Fig. 3: Dynamical behaviors of colloids in the transformations between half skyrmions and half bimerons.

a Image sequence of the colloidal response in the motion of a half-skyrmion string. The black double arrows indicate the top surface alignment. The half skyrmions are transformed in the following order: half-anti-skyrmion (1/2, − 1/2, 0, 0) (t = 0 s), half-Néel-bimeron (1/2, 0, 0, π/2) (t = 205 s), half-Néel-skyrmion (1/2, 1/2, 0, π) (t = 355 s), half-Néel-bimeron (1/2, 0, 0, −π/2) (t = 450 s) and half-anti-skyrmion (1/2, − 1/2, 0, 0) (t = 638 s). The colored trajectories of colloids ①, ② and ③ are shown in the image at t = 638 s. b Image sequence of the rotations of colloids ①, ② and ③ (① in violet frame, ② in red frame and ③ in green frame from part (a)) as the string translates along the x-axis. c Free energy comparison of different half skyrmions. d Temporal dependence of φ for colloids ①, ② and ③. e Mapping of the interaction between colloids ② and ③ with half skyrmion at different time. This explains the colloidal orientations in the translational half skyrmion string. Red solid lines indicate the center of the skyrmion string (x = 0). f Image sequence of the colloidal chain response in the motion of a half-skyrmion string. The half skyrmion strings are transformed following the same order as in part(a). g Zoomed-in images of the collective dynamics of the colloidal chain from part (f). The white arrows indicate the translation direction. Black arrows point at the defects in (b) and (g). HAS (1/2, − 1/2, 0, 0) indicates half-anti-skyrmion, HNS (1/2, 1/2, 0, π) indicates half-Néel-skyrmion, HNB (1/2, 0, 0, − π/2) and HNB (1/2, 0, 0, π/2) indicate half-Néel-bimerons. (Scale bar, 50 μm).