Persistent spin dynamics and absence of spin freezing in the $H$-$T$ phase diagram of the 2D triangular antiferromagnet YbMgGaO$_4$

We report results of muon spin relaxation and rotation ($\mu$SR) experiments on the spin-liquid candidate~YbMgGaO$_{4}$. In zero field no static magnetism $\gtrsim 0.003\mu_B$ per Yb ion, ordered or disordered, was observed down to 22~mK\@. Dynamic muon spin relaxation rates are the same at 22~mK and 0.20~K for fields up to at least 0.8~kOe, indicating a temperature-independent state with no phase transition in this region. Frequency shift measurements in a 10-kOe transverse field reveal two lines with nearly equal amplitudes, and muon depolarization in zero and longitudinal field exhibits two-exponential dynamic relaxation, also with equal amplitudes. We infer that implanted muons stop at two interstitial sites associated with the two inequivalent oxygen locations in the unit cell. Further evidence for this is agreement between the ratio of the two measured relaxation rates and that of calculated mean-square local Yb$^{3+}$ dipolar fields at candidate muon sites. We conclude that two muon stopping sites in YbMgGaO$_{4}$ are the major source of spatial inhomogeneity observed in $\mu$SR experiments, rather than Mg$^{2+}$/Ga$^{3+}$ site mixing or other local disorder. These results extend considerably the region of persistent spin dynamics and no spin freezing in the $H$-$T$ phase diagram, and lower the upper bound on a magnetic transition temperature by a factor of two.