An ab initio relativistic band structure calculation of spin Hall conductivity (SHC) (σ z xy ) in Pd and Au metals has been performed. It is found that at low temperatures, intrinsic SHCs for Pd and Au are, respectively, ∼ 1400( /e)(Ωcm) −1 and ∼ 400( /e)(Ωcm) −1 . The large SHC in Pd comes from the resonant contribution from the spin-orbit splitting of the doubly degenerated 4d bands near the Fermi level at symmetry Γ and X points, and the smaller SHC in Au is due to the broad free electron like 6s6p-bands. However, as the temperature increases, the SHC in Pd decreases monotonically and reduces to ∼ 330( /e)(Ωcm) −1 at 300 K, while the SHC in Au increases steadily and reaches ∼ 750( /e)(Ωcm) Spin transport electronics (spintronics) has recently become a very active research field in condensed matter and materials physics because of its potential applications in information storage and processing and other electronic technologies [1] and also because of many fundamental questions on the physics of electron spin [2]. Spin current generation is an important issue in the emerging spintronics. Recent proposals of the intrinsic spin Hall effect (SHE) are therefore remarkable [3,4]. In the SHE, a transverse spin current is generated in response to an electric field in a metal with relativistic electron interaction (spin-orbit coupling). This effect was first considered to arise extrinsically, i.e., by impurity scattering [5,6]. The scattering becomes spin-dependent in the presence of spin-orbit coupling (SOC), and this gives rise to the SHE. In the recent proposals, in contrast, the spin Hall effect can arise intrinsically in hole-doped (p-type) bulk semiconductors [3] and also in electrondoped (n-type) semiconductor heterostructures [4] due to intrinsic SOC in the band structure. The intrinsic SHE can be calculated and controlled, whereas the extrinsic SHE depends sensitively on details of the impurity scattering. Therefore, the intrinsic SHE is more important for applicational purposes, in comparison with the extrinsic SHE.In semiconductors, there have been experimental reports on the SHE in n-type GaAs [7], p-type GaAs [8] and n-type InGaN/GaN superlattices [9] in recent years. These experimental results have been discussed theoretically, and it is now recognized that the SHE in n-type GaAs is due to the extrinsic mechanisms, i.e., skew scattering and side-jump contributions [10,11], while that in p-type GaAs is mainly caused by the intrinsic mechanism [12,13]. This conclusion is supported by theoretical analysis of the impurity effect and vertex correction to SHE in the Rashba and Luttinger models [10,12]. In p-GaAs the fourfold degeneracy at the Γ-point of the valence bands acts as the Yang-monopole, which enhances the SU(2) non-Abelian Berry curvature [14].On the other hand, the SHE in metallic systems is currently attracting interest, stimulated by latest experimental reports on the SHE or inverse spin Hall effect (ISHE), i.e., the transverse voltage drop due to the spin current [15,16,17]. The spin Hall conduc...