Muon spin relaxation and hyperfine-enhanced $^{141}$Pr nuclear spin dynamics in (Pr,La)Os$\rm{_4}$Sb$\rm{_{12}}$ and Pr(Os,Ru)$\rm{_{4}}$Sb$\rm{_{12}}$*

The longitudinal-field muon relaxation experiments have been carried out in the Pr,La)Os$\rm{_4}$Sb$\rm{_{12}}$ and Pr(Os,Ru)$\rm{_{4}}$Sb$\rm{_{12}}$ alloy systems. At low temperatures, the dynamic fluctuations are involved in muon relaxation in addition to the contribution from a distributions of static muon local fields. The temperature and concentration dependencies of the muon damping rate $\Lambda$ indicate that this dynamic contribution is due to $^{141}$Pr nuclear magnetism, which is enhanced by hyperfine coupling to the Pr$^{3+}$ Van Vleck susceptibility. Further evidence comes from the field dependence of $\Lambda$, which is in reasonable agreement with the modified model for muon spin relaxation by dipole-coupled nuclear spins.