Mapping the fluctuating Ir$^{4+}$ dimers across the phase diagram of Cu(Ir$_{1-x}$Cr$_{x}$)$_{2}$S$_{4}$ (0$\leq$x$\leq$0.6)

Elucidating the role of fluctuations in systems with competing interactions, such as Cu(Ir$_{1-x}$Cr$_{x}$)$_{2}$S$_{4}$, enables comprehensive understanding of their physical properties. While CuIr$_{2}$S$_{4}$ exhibits complex behavior with metal-insulator transition accompanied by charge ordering and Ir$^{4+}$-spin-dimerization at 226~K, CuCr$_{2}$S$_{4}$ displays ferromagnetic metallic behavior (T$_{C}$$\sim$377~K) understood within the double exchange model. Intermediate composition range sees suppression of end-member properties, with broad features observed in susceptibility around 180~K attributed to Cr$^{3+}$ low spin to high-spin crossover [1]. Robust fluctuating Ir$^{4+}$ dimers are detected and their evolution examined across the phase diagram by the X-ray atomic pair distribution function method. Although their long range order is destroyed already by x$\approx$0.05, Ir$^{4+}$ dimers exist locally at low temperature at all compositions studied. We provide detailed account of the Cr-doping and temperature dependence of the local dimers, and estimate characteristic length-scale on which they are observable. Fluctuating dimers disappear on heating, for intermediate compositions at temperatures above 180~K. \\[4pt] [1] R. Endoh et al., Phys. Rev. B $\bf{68}$, 115106 (2003).