Origin of the fast magnetization tunneling in [Ni(hmp)(tBuEtOH)Cl]4

High-frequency (40-360~GHz), angle-dependent EPR data have been collected for single-crystals of [Ni(hmp)(dmb)Cl]$_{4}$, and [Ni$_{0.02}$Zn$_{0.98}$(hmp)(dmb)Cl]$_{4}$. The all-nickel complex behaves as a single-molecule magnet (SMM) at low temperatures, displaying hysteresis and magnetic quantum tunneling. However, in spite of its high symmetry (S$_{4})$, the relaxation is found to be very fast. We show that the origin of this behavior is related to a 4$^{th}$-order transverse crystal-field interaction, $B_{4}^{4}(S_{+}^{4}$~+~$S_{-}^{4})$, which produces a significant tunnel-splitting ($\sim $10~MHz) of the $m_{s}$~=~$\pm $4 ground state of this $S$~=~4 SMM. The fourth-order ($B_{4}^{4})$ and uniaxial ($D)$ crystal-field strengths can be related to the directionality and magnitude of the single-ion interactions ($D_{i}$ and $E_{i})$ at the individual Ni$^{II}$ sites, as determined for the doped crystals. Variable-temperature EPR measurements also reveal the locations of excited spin states ($S$~=~3, 2, etc..), enabling estimates of intra-molecular exchange coupling strengths.