Quantum spin liquid ground state in the trimer rhodate ${\mathrm{Ba}}_4{\mathrm{NbRh}}_3{O}_{12}$

Frustrated magnets offer a plethora of exotic magnetic ground states, including quantum spin liquids (QSLs), in which enhanced quantum fluctuations prevent a long-range magnetic ordering of the strongly correlated spins down to lowest temperature. Here we have investigated the trimer based mixed valence hexagonal rhodate ${\mathrm{Ba}}_4{\mathrm{NbRh}}_3{O}_{12}$ using a combination of dc and ac magnetization, electrical resistivity, specific heat, and muon spin rotation/relaxation ($\mu \mathrm{SR}$) measurements. Despite the substantial antiferromagnetic exchange interactions, as evident from the Weiss temperature (${\theta }_W\sim -35$ to $-45K$), among the Rh-local moments, neither long-range magnetic ordering nor spin freezing is observed down to at least 50 mK, in ac-susceptibility, specific heat, and zero-field $\mu \mathrm{SR}$ measurements (down to 0.26 K). We ascribe the absence of any magnetic transition to enhanced quantum fluctuations as a result of geometrical frustration arising out of the edge-sharing equilateral Rh-triangular network in the structure. Our longitudinal-field $\mu \mathrm{SR}$ result evidences persistent spin fluctuations down to 0.26 K, thus stabilizing a dynamic QSL ground state in ${\mathrm{Ba}}_4{\mathrm{NbRh}}_3{O}_{12}$. Furthermore, the magnetic specific heat data at low $T$ reveal a significant $T$-linear contribution plus a quadratic $T$ dependence, which may indicate the gapless Dirac QSL phenomenology of the spinon excitations with a linear dispersion.