We systematically measure and analyze the spin diffusion length and the spin Hall effect in Pt with a wide range of conductivities using the spin absorption method in lateral spin valve devices. We observe a linear relation between the spin diffusion length and the conductivity, evidencing that the spin relaxation in Pt is governed by the Elliott-Yafet mechanism. We find a single intrinsic spin Hall conductivity $({\sigma }_{\mathrm{SH}}^{\mathrm{int}}=1600\pm 150{\mathrm{\Omega }}^{-1}\mathrm{c}{\mathrm{m}}^{-1})$ for Pt in the full range studied which is in good agreement with theory. We have obtained the crossover between the moderately dirty and the superclean scaling regimes of the spin Hall effect by tuning the conductivity. This is equivalent to that obtained for the anomalous Hall effect. Our results explain the spread of the spin Hall angle values in the literature and find a route to maximize this important parameter.

We have studied the spin transport and the spin Hall effect as a function of temperature for platinum (Pt) and gold (Au) in lateral spin valve structures. First, by using the spin absorption technique, we extract the spin diffusion length of Pt and Au. Secondly, using the same devices, we have measured the spin Hall conductivity and analyzed its evolution with temperature to identify the dominant scattering mechanisms behind the spin Hall effect. This analysis confirms that the intrinsic mechanism dominates in Pt whereas extrinsic effects are more relevant in Au. Moreover, we identify and quantify the phonon-induced skew scattering. We show that this contribution to skew scattering becomes relevant in metals such as Au, with a low residual resistivity.

Recent progress in wave packet dynamics based on the insight of Berry pertaining to adiabatic evolution of quantum systems has led to the need for a new property of a Bloch state, the Berry curvature, to be calculated from first principles. We report here on the response to this challenge by the ab initio community during the past decade. First we give a tutorial introduction of the conceptual developments we mentioned above. Then we describe four methodologies which have been developed for first-principle calculations of the Berry curvature. Finally, to illustrate the significance of the new developments, we report some results of calculations of interesting physical properties such as the anomalous and spin Hall conductivity as well as the anomalous Nernst conductivity and discuss the influence of the Berry curvature on the de Haas-van Alphen oscillation.

We present an ab~initio description of the spin Hall effect in metals. Our approach is based on density functional theory in the framework of a fully relativistic Korringa-Kohn-Rostoker method and the solution of a linearized Boltzmann equation including the scattering-in term (vertex corrections). The skew scattering mechanism at substitutional impurities is considered. Spin-orbit coupling in the host as well as at the impurity atom and the influence of spin-flip processes are fully taken into account. A sign change of the spin Hall effect in Cu and Au hosts is obtained as a function of the impurity atom, and even light elements like Li can cause a strong effect. It is shown that the gigantic spin Hall effect in Au can be caused by skew scattering at C and N impurities which are typical contaminations in a vacuum chamber.

A fully relativistic description of the spin-orbit induced spin Hall effect is presented that is based on Kubo's linear response formalism. Using an appropriate operator for the spin-current density a Kubo-St\ifmmode \check{r}\else \v{r}\fi{}eda-like equation for the spin Hall conductivity (SHC) is obtained. An implementation using the Korringa-Kohn-Rostoker band structure method in combination with the coherent potential approximation allow detailed investigations on various alloy systems. A decomposition of the SHC into intrinsic and extrinsic contributions is suggested. Accompanying calculations for the skew-scattering contribution of the SHC using the Boltzmann equation demonstrate the equivalence to the Kubo formalism in the dilute alloy regime and support the suggested decomposition scheme.

We performed ab initio studies to search for materials where a large spin Hall effect caused by skew scattering is accompanied by a long spin diffusion length. Samples with such properties are promising candidates for all-metallic spintronics devices. Here we consider Cu, Au, and Pt hosts which are typical materials used in experiments. In particular, we identified light impurities such as C and N in Au and heavy impurities such as Bi in Cu to meet this criterion. They exhibit a large spin Hall angle ($\alpha${}>0.06) and an appropriate spin diffusion length of about 100 nm. In addition, a pronounced dependence of the spin diffusion length on the scattering properties of the impurity is found for Cu and Au hosts, in contrast to Pt where much smaller variations are obtained.