Gapless dynamic magnetic ground state in the charge-gapped trimer iridate Ba$_4$NbIr$_3$O$_{12}$

We present an experimental investigation of the magnetic ground state in Ba$_4$NbIr$_3$O$_{12}$, a fractional valent trimer iridate. X-ray absorption and photoemission spectroscopy show that the Ir valence lies between 3+ and 4+ while Nb is pentavalent. Combined dc/ac magnetization, specific heat, and muon spin rotation/relaxation ($\mu$SR) measurements reveal no magnetic phase transition down to 0.05~K. Despite a significant Weiss temperature ($\Theta_{\mathrm{W}} \sim -15$ to $-25$~K) indicating antiferromagnetic correlations, a quantum spin-liquid (QSL) phase emerges and persists down to 0.1~K. This state likely arises from geometric frustration in the edge-sharing equilateral triangle Ir network. Our $\mu$SR analysis reveals a two-component depolarization, arising from the coexistence of rapidly (90\%) and slowly (10\%) fluctuating Ir moments. Powder x-ray diffraction and Ir-L$_3$edge x-ray absorption fine structure spectroscopy identify ~8-10\% Nb/Ir site-exchange, reducing frustration within part of the Ir network, and likely leading to the faster muon spin relaxation, while the structurally ordered Ir ions remain highly geometrically frustrated, giving rise to the rapidly spin-fluctuating QSL ground state. At low temperatures, the magnetic specific heat varies as $\gamma T + \alpha T^2$, indicating gapless spinon excitations, and possible Dirac QSL features with linear spinon dispersion, respectively.