Fig. 5: Field-driven dynamics of a domain wall–skyrmions train in granular nanotrack.

a Three different realizations of the granular nanotrack with an average grain size of 20 nm by Voronoi tessellation. In each grain, the strength of perpendicular magnetic anisotropy K_u is randomly distributed around the average value K_u0 = 0.8 MJm⁻³ with a Gaussian distribution of the deviation ∆K (= K_u ‒ K_u0). In this figure, ∆K = 2%K_u0 is shown. The color code indicates the strength of K_u. b Under field strength H = 300 Oe, the ensemble can move, without pinning, in the sample with ∆K = 2%K_u0 (K_u0 = 0.8 MJm⁻³ and Dzyaloshinskii-Moriya interaction strength D = 3.5 mJm⁻²). However, different from in the clean sample, the ensemble travels different distances ∆x over the same time intervals ∆t. Accordingly, we derive the average ensemble velocity by fitting the positions against time.