae-yoon Choi

  2. Nambu Yoichiro Institute of Theoretical and Experimental Physics, Osaka Metropolitan University, Osaka, Japan

    Hiromitsu Takeuchi

  3. Department of Physics, Osaka Metropolitan University, Osaka, Japan

    Hiromitsu Takeuchi

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  1. SeungJung Huh
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Contributions

All authors contributed substantially to the work presented in this paper. J.-y.C., S.-J.H., S.K.K. and H.T. conceived and supervised the project. S.-J.H., G.Y. and S.H. carried out the experiment. S.-J.H., S.H., K.K. and J.H. maintained the experimental apparatus, and W.Y. and S.L. performed the numerical simulation. All authors contributed to the data analysis, discussion of the results and writing of the paper.

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Correspondence to Hiromitsu Takeuchi, Se Kwon Kim or Jae-yoon Choi.

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Extended data

Extended Data Fig. 1 Experiments of the quantum Kelvin-Helmholtz instability.

a, Schematic plot of the experimental sequence (not in scale). It consists of four different time zones: degenerate gas production, domain wall preparation, counterflow injection, and hold time without field gradient. b, Optical density image of the polar condensate before quenching the quadratic Zeeman energy (QZE). A field gradient \({B}_{{\rm{DW}}}^{{\prime} }\) is applied along the y-axis to prepare a well-aligned single-domain wall state during the coarsening dynamics. The counterflow in the interface layer is generated by different gradient fields \({B}_{c}^{{\prime} }\) along the x-axis. c, The snapshot images of longitudinal magnetization distribution Fz during the experimental sequences. The gradient pulse also introduces a rotational motion of the DW boundary. After a hold time of (th = 30 ms), flutter-finger patterns are well developed. The scale bar corresponds to 100 μm.

Extended Data Fig. 2 Broken-axis core domain wall.

a, Longitudinal magnetization density Fz of the broken-axis (BA) core domain wall state at q/h = − 20 Hz. b, Density profile the spin \(| 0\rangle\) state, and c, its transverse magnetization density Fx of the BA-core domain wall. The transverse magnetization Fx turns its sign at the Bloch line. The Bloch line is represented as the opposite spin vector in the transverse magnetization. d, Central cross-section profile of the longitudinal magnetization (yellow dashed line in a). e-g, BA-core domain wall without the Bloch line. The transverse spin vector points in the same direction. h, The histogram of the spin-flip occurrence at the interfaces of the domain wall.

Source data

Extended Data Fig. 3 Data analysis for Kelvin-Helmholtz instability.

a, Exemplary image of longitudinal magnetization Fz, displaying the flutter-finger pattern. b, Trajectory of domain wall in (a), which is obtained by finding the points where Fz(rDW) = 0. c, The height difference from the linear fit results as a function of the projected distance along the fitted line. d, Spline interpolated power spectrum of the interface modulation. e, Averaged power spectrum of domain wall waves for various pulse durations.

Source data

Extended Data Fig. 4 Numerical simulation of the Kelvin-Helmholtz instability and EFS pair generation.

a-d, Longitudinal spin density Fz at different hold times t. Because of the harmonic potential, the domain wall axis rotates. b, The KHI is represented as the Flutter-Finger pattern at t = 0.08 s. c, At a later time, a single magnetic droplet is emitted from the fingertip (yellow box), d, and split into two magnetic droplets like in the experiment. e, The Zoomed plot for local spin vector, f, longitudinal spin density Fz, and g, density distribution n0 of spin \(| 0\rangle\) state for c and d. The yellow circles indicate the region where the BEC is in the local antiferromagnetic phase with zero spin density. h, After 25 ms, two EFSs with the same spin vorticity are generated from the skyrmion-like spin texture. As a result, i, two magnetic droplets and j, two ‘C’ shapes are observed in the Fz and n0, respectively. The spin singular points in e and h are present at the same locations as the dark nodes of the ‘C’ shape in g and i, respectively. One can find the movie files of the numeric simulation for Fz and n0 in the OSF storage (https://osf.io/4hk9v/files/osfstorage?view_only=).

