Spin fluctuation is presumed to be one of the key properties in understanding the microscopic origin of heavyfermion-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 ≡ 1/T 1 ) in these compounds exhibits a common trend of leveling off to a constant value (λ ∼ const.) below a characteristic temperature, T * . This is in marked contrast to the behavior predicted for normal metals from the Korringa relation, λ ∝ T/ν, where the spin fluctuation rate (ν) in the Pauli paramagnetic state is given as a constant, ν ≃ 1/[hD(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 ∝ T , suggesting that heavy quasiparticles develop in a manner satisfying D(E F ) ∝ (m * ) σ ∝ 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 ∝ 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.