Spin dynamics in LiY$_{0.998}$Ho$_{0.002}$F$_4$ via $^{19}$F NMR and $\mu$SR*

The $^{3+}$Ho ion doped into the host LiYF$_4$ is a single-ion magnet demonstrating slow dynamics at the avoided level crossings (ALCs) in the hyperfine-coupled electronuclear Zeeman diagram. We have studied $^{19}$F NMR and $\mu$SR in dilute LiY$_{0.998}$Ho$_{0.002}$F$_4$ to probe these dynamics and find clear evidence for an increase in the spin-lattice relaxation rate {\it{1/T$_1$}} at field values corresponding to ALCs using both techniques. We will discuss using these signatures as probes to measure the tunnel splitting $\Delta$ and the level broadening, as well as the onset of magnet correlations for increasing Ho concentration.