Fig. 3: Skyrmion ordering.

a The MFM image of a Fe3GaTe2 with 8.5% Feint nanoflake at room temperature and zero field exhibits two distinct skyrmion lattices. b Zoom in on the dark red box in Fig. 3a. The orange dotted line denotes the skyrmionic phase boundary. The contrast frequency shift of the disordered skyrmion lattice (Ferro-phase) is typically higher than that of the ordered skyrmions (Ferri-phase). Also, the disordered skyrmion size is non-uniform compared to the relatively uniform size of the ordered skyrmions. c Statistical histogram of skyrmion counts as a function of the contrast frequency shift in Fig. 3a. The dark yellow curve is the overall fit of the Gaussian function in Fig. 3c. The high-frequency contrast range (blue curve) refers to the Ferro-phase, while the low-frequency contrast range (dark green curve) corresponds to the Ferri-phase. d, e Nearest neighbor (Nnn) and bond orientational (\(\left|{\psi }_{6}\right|\)) maps of the zoom in Fig. 3a. Statistical analysis was conducted following the same methodology as in the previous reference40. f The MFM image of a Fe3GaTe2 with 65.3% Feint nanoflake at room temperature and zero field shows a disordered skyrmion lattice. g Statistical histogram of skyrmion counts as a function of the contrast frequency shift in Fig. 3f. Only one peak fits the curve well, indicating single-phase skyrmions. h The induction field mapping of a typical ordered Néel-type skyrmion, observed in Fe2.5Co2.5GeTe2 (190 nm) with a global breaking inversion symmetry at room temperature, is composed of clockwise and counterclockwise spin curl. i The induction field mapping of a disordered skyrmion in a 200-nm-thick Fe3GaTe2 with 8.5% Feint nanoflake at room temperature displays a more complex feature, likely reflecting a 3D spin texture.