We have investigated the nature of the short-range magnetic phase region of ${\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{IrO}}_4$ ($0\le x\le 0.14$). This so-called spin-orbit Mott insulator's predicted transition to superconductivity with electron doping has remained elusive. Instead, short-range magnetism prevails over an extensive doping range up to the La solubility limit. We find evidence for quantum critical-like fluctuations of the short-range magnetic phase, in both a scaling relation of the ac susceptibility $\chi T^{\alpha }$ and the magnetization $M{T}^{\alpha -1}$ with $\alpha =0.4–0.5$, as well as in the time-field scaling ($t/H^{\gamma }$) of the $\mu \mathrm{SR}$ asymmetry function. Our combined study of ac susceptibility and $\mu \mathrm{SR}$, on the one hand, uncovers a two-stage weak symmetry breaking to spin freezing or proximate spin glass and to a subsequent spin glass within the short-range magnetic phase. On the other hand, we demonstrate that magnetic correlations become more static above $x=0.06$ in spite of an apparent dilution of magnetic moments, indicative of enhanced inhomogeneities in a higher La-doping regime.

• Received 19 July 2018
• Revised 19 November 2018

DOI:https://doi.org/10.1103/PhysRevB.98.214412