Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Thermal skyrmion diffusion used in a reshuffler device


Magnetic skyrmions in thin films can be efficiently displaced with high speed by using spin-transfer torques1,2 and spin–orbit torques3,4,5 at low current densities. Although this favourable combination of properties has raised expectations for using skyrmions in devices6,7, only a few publications have studied the thermal effects on the skyrmion dynamics8,9,10. However, thermally induced skyrmion dynamics can be used for applications11 such as unconventional computing approaches12, as they have been predicted to be useful for probabilistic computing devices13. In our work, we uncover thermal diffusive skyrmion dynamics by a combined experimental and numerical study. We probed the dynamics of magnetic skyrmions in a specially tailored low-pinning multilayer material. The observed thermally excited skyrmion motion dominates the dynamics. Analysing the diffusion as a function of temperature, we found an exponential dependence, which we confirmed by means of numerical simulations. The diffusion of skyrmions was further used in a signal reshuffling device as part of a skyrmion-based probabilistic computing architecture. Owing to its inherent two-dimensional texture, the observation of a diffusive motion of skyrmions in thin-film systems may also yield insights in soft-matter-like characteristics (for example, studies of fluctuation theorems, thermally induced roughening and so on), which thus makes it highly desirable to realize and study thermal effects in experimentally accessible skyrmion systems.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Trajectories of selected skyrmions at 296 K.
Fig. 2: Temperature dependence of the evaluated skyrmion diffusion coefficient considering all the observed skyrmions.
Fig. 3: Observation of the skyrmion reshuffler device operation.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Jonietz, F. et al. Spin transfer torques in MnSi at ultralow current densities. Science 330, 1648–1651 (2010).

    CAS  Article  Google Scholar 

  2. 2.

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

    CAS  Article  Google Scholar 

  3. 3.

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

    CAS  Article  Google Scholar 

  4. 4.

    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).

    CAS  Article  Google Scholar 

  5. 5.

    Litzius, K. et al. Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy. Nat. Phys. 13, 170–175 (2017).

    CAS  Article  Google Scholar 

  6. 6.

    Fert, A., Cros, V. & Sampaio, J. Skyrmions on the track. Nat. Nanotechnol. 8, 152–156 (2013).

    CAS  Article  Google Scholar 

  7. 7.

    Zhang, X. et al. Skyrmion–skyrmion and skyrmion–edge repulsions in skyrmion-based racetrack memory. Sci. Rep. 5, 7643 (2015).

    CAS  Article  Google Scholar 

  8. 8.

    Lin, S.-Z., Reichhardt, C., Batista, C. D. & Saxena, A. Particle model for skyrmions in metallic chiral magnets: dynamics, pinning, and creep. Phys. Rev. B 87, 214419 (2013).

    Article  Google Scholar 

  9. 9.

    Reichhardt, C. & Reichhardt, C. J. O. Thermal creep and the skyrmion Hall angle in driven skyrmion crystals. J. Phys. Condens. Matter 31, 07LT01 (2019).

    CAS  Article  Google Scholar 

  10. 10.

    Troncoso, R. E. & Núñez, Á. S. Brownian motion of massive skyrmions in magnetic thin films. Ann. Phys. (N. Y.) 351, 850–856 (2014).

    CAS  Article  Google Scholar 

  11. 11.

    Xing, X., Pong, P. W. T. & Zhou, Y. Skyrmion domain wall collision and domain wall-gated skyrmion logic. Phys. Rev. B 94, 1–11 (2016).

    Google Scholar 

  12. 12.

    Huang, Y., Kang, W., Zhang, X., Zhou, Y. & Zhao, W. Magnetic skyrmion-based synaptic devices. Nanotechnology 28, 08LT02 (2017).

    Article  Google Scholar 

  13. 13.

    Pinna, D. et al. Skyrmion gas manipulation for probabilistic computing. Phys. Rev. Appl. 9, 064018 (2017).

    Article  Google Scholar 

  14. 14.

    Rózsa, L. et al. Skyrmions with attractive interactions in an ultrathin magnetic film. Phys. Rev. Lett. 117, 157205 (2016).

    Article  Google Scholar 

  15. 15.

    Díaz, S. A., Reichhardt, C. J. O., Arovas, D. P., Saxena, A. & Reichhardt, C. Fluctuations and noise signatures of driven magnetic skyrmions. Phys. Rev. B 96, 085106 (2017).

    Article  Google Scholar 

  16. 16.

    Schütte, C., Iwasaki, J., Rosch, A. & Nagaosa, N. Inertia, diffusion, and dynamics of a driven skyrmion. Phys. Rev. B 90, 174434 (2014).

    Article  Google Scholar 

  17. 17.

    Miltat, J., Rohart, S. & Thiaville, A. Brownian motion of magnetic domain walls and skyrmions, and their diffusion constants. Phys. Rev. B 97, 214426 (2018).

    CAS  Article  Google Scholar 

  18. 18.

    Mehrer, H. Diffusion in Solids: Fundamentals, Methods, Materials, Diffusion-controlled Processes (eds Cordona, M., Fulde, P., von Klitzing, K. & Queisser, H.-J.) (Solid State Sciences Vol. 155, Springer, 2007).

  19. 19.

    Nozaki, T. et al. Brownian motion of skyrmion bubbles and its control by voltage applications. Appl. Phys. Lett. 114, 012402 (2019).

    Article  Google Scholar 

  20. 20.

    Gupta, P. K. & Kumaresan, R. Binary multiplication with PN sequences. IEEE Trans. Acoust. 36, 603–606 (1988).

