(H,Li)\(_{6}\)Ru\(_{2}\)O\(_{6}\) : a zero-field Ru\(^{3+}\)-based Kitaev Quantum Spin Liquid

We report the synthesis and properties of (H,Li)\(_{6}\)Ru\(_{2}\)O\(_{6}\), which is shown to be a \(J_{\text{eff}}=\frac{1}{2}\) system made out of Ru\(^{3+}\) moments in a honeycomb geometry. Bulk magnetization, heat capacity, nuclear magnetic resonance (NMR), and muon spin relaxation (\(\mu\)SR) rule out the presence of static moments or any spin glass phase down to 500 mK. All techniques suggest a crossover to a liquid-like state below about 40 K. The \(^{7}\)Li nuclear magnetic resonance (NMR) shift data suggest a non-zero \(T\)-independent spin susceptibility at low \(T\). In zero field, \(C_m/T\) shows \(T^{-1}\) divergence which is consistent with vacancy-induced effects on low-energy excitations of the pristine Kitaev spin liquid. With field, power-law variations in the \(^{7}\)Li NMR spin-lattice relaxation rate 1/T\(_{1}\) and magnetic heat capacity \(C_{m}\) show quantitatively new scaling behaviors. A two-step entropy release in heat capacity is also observed putatively from \(Z_{2}\) flux (low-\(T\) step) and itinerant Majorana fermions (high-\(T\) step). Based on these findings, we propose that (H,Li)\(_{6}\)Ru\(_{2}\)O\(_{6}\) realizes a Kitaev spin liquid with no evidence of inherent magnetic ordering in zero field unlike \(\alpha\)-RuCl\(_{3}\) where approximately \(8\) Tesla field is required to suppress magnetic order.