Spin Fluctuations from Hertz to Terahertz on a Triangular Lattice

The temporal magnetic correlations of the triangular lattice antiferromagnet NiGa${}_2$S${}_4$ are examined through thirteen decades (${10}^{-13}-1$~sec) using ultra-high-resolution inelastic neutron scattering, muon spin relaxation, AC and nonlinear susceptibility measurements. Unlike the short-ranged {\it spatial} correlations, the temperature dependence of the {\it temporal} correlations show distinct anomalies. The spin fluctuation rate decreases precipitously upon cooling towards $T^{\ast }=8.5$~K, but fluctuations on the microsecond time scale then persist in an anomalous dynamical regime for 4 K $<T\le T^{\ast }$. As this time scale exceeds that of single site dynamics by six orders of magnitude, these fluctuations bear evidence of emergent degrees of freedom within the short-range correlated incommensurate state of NiGa${}_2$S${}_4$.