Description of the intrinsic spin Hall effect via Korringa-Kohn-Rostoker density functional theory

Abstract

The first part of this thesis deals with the ab initio description of the spin Hall effect in the full-relativistic Korringa-Kohn-Rostoker (FR-KKR) density functional theory (DFT). A new approach to calculate the magnetization accumulation within the full quantum mechanical Keldysh formalism is compared to a semiclassical Boltzmann approach. Both methods rely on the same underlying FR-KKR framework. The comparison focuses on the odd-under-spatial-magnetization-reversal part of the surface magnetization accumulation that solely stems from the band structure properties at the Fermi surface. The comparison shows that both methods yield the same trend for a series of metals with a significant influence of spin-orbit coupling rendering the new Keldysh method a valid and credible candidate for the description of the surface accumulation driven by the spin Hall effect. Contrary to most theoretical approaches, which calculate the bulk property of spin conductivity, the thin-film nature and surface influences are considered here, making direct contact with experiments. When compared to a series of values obtained experimentally, both methods reproduce the trend for the spin Hall angle. The second part of this thesis deals with interpreting the self-energy in the Büttiker scattering formalism (virtual terminal approach) established in the KKR. The relation between the self-energy Σ and the relaxation time τ used in semiclassical approaches is studied. Understanding this relation plays an important role when comparing the results of the Keldysh formalism with virtual terminal scattering to the Boltzmann scattering description. In the constant relaxation time approximation (CRTA), the thermopower is independent of the relaxation time in the Boltzmann approach. This independence is valid for free electrons and Cu in the low scattering regime but fails for Pd completely. This failure is attributed to the complexity of the Fermi surface of Pd. Further, a sufficient resolution for the occurring scattering events is necessary for the virtual terminal approach to work. Based on these findings, the scalability of the approach is discussed as the introduction of scattering could make it possible to consider spin relaxation effects for the spin Hall effect.