Muon spin rotation and relaxation in Pr$_{1-x}$Nd$_x$Os$_4$Sb$_{12}$: Paramagnetic states

Positive-muon ($\mu^+$) Knight shifts have been measured in the paramagnetic states of Pr$_{1-x}$Nd$_x$Os$_4$Sb$_{12}$ alloys, where $x =$ 0, 0.25, 0.45, 0.50, 0.55, 0.75, and 1.00. In Pr-substituted NdOs$_4$Sb$_{12}$ ($x \le$ 0.75), but not in NdOs$_4$Sb$_{12}$, Clogston-Jaccarino plots of $\mu^+$ Knight shift~$K$ versus magnetic susceptibility~$\chi$ exhibit an anomalous saturation of $K(\chi)$ at $\sim-$0.5% for large susceptibilities (low temperatures), indicating a reduction of the coupling strength between $\mu^+$ spins and $4f$ paramagnetism for temperatures $\lesssim$ 15~K. We speculate that itinerant Pr$^{3+}$ quadrupolar excitations, invoked to mediate the superconducting Cooper-pair interaction, might modify the $\mu^+$-$4f$ ion indirect spin-spin interaction.