Novel quantum spin liquid ground state in the trimer rhodate Ba₄NbRh₃O₁₂

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 Ba₄NbRh₃O₁₂ using a combination of dc and ac magnetization, electrical resistivity, specific heat, and muon spin rotation/relaxation (μSR) measurements. Despite the substantial antiferromagnetic exchange interactions, as evident from the Weiss temperature (θW~ -35 to -45 K), 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 ZF-μSR 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 μSR result evidences persistent spin fluctuations down to 0.26~K, thus stabilizing a dynamic QSL ground state in Ba₄NbRh₃O₁₂. Furthermore, the magnetic specific heat (Cₘ) data at low-T reveal a significant T-linear contribution plus a quadratic T-dependence. A T-linear behavior is evocative of gapless spin excitations, while the T²-term of Cₘ may indicate the Dirac QSL phenomenology of the spinon excitations with a linear dispersion.