Theoretical $T_1$ Calculation for Isotropic High Spin Molecules

We calculate the molecular-spin ($S$), temperature ($T$), and field ($H$) dependence of $1/T_1$ for a local magnetic probe coupled to an isotropic high spin molecule, based on spin-phonon interaction. We compare the calculation to recent NMR and $\mu$SR experiments in CrCu$_6$ ($S = 9/2$), CrNi$_6$ ($S = 15/2$) and CrMn$_6$ ($S = 27/2$). Although we can account for the high and intermediate temperature regimes, the calculation is fundamentally different from the data at $T \longrightarrow 0$. Since $1/T_1$ must be due to coupling of the molecular spin to an external heat bath, and since phonon contribution is ruled out at low $T$, we conclude that at these temperatures hyperfine interactions must play an important role in the molecular spin dynamic.