Fully-Relativistic Full-Potential Multiple Scattering Theory: Method and Applications

Relativistic effects (spin-orbit coupling in particular), are the origin of a rich diversity of phenomena of great interest to technological applications, such as spin-Hall effect, chiral spin texture, Rashba effect, and magnetocrystalline anisotropy. Multiple scattering theory (MST), on the other hand, is a powerful first principles method that is particularly useful for the investigation of complex condensed matter systems, such as impurities, alloys, and nanostructures. In this thesis, combination of the two is achieved with a state of the art single-site solver that directly solves the full-potential Dirac equation, in which the relativistic effects and full potential effects are treated on an equal footing. Compared to previous implementations of the full-potential relativistic MST, the generalized variable phase (sine and cosine scattering matrices) approach used here has the feature that all couplings of the solutions are retained and the solutions are expressed in terms of the free-space solutions, with no matching procedure required.
A persistent problem in previous implementation of the full-potential MST is that the charge density calculated within a sizable fraction of the mun-tin radius are numerically
unstable. In this thesis we present a new scheme to carry out the energy integration of the Green function. By using an efficient pole-searching technique to identify zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to self-consistently calculate the bulk properties of polonium, which is challenging for a conventional real-energy
scheme. The last chapter of this thesis is devoted to the application of our method to study magnetic anisotropy. This is in light of the rapid progress in recent years on the
technology of perpendicular magnetic anisotropy for magnetic tunnel junctions (MTJ). As a preliminary study, the magnetic anisotropy energy of a free-standing Fe monolayer
is calculated and good agreement with other methods is obtained. This study lays foundation for future research on large scale simulation of magnetic multilayer systems.