Magnetic ground state of distorted 6H perovskite Ba$_3$CdIr$_2$O$_9$

Perovskite iridates of 6H hexagonal structure present a plethora of possibilities in terms of the variety of ground states resulting from a competition between spin-orbit coupling (SOC), hopping, noncubic crystal field ($\Delta_{CFE}^{NC}$) and superexchange energy scales within the Ir$_2$O$_9$ dimers. Here we have investigated one such compound Ba$_3$CdIr$_2$O$_9$ by x-ray diffraction, dc magnetic susceptibility($\chi$), heat capacity($C_p$) and also ${}^{113}$Cd nuclear magnetic resonance (NMR) spectroscopy. We have established that the magnetic ground state has a small but finite magnetic moment on Ir$^{5+}$ in this system, which likely arises from intradimer Ir-Ir hopping and local crystal distortions. Our heat capacity, NMR, and dc magnetic susceptibility measurements further rule out any kind of magnetic long-/short-range ordering among the Ir moments down to at least 2K. In addition, the magnetic heat capacity data shows linear temperature dependence at low temperatures under applied high fields ($>$ 30 kOe), suggesting gapless spin-density of states in the compound.