Stochastic dynamics of Galton board based on magnetic skyrmions

Conventional Galton board is an iconic model in statistics to study the stochastic dynamics of particle with ideal hypothesis of equal probability. To test this hypothesis, we introduce an artificial spin network by utilizing skyrmion clusters in ultrathin ferromagnetic films, resembling a nanoscale magnetic Galton board. We show that the board output exhibits a standard Gaussian distribution when the external magnetic field oscillates with the lowest frequency of skyrmion gyration, recovering the results of conventional Galton board. The stochastic response of magnetic Galton board can be tailored by tuning the direction of external magnetic field and modifying the local geometry. Notably, the distribution deviates the Gaussian profile when applies magnetic fields with higher frequencies. We interpret it in terms of the breaking of equal-probability hypothesis due to the phase gradient between adjacent skyrmions. Our work provides theoretical reference for understanding the random properties of skyrmion clusters and for their potential applications in future neural network computing.