Fig. 3.

Manipulation of the ODL state. a Fit of the cubic model (red line) to the 300 K CuIr₂S₄ data (blue open circles). b Fit of the cubic model (red line) to the 300 K CuIr₂Se₄ data (blue open circles). c Compositional stack of 300 K data for Zn-substituted CuIr₂S₄ with Zn content ranging from 0% (blue line) to 70% (red line) in 10% increments (gray lines). The differences between the CuIr₂S₄ parent and all other datasets are stacked underneath, offset for clarity. The largest difference between the 0% Zn and 70% Zn datasets is shown in green, other differences in gray, evolving uniformly with Zn content. d Fit of the cubic model (red line) to the 300 K 70% Zn-substituted CuIr₂S₄ data (blue open circles). e, f Fit of the undistorted cubic model (red lines) to the 300 K 5% and 8% Cr-substituted CuIr₂S₄ data (blue open circles), respectively. g Molecular-orbital (MO) view, from left to right, of degenerate MO, degeneracy-lifted MO, dimerized, and non-dimerized Ir–Ir contacts. In the legend, DEG (Ir^3.5+), ODL (Ir^3.5+), DIMER (Ir⁴⁺), and NONDIMER (Ir³⁺). h Sketch of [1, 1, 0]-type Ir t_2g overlaps (bottom) and six choices for each Ir to form an ODL state (top). i Evolution of the ODL distortion, defined as the difference of the Ir–Ir nearest neighbor distance on a pyrochlore lattice extracted from local tetragonal model, with the average Ir–Ir separation in the cubic structure. These are extracted from fits to 300 K data of Cr-substituted (red circles, 0 < x < 0.6) and Zn-substituted (green circles, 0 < x < 0.7) samples, as well as pure CuIr₂S₄ (gray circle) and CuIr₂Se₄ (blue circle). Error bars represent estimated standard uncertainties on the refined parameters. Gray shaded region marks 2σ uncertainty for detecting small tetragonal distortions by the approach utilized here. In CuIr₂S₄ there are 0.5 t_2g holes per Ir (one hole per pair)³⁸. Vertical gray dashed lines in b, i refer to CuIr₂S₄