Abstract
Some magnetic systems feature spin textures, real-space patterns in the orientation of spins that can topologically form non-trivial configurations. Among them, a vortex-like spin swirling texture known as a magnetic skyrmion has attracted particular attention. Lattices of skyrmions form in the helimagnet MnSi with a periodicity of 18 nm, which makes them amenable to investigation by Lorentz transmission electron microscopy in real space and by small-angle neutron scattering in momentum space. However, the dynamics of the skyrmion lattice are difficult to measure at the microelectronvolts energy scale at small wavevectors. Here we examine the low-energy excitations of the skyrmion state in MnSi by using the neutron spin-echo technique under small-angle neutron scattering conditions. We observe an asymmetric dispersion of the phason excitations of the lattice because of the string-like structure of the skyrmion cores.
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Change history
02 October 2023
A Correction to this paper has been published: https://doi.org/10.1038/s41567-023-02241-x
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Acknowledgements
We greatly appreciate the fruitful discussions with W. Koshibae, G. Tatara and S. Hoshino. We thank K. Beauvois for providing access to OrientExpress, the test Laue neutron diffractometer at the Institut Laue-Langevin. Travel expenses for the neutron experiment performed using IN15 at ILL, France, were supported by the General User Program for Neutron Scattering Experiments, Institute for Solid State Physics, The University of Tokyo (proposal no. 18812), at JRR-3, Japan Atomic Energy Agency, Tokai, Japan. The work was supported by JST, CREST, grant no. JPMJCR20T1, Japan. The work was supported by Czech Ministry of Education, Youth and Sports (MEYS), project LTT20014.
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M.S. and H.K.-F. planned the neutron scattering experiments. M.S., E.M.F., E.B., V.R., I.H., E.C. and H.K.-F. carried out the neutron spin-echo experiments. Data analysis was done by M.S. in discussion with E.M.F. and E.B. The samples were grown by A.K. The paper was written by M.S., with additional material from E.M.F. and E.B. All other co-authors actively contributed to the final version.
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Nature Physics thanks J. R. Stewart, D. Cabra and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Supplementary Information
Supplementary Sections 1–4, Figs. 1–5, Tables 1 and 2 and source data list.
Supplementary Data
Expected phase shifts for Supplementary Fig. 2. Variations in the echo phase shift for Supplementary Fig. 3. Energy estimated from the phase shift in the helical state for Supplementary Fig. 5.
Supplementary Code
Expected phase shifts for Supplementary Fig. 2. Proposed dispersion curve for Supplementary Fig. 4. Intermediate scattering function and phase shift for Fig. 3.
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Source Data Fig. 1
Source data for graph and contour plot.
Source Data Fig. 2
Source data for graph and contour plot.
Source Data Fig. 3
Source data for graph.
Source Data Fig. 5
Source data for graph.
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Soda, M., Forgan, E.M., Blackburn, E. et al. Asymmetric slow dynamics of the skyrmion lattice in MnSi. Nat. Phys. 19, 1476–1481 (2023). https://doi.org/10.1038/s41567-023-02120-5
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DOI: https://doi.org/10.1038/s41567-023-02120-5
