Zero- and longitudinal-field muon spin relaxation (MuSR) experiments have been carried out in the alloy series Pr(Os1-xRux)4Sb12 and Pr1-yLayOs4Sb12 to elucidate the anomalous dynamic muon spin relaxation observed in these materials. The damping rate associated with this relaxation varies with temperature, applied magnetic field, and dopant concentrations x and y in a manner consistent with the ``hyperfine enhancement of 141Pr nuclear spins first discussed by Bleaney in 1973. This mechanism arises from Van Vleck-like admixture of magnetic Pr3+ crystalline-electric-field-split excited states into the nonmagnetic singlet ground state by the nuclear hyperfine coupling, thereby increasing the strengths of spin-spin interactions between 141Pr and muon spins and within the 141Pr spin system. We find qualitative agreement with this scenario, and conclude that electronic spin fluctuations are not directly involved in the dynamic muon spin relaxation.
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