Correlation between antiferromagnetic and Mott states in spin orbit coupled Sr 2 Ir O 4 : A study of Sr 2 Ir 1 − x M x O 4 ( M = Fe or Co)

${\mathrm{Sr}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$ is an archetypal spin-orbit-coupled Mott insulator with an antiferromagnetic state below 240 K. Here we report results of our study on single crystals of ${\mathrm{Sr}}_{2}{\mathrm{Ir}}_{1\ensuremath{-}x}\mathbf{F}{\mathbf{e}}_{x}{\mathrm{O}}_{4}$ ($0\ensuremath{\le}xl0.32$) and ${\mathrm{Sr}}_{2}{\mathrm{Ir}}_{1\ensuremath{-}x}\mathbf{C}{\mathbf{o}}_{x}{\mathrm{O}}_{4}$ ($0\ensuremath{\le}xl0.22$). Fe doping retains the antiferromagnetic state but simultaneously precipitates an emergent metallic state whereas Co doping causes a rapid collapse of both the antiferromagnetic and Mott states, giving rise to a confined metallic state featuring a pronounced linearity of the basal-plane resistivity up to 700 K. The results indicate tetravalent ${\mathrm{Fe}}^{4+}(3{d}^{4})$ ions in the intermediate spin state with $S=1$ and ${\mathrm{Co}}^{4+}(3{d}^{5})$ ions in the high spin state with $S=5/2$ substituting for ${\mathrm{Ir}}^{4+}(5{d}^{5})$ ions in ${\mathrm{Sr}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$, respectively. The effective magnetic moment closely tracks the N\'eel temperature as doping increases, suggesting that the spin state of the dopant predominately determines the magnetic properties in doped ${\mathrm{Sr}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$. Furthermore, all relevant properties including charge-carrier density (e.g., ${10}^{28}/{\mathrm{m}}^{3}$), Sommerfeld coefficient (e.g., $19\phantom{\rule{0.16em}{0ex}}\mathrm{mJ}/\mathrm{mole}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{2}$), and Wilson ratio (e.g., 2.6) consistently demonstrate an emergent metallic state that is both robust and highly correlated in the two systems, arising from the percolation of bound states and the weakening of structural distortions. This study strongly indicates that the antiferromagnetic and Mott states are correlated in an unconventional manner in ${\mathrm{Sr}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$.