Fig. 5: Phase diagram, modelization and structure factors.

a Schematic phase diagram in Sr_14 − xCa_xCu₂₄O₄₁ (SCCO-x) showing the evolution of the loop current (LC) pattern as a function of the Ca content (x_Ca). At large doping, magnetic correlations develop between ladders at the onset temperature T_mag (red crosses). In heavily doped samples, a magnetic long-range order (LRO) further develops below a Néel temperature T_N of a few K³¹. Insets: a (top) CC-Θ_II^7,8 and (down) CC-Θ_III^10,11,12 models built on single ladder with two staggered Cu–O orbital currents per Cu site flowing clockwise (red triangles) and anticlockwise (blue triangles). Both models describe nicely the experimental results shown in panel b. b CC-Θ_II and (down) CC-Θ_III models with additional interladders correlations within the ladder unit cell. Both models describe nicely the experimental results shown in panel c. b, c H-scan of the (H,0,1) rod, the inter-ladders direction (rungs) showing the modulation of the out-of-plane magnetic intensity, I_b extracted from XYZ polarization analysis (PA) (squares) compared with magnetic structure factors deduced from 2 loop currents models, labeled CC-Θ_II (solid line)^7,8 and CC-Θ_III (dashed line)^10,11,12 in b SCCO-5 and c SCCO-8. Error bars represent one standard deviation.