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Spin-orbit coupling (SOC) often gives rise to interesting electronic andmagnetic phases in an otherwise ordinary pool of paramagnetic heavy metaloxides. In presence of strong SOC, assumed to be working in $j$-$j$ couplingregime, 5$d^4$ iridates are generally speculated to possess a nonmagnetic$J_{eff}$~=~0 singlet ground state, which invariably gets masked due todifferent solid-state effects (e.g. hopping). Here, we try to probe thetrueness of the atomic SOC-based proposal in an apparently 1-dimensionalsystem, Sr$_3$NaIrO$_6$, possessing a 2$H$ hexagonal structure with wellseparated Ir$^{5+}$ (5$d^4$) ions. But all the detailed experimental as well astheoretical characterizations reveal that the ground state of Sr$_3$NaIrO$_6$is not nonmagnetic, rather accommodating a significantly high effectivemagnetic moment on Ir$^{5+}$ ion. However our combined dc susceptibility($\chi$), ${}^{23}$Na nuclear magnetic resonance (NMR),muon-spin-relaxation/rotation ($\mu$SR) and heat capacity ($C_p$) measurementsclearly refute any sign of spin-freezing or ordered magnetism among theIr$^{5+}$ moments due to geometrical exchange frustration, while in-depthzero-field (ZF) and longitudinal field (LF) $\mu$SR investigations stronglypoint towards inhomogeneous quantum spin-orbital liquid (QSOL)-like groundstate. In addition, the linear temperature dependence of both the NMRspin-lattice relaxation rate and the magnetic heat capacity at low temperaturessuggest low-lying gapless spin excitations in the QSOL phase of this material.Finally, we conclude that the effective SOC realised in $d^4$ iridates areunlikely to offer a ground state which will be consistent with a purely atomic$j$-$j$ coupling description.

Failure to achieve the $J_{eff}$~=~0 state even in nearly isolated  Ir$^{5+}$ in Sr$_3$NaIrO$_6$: are iridates enough for realizing true $j$-$j$  coupling?