In the presence of strong atomic spin-orbit coupling (SOC), tending to the $j\text{−}j$ coupling limit, $5d^4$ iridates are speculated to possess a nonmagnetic $J_{\mathrm{eff}}=0$ singlet ground state from atomic consideration, which invariably gets masked due to different solid-state effects (e.g., hopping). Here, we try to probe the trueness of the atomic SOC-based proposal in an apparently one-dimensional system, ${\mathrm{Sr}}_3{\mathrm{NaIrO}}_6$, with well-separated ${\mathrm{Ir}}^{5+}$ $\left(5d^4\right)$ ions. But all the detailed experimental as well as theoretical characterizations reveal that the ground state of ${\mathrm{Sr}}_3{\mathrm{NaIrO}}_6$ is not nonmagnetic. However, our combined dc susceptibility $\chi$, ${}^{23}\mathrm{Na}$ nuclear magnetic resonance (NMR), muon spin relaxation/rotation $\left(\mu \mathrm{SR}\right)$, and heat capacity $C_p$ measurements clearly refute any sign of spin freezing or ordered magnetism among the ${\mathrm{Ir}}^{5+}$ moments due to geometrical exchange frustration, while in-depth zero-field and longitudinal field $\mu \mathrm{SR}$ investigations strongly point towards an inhomogeneous quantum spin liquid (QSL)-like ground state. In addition, the linear temperature dependence of both the NMR spin-lattice relaxation rate and the magnetic heat capacity at low temperatures suggest low-lying gapless spin excitations in the QSL phase of this material. Finally, we conclude that the effective SOC realized in $d^4$ iridates is unlikely to offer a ground state which will be consistent with a purely atomic $j\text{−}j$ coupling description.

• Received 6 July 2021
• Revised 11 March 2022
• Accepted 11 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.104431