Abstract
Na${}_{4}$Ir${}_{3}$O${}_{8}$ is a candidate material for a three-dimensional quantum spin liquid on the hyperkagome lattice. We present thermodynamic measurements of heat capacity $C$ and thermal conductivity $\ensuremath{\kappa}$ on high-quality polycrystalline samples of Na${}_{4}$Ir${}_{3}$O${}_{8}$ down to $T=500$ and 75 mK, respectively. Absence of long-range magnetic order down to $T=75$ mK strongly supports claims of a spin-liquid ground state. The constant magnetic susceptibility $\ensuremath{\chi}$ below $T\ensuremath{\approx}25$ K and the presence of a small but finite linear-$T$ term in $C(T)$ suggest the presence of gapless spin excitations. Additionally, the magnetic Gr$\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\mathrm{u}}$neisen ratio shows a divergence as $T\ensuremath{\rightarrow}0$ K and a scaling behavior, which clearly demonstrates that Na${}_{4}$Ir${}_{3}$O${}_{8}$ is situated close to a zero-field QCP.
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