Gapless quantum spin liquid in the triangular system Sr${}_3$CuSb${}_2$O${}_9$

We report gapless quantum spin liquid behavior in the layered triangular Sr${}_3$CuSb${}_2$O${}_9$ (SCSO) system. X-ray diffraction shows superlattice reflections associated with atomic site ordering into triangular Cu planes well-separated by Sb planes. Muon spin relaxation ($\mu$SR) measurements show that the $S=\frac{1}{2}$ moments at the magnetically active Cu sites remain dynamic down to 65 mK in spite of a large antiferromagnetic exchange scale evidenced by a large Curie-Weiss temperature ${\theta }_{\mathrm{c}\mathrm{w}}\simeq$ -143 K as extracted from the bulk susceptibility. Specific heat measurements also show no sign of long-range order down to 0.35 K. The magnetic specific heat ($C$${}_{\mathrm{m}}$) below 5 K reveals a $C$${}_{\mathrm{m}}$ $=$ $\gamma T$ + $\alpha T$${}^2$ behavior. The significant $T$${}^2$ contribution to the magnetic specific heat invites a phenomenology in terms of the so-called Dirac spinon excitations with a linear dispersion. From the low-$T$ specific heat data, we estimate the dominant exchange scale to be $\sim$ 36 K using a Dirac spin liquid ansatz which is not far from the values inferred from microscopic density functional theory calculations ($\sim$ 45 K) as well as high-temperature susceptibility analysis ($\sim$ 70 K). The linear specific heat coefficient is about 18 mJ/mol-K${}^2$ which is somewhat larger than for typical Fermi liquids.