The magnetic properties of a Terbium single ion magnetic system will be studied using implanted muons. The system is based on a polyoxometallate ion that provides good isolation between magnetic sites and thus extremely long spin coherence times, as demonstrated in previous epr studies of similar systems. The present system has an unusual five-fold crystal field symmetry that induces a strong mixing between opposite spin states in the lowest two electronic levels. This contrasts with the previously studied Ho system that only achieves mixing of different electronic states under avoided level crossing conditions at finite magnetic fields via tuning of Zeeman splitting to nuclear hyperfine splittings. Temperature and field dependence of the muon spin relaxation will be studied for the Tb system to extract characteristic spin fluctuation and coherence times and compare with the Ho system.