Fig. 3

Fractal magnetic patterns. a The AFM domain map at 130 K (warming cycle) is binarized to highlight the AFM domains at the ordering vector probed here (yellow), vs. other, symmetry-equivalent ones to which we are not sensitive in the present geometry (blue). b The logarithmically binned AFM domain area distributions follow a scale-free power-law distribution (D~A^−τ) with the critical exponent τ = 1.25 ± 0.04. Dashed lines are power-law fits to the experimental data points. Hollow markers represent points excluded from the fit. c, d Domain perimeter (P) and area (A) vs. gyration radius (R_g) with logarithmic binning. Dashed lines are power-law fits of \(P\sim R_{\mathrm{g}}^{d_h}\) and \(A\sim R_{\mathrm{g}}^{d_v}\)with the critical exponents d_h = 1.23 ± 0.03 and d_h = 1.78 ± 0.07. The power-law scaling and corresponding critical exponents (d_h, d_v) reveal a robust scale-invariant texture at all temperatures. e Pair connectivity function vs. distance (r) with logarithmic binning. The dash lines are fits to a power-law function with an exponential cutoff\(g_{{\mathrm{conn}}}\sim r^{ - \eta }e^{ - x/\xi }\) where ξ is the correlation length and η = 0.32 ± 0.13 is the exponent for the connectivity function. f Overlay of the temperature dependence of the [¼, ¼, ¼]_pc AFM Bragg peak intensity with the correlation lengths extracted from the pair connectivity function. The error bars for correlation lengths at 130 K are smaller than marker size