Quantum critical nature of the short-range magnetic order in Sr2-xLaxIrO4

We have investigated the nature of the short-range magnetic phase region of Sr2-xLaxIrO4 (0 <= x <= 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 MT alpha-1 with alpha = 0.4-0.5, as well as in the time-field scaling (t/H-gamma) of the mu SR asymmetry function. Our combined study of ac susceptibility and mu 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.