We present a microscopic study of a doped quantum spin liquid candidate, the hyperkagome ${\mathrm{Na}}_3{\mathrm{Ir}}_3{\mathrm{O}}_8$ compound, by using ${}^{23}\mathrm{Na}$ NMR. We determine the intrinsic behavior of the uniform q = 0 susceptibility via shift measurements and the dynamical response by probing the spin-lattice relaxation rate. Throughout the studied temperature range, the susceptibility is consistent with a semimetal behavior, though with electronic bands substantially modified by correlations. Remarkably, the antiferromagnetic fluctuations present in the insulating parent compound ${\mathrm{Na}}_4{\mathrm{Ir}}_3{\mathrm{O}}_8$ survive in the studied compound. The spin dynamics are consistent with ${120}^{\circ }$ excitation modes displaying short-range correlations.

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• Frustrated magnetism
• Quantum spin liquid
• Spin-orbit coupling
• Kagome lattice
• Nuclear magnetic resonance