Extended Data Fig. 5 Spin singularity along the domain wall.

a, Longitudinal magnetization after applying gradient pulse. b, Absorption image of the spin \(| 0\rangle\) state. Anti-ferromagnetic spin singular point is highlighted by the white circle. c, Density profile of the along the domain wall. Density dips (red arrows) denote the singular point.

Source data

Extended Data Fig. 6 Matter-wave interference using two-photon Raman transition.

a, Schematic diagram of Raman transition. All Raman beams are 4 GHz red detuned to D1 transition line, and the frequency difference is set to Δν = ν1 − ν2 = 803.8 MHz, corresponding to the hyperfine splitting between the \(\left\vert 1,1\right\rangle\) and \(\left\vert 2,2\right\rangle\) states. The laser beams have lin⊥lin configuration and their beam waist are 1 mm, larger than the condensate diameter (~ 300 μm). b, Experimental sequence for matter-wave interference. We first apply the π/2 pulse of the Raman transition with a counterpropagating configuration (k, − k). Then, the copy of condensate in \(\left\vert 2,2\right\rangle\) state can move along the direction of Raman lasers with a photon recoil momentum 2ℏk. Having a time interval of ΔtR = 200μs between the two Raman pulses, the condensates in each hyperfine spin state have Δr = 34 μm of spatial displacement. The sequence ends with applying the second π/2 pulse of Raman beams with its mutual angle of 3∘. The difference in photon recoil momentum from the Raman pulse results in the spatial modulation in the atomic density profile. c, When the condensate contains EFS, the spin \(| 1\rangle\) state contains unity charge vortex. After the matter-wave interference, it displays two Y-shaped patterns because of the finite displacement Δr.

Extended Data Fig. 7 Eccentric fractional skyrmions.

Representative experimental images of showcasing the EFS. At a fixed hold time ts = 60 ms, we repeat the experiment at the same experimental conditions and measure the density profiles of all spin states and spin \(| 1\rangle\) state after two-photon Raman interference. a-e, Longitudinal magnetization, f-j,\(| 0\rangle\) state density, and k-p, interference pattern in the \(| 1\rangle\) state. Images in each column are measured in the same experimental sequence. Yellow boxes represent the same area, and yellow arrows indicate the spin singular point. The mass vorticity is represented in the Y-shaped patterns in (k-p), highlighted with yellow lines.

Extended Data Fig. 8 Classifying spin textures.

By measuring the density (top row) and relative phase information (bottom row) in the \(| 1\rangle\) state simultaneously, the magnetic droplets can be categorized to have different types of spin textures: a, trivial (Nv = 0, straight interference fringe) b, EFS (Nv = 1, Y-shaped pattern) c, and integer skyrmion (Nv = 2, fork-shaped pattern).

Extended Data Fig. 9 Spin texture after 2s of hold time.

a, Longitudinal magnetization, Fz, b, interference pattern in the \(| 1\rangle\) spin state, and c, angular density distribution of the \(| 0\rangle\) state at the domain wall boundary Fz = 0. Inset image displays the density profile, and yellow boxes correspond to the same region. d,e, Longitudinal magnetization and f,g, Raman interference images with EFS after 2 s of hold time. The EFS can be survived even after 2s (a-c) or lost by drifting outside of the condensate (d,f) or decay to a vortex without a magnetic core (e,f).

Source data

Source data

Source Data Fig. 2

Source data for Fig. 2c–f.

Source Data Fig. 4

Source data for Fig. 4c.

Source Data Fig. 5

Source data for Fig. 5a,b.

Source Data Extended Data Fig. 2

Source data for Extended Data Fig. 2d,h.

Source Data Extended Data Fig. 3

Source data for Extended Data Fig. 3c,d,f.

Source Data Extended Data Fig. 5

Source data for Extended Data Fig. 5c.

Source Data Extended Data Fig. 9

Source data for Extended Data Fig. 9c.

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Huh, S., Yun, W., Yun, G. et al. Stable singular fractional skyrmion spin texture from the quantum Kelvin–Helmholtz instability. Nat. Phys. 21, 1398–1403 (2025). https://doi.org/10.1038/s41567-025-02982-x

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