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Slow spin fluctuations ($\nu < 10^{12}$ s$^-1$) observed by the muon spinrelaxation technique in Y$_{1-x}$Sc$_x$Mn$_2$ exhibits a power law dependenceon temperature ($\nu \propto T^\alpha$), where the power convergesasymptotically to unity ($\alpha\rightarrow 1$) as the system moves away fromspin-glass instability with increasing Sc content $x$. This linear $T$dependence, which is common to that observed in LiV$_2$O$_4$, is in line withthe prediction of the "intersecting Hubbard chains" model for a metallicpyrochlore lattice, suggesting that the geometrical constraints to t2g bandsspecific to the pyrochlore structure serve as a basis of the $d$-electronheavy-fermion state.

Quasi-One-Dimensional Spin Dynamics in $d$-Electron Heavy-Fermion Metal Y$_{1-x}$Sc$_x$Mn$_2$