Development of a relativistic full-potential firstprinciples multiple scattering Green function method applied to complex magnetic textures of nano structures at surfaces

This thesis is concerned with the quantum mechanical investigation of a novel class of magnetic phenomena in atomic- and nanoscale-sized systems deposited on surfaces or embedded in bulk materials that result from a competition between the exchange and the relativistic spin-orbit interactions. The thesis is motivated by the observation of novel spin-textures of one- and two-dimensional periodicity of nanoscale pitch length exhibiting a unique winding sense observed in ultra-thin magnetic lms on nonmagnetic metallic substrates with a large spin-orbit interaction. The goal is to extend this eld to magnetic clusters and nano-structures of nite size in order to investigate in how far the size of the cluster and the atoms at the edge of the cluster or ribbon that are particular susceptible to relativistic eects change the balance between dierent interactions and thus lead to new magnetic phenomena. As an example, the challenging problem of Fe nano-islands on Ir(111) is addressed in detail as for an Fe monolayer on Ir(111) a magnetic nanoskyrmion lattice was observed as magnetic structure. To achieve this goal a new rst-principles all-electron electronic structure code based on density functional theory was developed. The method of choice is the Korringa- Kohn-Rostoker (KKR) impurity Green function method, resorting on a multiple scattering approach. This method has been conceptually further advanced to combine the neglect of any shape approximation to the full potential, with the treatment of non-collinear magnetism, of the spin-orbit interaction, as well as of the structural relaxation together with the perfect embedding of a nite size magnetic cluster of atoms into a surface or a bulk environment. For this purpose the formalism makes use of an expansion of the Green function involving explicitly left- and right-hand side scattering solutions. Relativistic eects are treated via the scalar-relativistic approximation and a spin-orbit coupling term treated self-consistently. This required the development of a new algorithm to solve the relativistic quantum mechanical scattering problem for a single atom with a non-spherical potential formulated in terms of the Lippmann-Schwinger integral equation. Prior to the investigation of the Fe nano-islands, the magnetic structure of an Fe monolayer is studied using atomistic spin-dynamics on the basis of a classical model Hamiltonian, which uses realistic coupling parameters obtained from rst principles. It is shown that this method is capable to nd the experimentally determined magnetic structure.