Fig. 1: Skyrmion, toron and polyskyrmionomer.
a Schematic of a 2D skyrmion with n(r) shown by arrows according to the coloured sphere (bottom inset) representing the order parameter space of vectorized n(r). b n(r) (left) and assembly of preimages (right) of a toron, shown by means of the same colouring scheme, where a preimage is the region in \({{\mathbb{R}}}^{3}\) (3D space) that maps to a certain single orientation on target order parameter space, and we marked the eight orientations on the top-right inset. The elementary toron comprises an internal skyrmion, capped by +1 (red sphere) and -1 (blue sphere) point defects33. c n(r) (left) and preimage assembly (right) of an \({{{{{{\rm{S}}}}}}}_{2}^{2}\), which comprises two skyrmion tubes at the top, two skyrmion tubes at the bottom, and six-point defects. d n(r) (left) and preimage (right) of an \({{{{{{\rm{S}}}}}}}_{1}^{2}\), with the defects positioned asymmetrically along the z direction. e The distribution of the skyrmion number along the x and z directions of an \({{{{{{\rm{S}}}}}}}_{1}^{3}\) mode, with its preimage. f Preimages of \({{{{{{\rm{S}}}}}}}_{6}^{6}\) (left) and \({{{{{{\rm{S}}}}}}}_{3}^{6}\,\)(right) modes. The colouring schemes in (c–f) for arrows and preimages are same to (b), and we select eight orientations as the top-right insets shown on the preimages. g, h, Polarizing optical micrographs (POMs) (left) and brightfield transmission-mode optical images (right) of \({{{{{{\rm{S}}}}}}}_{1}^{2}\) (g) and \({{{{{{\rm{S}}}}}}}_{1}^{3}\) (h) modes. Computer-simulated counterparts of the POMs are shown in the bottom insets. i POMs of curving hexamers, which represent word “CU” that can be robustly kept by the setting. j The POM and brightfield transmission-mode optical image of a polyskyrmionomer of order 21. Scale bars indicate 5 μm in (g–i), and 10 μm in (j). Crossed polarizers in POMs are shown by double arrows.
