Tuning a spin-liquid into a correlated metal in Na$_{4-x}$Ir$_3$O$_{8-\delta}$

Na$_4$Ir$_3$O$_8$ is a candidate material for a 3D quantum spin-liquid. We present a comprehensive study of the structure, magnetic susceptibility, heat capacity, and electrical transport on polycrystalline samples with nominal composition Na$_{4-x}$Ir$_3$O$_8$ ($x \approx -.08~{\rm to}~1$). The structure refinement shows that even though Na vacancies are being introduced the lattice parameters do not change much with $x$. The $x \geq 0$ samples show insulating behavior with strong antiferromagnetic interactions between effective $S = 1/2$ Ir$^{4+}$ moments. For the Na$_{4.08}$Ir$_3$O$_8$ sample, magnetic susceptibility suggests a magnetic transition below $\approx 15 K$. The $x \approx 1$ sample is a paramagnetic (semi)metal with various physical properties suggesting strong electronic correlations. The materials mid-way between the insulating and metallic samples show indication of having both localized and itinerant electrons. The strong antiferromagnetic interactions present in the $x = 0$ material survive in these mixed materials making them candidate spin-liquids in the presence of itinerant electrons. The electrical transport of the doped materials are consistent with the behavior of a semi-metal/semi-conductor with low carrier concentrations.