Decoupling of the antiferromagnetic and insulating states in Tb-doped Sr2IrO4

$\mathrm{S}{\mathrm{r}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$ is a spin-orbit-coupled insulator with an antiferromagnetic (AFM) transition at ${T}_{N}=240\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. We report results of a comprehensive study of single-crystal $\mathrm{S}{\mathrm{r}}_{2}\mathrm{I}{\mathrm{r}}_{1\ensuremath{-}x}\mathrm{T}{\mathrm{b}}_{x}{\mathrm{O}}_{4}\phantom{\rule{0.16em}{0ex}}(0\ensuremath{\le}x\ensuremath{\le}0.03)$. This study found that a mere 3% $(x=0.03)$ of tetravalent $\mathrm{T}{\mathrm{b}}^{4+}(4{\mathrm{f}}^{7})$ substituting for $\mathrm{I}{\mathrm{r}}^{4+}$ (rather than $\mathrm{S}{\mathrm{r}}^{2+}$) completely suppresses the long-range collinear AFM transition but retains the insulating state, leading to a phase diagram featuring a decoupling of the magnetic interactions and charge gap. The insulating state at $x=0.03$ is characterized by an unusually large specific heat at low temperatures and an incommensurate magnetic state having magnetic peaks at (0.95,0,0) and (0,0.95,0) in the neutron diffraction, suggesting a spiral or spin-density-wave order. It is apparent that Tb doping effectively changes the relative strength of the spin-orbit interaction (SOI) and the tetragonal crystal electric field and enhances the Hund's rule coupling that competes with the SOI, and destabilizes the AFM state. However, the disappearance of the AFM is accompanied by no metallic state chiefly because an energy level mismatch for the Ir and Tb sites weakens charge carrier hopping and causes a persistent insulating state. This work highlights an unconventional correlation between the AFM and insulating states in which the magnetic transition plays no critical role in the formation of the charge gap in the iridate.