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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.

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

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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.

Competing interests

The authors declare no competing interests.

Correspondence to Mathias Kläui.

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.

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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.