    Article  Google Scholar 

  21. 21.

    Yu, G. et al. Room-temperature creation and spin–orbit torque manipulation of skyrmions in thin films with engineered asymmetry. Nano Lett. 16, 1981–1988 (2016).

    CAS  Article  Google Scholar 

  22. 22.

    Soumyanarayanan, A. et al. Tunable room-temperature magnetic skyrmions in Ir/Fe/Co/Pt multilayers. Nat. Mater. 16, 898–904 (2017).

    CAS  Article  Google Scholar 

  23. 23.

    Büttner, F. et al. Magnetic states in low-pinning high-anisotropy material nanostructures suitable for dynamic imaging. Phys. Rev. B 87, 134422 (2013).

    Article  Google Scholar 

  24. 24.

    Jaiswal, S. et al. Investigation of the Dzyaloshinskii–Moriya interaction and room temperature skyrmions in W/CoFeB/MgO thin films and microwires. Appl. Phys. Lett. 111, 022409 (2017).

    Article  Google Scholar 

  25. 25.

    Lemesh, I., Büttner, F. & Beach, G. S. D. Accurate model of the stripe domain phase of perpendicularly magnetized multilayers. Phys. Rev. B 95, 174423 (2017).

    Article  Google Scholar 

  26. 26.

    Sitte, M. et al. Current-driven periodic domain wall creation in ferromagnetic nanowires. Phys. Rev. B 94, 064422 (2016).

    Article  Google Scholar 

  27. 27.

    Stier, M., Häusler, W., Posske, T., Gurski, G. & Thorwart, M. Skyrmion–anti-skyrmion pair creation by in-plane currents. Phys. Rev. Lett. 118, 267203 (2017).

    Article  Google Scholar 

  28. 28.

    Büttner, F. et al. Field-free deterministic ultrafast creation of magnetic skyrmions by spin–orbit torques. Nat. Nanotechnol. 12, 1040–1044 (2017).

    Article  Google Scholar 

  29. 29.

    Everschor-Sitte, K., Sitte, M., Valet, T., Abanov, A. & Sinova, J. Skyrmion production on demand by homogeneous DC currents. New J. Phys. 19, 092001 (2017).

    Article  Google Scholar 

  30. 30.

    Lo Conte, R. et al. Role of B diffusion in the interfacial Dzyaloshinskii–Moriya interaction in Ta/Co20Fe60B20/MgO nanowires. Phys. Rev. B 91, 014433 (2015).

    Article  Google Scholar 

  31. 31.

    Jiang, W. et al. Direct observation of the skyrmion Hall effect. Nat. Phys. 13, 162–169 (2017).

    CAS  Article  Google Scholar 

  32. 32.

    Schindelin, J. et al. Fiji: an open-source platform for biological-image analysis. Nat. Methods 9, 676–682 (2012).

    CAS  Article  Google Scholar 

  33. 33.

    Jaqaman, K. et al. Robust single-particle tracking in live-cell time-lapse sequences. Nat. Methods 5, 695–702 (2008).

    CAS  Article  Google Scholar 

  34. 34.

    Tinevez, J. Y. et al. TrackMate: an open and extensible platform for single-particle tracking. Methods 115, 80–90 (2017).

    CAS  Article  Google Scholar 

  35. 35.

    Tejedor, V. et al. Quantitative analysis of single particle trajectories: mean maximal excursion method. Biophys. J. 98, 1364–1372 (2010).

    CAS  Article  Google Scholar 

Download references


The project was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) project nos 403502522 and 49741853, SFB 767 and SFB TRR173, and grant no. EV 196/2-1. M.K., S.J. and G.J. acknowledge support from the WALL project (FP7-PEOPLE-2013-ITN 608031). L.R. acknowledges the support of the Alexander von Humboldt Foundation. P.V. thanks the DFG TRR146 for partial financial support. J.Z. acknowledges the help and advice of the technicians of the Kläui group, especially S. Kauschke.

Author information




M.K. and U.N. proposed and supervised the study. J.Z., S.J. and K.L. fabricated devices and characterized the multilayer samples. J.Z. and D.H. prepared the measurement set-up and, together with N.K. and S.K., conducted the experiments using the Kerr microscope. J.Z. and D.H. evaluated the experimental data with the help of P.V. and G.J. F.J. and A.D. performed the theoretical calculations and atomistic simulations of skyrmion diffusion. L.R. calculated the model parameters. J.Z. produced, measured and analysed the skyrmion reshuffler under the supervision of D.P., K.E.-S. and M.K. J.Z. drafted the manuscript with the help of M.K. and U.N. All the authors commented on the manuscript.

Corresponding author

Correspondence to Mathias Kläui.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Figs. 1–6 and Supplementary Tables 1 and 2.

Supplementary Video 1

Skyrmion nucleation with current pulses.

Supplementary Video 2

Skyrmion motion in a relaxed state at T = 296 K in a constant 0.35 mT out-of-plane field.

Supplementary Video 3

Motion tracking of five selected skyrmions at a temperature of 296 K.

Supplementary Video 4

Simulation of skyrmion diffusion at kBT/J0 = 0.002.

Supplementary Video 5

Operation of the skyrmion reshuffler device upon application of a d.c. current.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zázvorka, J., Jakobs, F., Heinze, D. et al. Thermal skyrmion diffusion used in a reshuffler device. Nat. Nanotechnol. 14, 658–661 (2019).

Download citation


Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research