Fig. 3: Heat flow-driven skyrmion motion in a Cu₂OSeO₃ thin plate.

a, b Lorentz TEM images observed before (a) and during (b) a 10 µA current flowing through the heater. c Skyrmion (white dot) domain coexistent with a vertical C domain (monotonic contrast) observed under a normal field of 160 mT at 20 K in the (111) thin Cu₂OSeO₃. The boundaries between the skyrmion domain and C domain are signed by yellow dashed lines. d The domain boundaries between skyrmions and C domain drift from the lower left to the upper right (indicated by orange dashed lines) when a 50 µA current flows through the heater (H) set on the right side of the device (Fig. 1c, d). e–g The left skyrmion island (encircled by a dotted yellow line) flows towards the right one (encircled by dotted blue line) with 100 µA current flow. h T-map of the thin Cu₂OSeO₃ during a 50 µA current flow. Color bar indicates the T-scale. i Line profiles of ∇T in the Lorentz TEM view area (the red line) and in the bulky Cu₂OSeO₃ (thicker regions, the black line) at I_H = 50 µA. j Calculated ∇T versus I_H in the Lorentz TEM view area. The inset is an enlargement of the ∇T profile at a range of I_H from 0 to100 µA. k Variation of the averaged velocity v̅ (red circles) of the domain wall (the boundary between skyrmion domain and C domain) and Hall angle (blue triangular) of the front skyrmion at the boundary with an increase of ∇T, observed while holding a constant field of 160 mT. The v̅ is a ratio of the total drift distance to the duration (the duration is 1.36 s for the heater current I_H = 0.3, 0.5 mA, while it is 1.68 s for I_H = 0.3, 0.05, 0.1 mA) of skyrmion motions. The error bars represent the maximal and minimal averaged velocities deduced from the locally-averaged values approximately over the shorter time period of 0.2–0.6 s, as detailed in Supplementary Fig. 1. The pink and blue lines are eye guides for the changes of the velocity and Hall angle, respectively.