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Quest for the Origin of Heavy Fermion Behavior in $d$-Electron Systems

Spin fluctuation is presumed to be one of the key properties in understanding the microscopic origin of heavy-fermion-like behavior in the class of transition-metal compounds, including LiV$_2$O$_4$, Y(Sc)Mn$_2$, and YMn$_2$Zn$_{20}$. In this review, we demonstrate by our recent study of muon spin rotation/relaxation that the temperature ($T$) dependence of the longitudinal spin relaxation rate ($λ\equiv 1/T_1$) in these compounds exhibits a common trend of leveling off to a constant value ($λ\sim const$.) below a characteristic temperature, $T^*$. This is in marked contrast to the behavior predicted for normal metals from the Korringa relation, $λ\propto T/ν$, where the spin fluctuation rate ($ν$) in the Pauli paramagnetic state is given as a constant, $ν\simeq 1/[h D(E_F)]$ [with $D(E_F)$ being the density of states at the Fermi energy]. Thus, the observed behavior of $λ$ implies that the spin fluctuation rate becomes linearly dependent on temperature, $ν\propto T$, suggesting that heavy quasiparticles develop in a manner satisfying $D(E_F)\propto (m^*)^σ\propto 1/T$ at lower temperatures ($σ$ determined by the electronic dispersion). Considering that the theory of spin correlation for intersecting Hubbard chains as a model of pyrochlore lattice predicts $ν\propto T$, our finding strongly indicates the crucial role of $t_{2g}$ bands which preserve the one-dimensional character at low energies due to the geometrical frustration specific to the undistorted pyrochlore lattice.