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

Slow spin fluctuations ($\nu < 10^{12}$ s$^-1$) observed by the muon spin relaxation technique in Y$_{1-x}$Sc$_x$Mn$_2$ exhibits a power law dependence on temperature ($\nu \propto T^\alpha$), where the power converges asymptotically to unity ($\alpha\rightarrow 1$) as the system moves away from spin-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 with the prediction of the "intersecting Hubbard chains" model for a metallic pyrochlore lattice, suggesting that the geometrical constraints to t2g bands specific to the pyrochlore structure serve as a basis of the $d$-electron heavy-fermion state.