Local Probe Studies of the Quantum Honeycomb Antiferromagnet Ba$_3$CuSb$_2$O$_9$*

The 6H-perovskites, Ba$_3M$Sb$_2$O$_9$, have generated an enormous amount of interest in the last two years following the possible discovery of quantum spin liquid physics in two such materials. We present local probe studies (muon spin rotation and nuclear magnetic resonance) on the spin-1/2 honeycomb antiferromagnet Ba$_3$CuSb$_2$O$_9$. We show that the system presents no spin freezing down to temperatures as low as 20 mK. NMR measurements show evidence of a spin gap and suggest that the material has a random singlet ground state rather than the alternative spin-orbital liquid state.