Fig. 1: Enhanced topological Hall resistivity (ρ^THE) for isolated skyrmions compared with dense skyrmion arrays.

a–c ρ^THE(H) of isolated skyrmion configurations observed in [Fe2/Co8]₂₀, [Fe2/Co6]₂₀, and [Fe2/Co5]₂₀. d–f ρ^THE(H) of dense skyrmion arrays observed in [Fe5/Co5]₂₀, [Fe4/Co6]₂₀, and [Fe4/Co4]₂₀. g Δ_ρ/M ≡ n_sk(THE)/n_sk(MFM) estimated from transport and imaging experiments shown in (a–f) and in Section 1 of the Supplementary Information. n_sk(THE) is given by ρ^THE/(P ⋅ R₀ ⋅ Φ₀) with P = 0.56 and n_sk(MFM) is estimated from MFM images; details of our image analysis methods can be found in our earlier reports^{5, 9, 30}. The detailed evolution of magnetic textures with H can be found in Section 1 of the Supplementary Information. Scale bars in white (MFM images corresponding to (a–e)) are 1 μm and in black (MFM images corresponding to (f)) 0.5 μm. All the images are acquired at a scan height of 20 nm. The color scale represents the phase shift in the MFM signal due to the magnetic force acting on the tip. The ρ^THE(H) profiles show a small non-zero offset ≤2 nΩ cm above the saturation field of the magnetization (H > H_s): this is a systematic offset due to our fitting procedure (which is designed to avoid any “false positive” THE detection) and hence reflects the maximum error in the magnitude of ρ^THE(H) shown in Fig. 1g.