Topological transport in non-Abelian spin textures from first principles

Recently, skyrmions attracted huge attention due to their topological character which ensures surprisingly stable, particle-like magnetic excitations on small scales with distinctive dynamical properties. Their characteristic transport signature—the topological Hall effect—has become an established tool for detection of topologically non-trivial ferromagnetic textures. However,this attribute vanishes when considering degenerate antiferromagnetic structures as theassociated emergent magnetic field is spin-dependent. This thesis demonstrates the emergence of an alternative transport signature in case of antiferromagnetic skyrmion textures—the topological spin Hall effect. Firstly, a computational scheme is developed which estimates the topological spin Hall effect based on semiclassical wave-packet dynamics. In the adiabatic limit, their equations of motion allow to treat large-scale magnetic textures on top of locally collinear, small-scale Hamiltonians, here based on density functional theory. Transport expressions are extracted by combination of the equations of motion and the Boltzmann formalism. While the analogous procedure is straightforward for ferromagnetic materials, the wave-packet’s $\textit{SU}$(2)-nature, caused by degenerate bands, results in additional spin dynamics and non-abelian Berry curvatures which inhibit direct transport evaluation. While the reciprocal-space dynamics are treated on the Boltzmann level, the spin and real-space dynamics are solved iteratively starting from multiple initial positions. Evaluation of the traversed paths results in integrated expressions for the topological spin Hall effect. Sizable topological spin Hall responses are predicted in simulations for the exemplary Fe/Cu/Fe-trilayers and thin chromium layers when artificially imprinting synthetic and intrinsic antiferromagnetic skyrmions, respectively. The importance of the non-abelian dynamics is demonstrated by large differences relative to comparative calculations of decoupled antiparallel ferromagnets. While the spin evolution results in surprisingly homogeneous transport modifications, the $\textbf{k}$-resolved intra-band overlap has a particularly unpredictable distribution requiring precise density functional theory calculations. Further numerical thoroughness isrequired because of extreme sensitivity with respect to small reciprocal-space modificationssuch as slight Fermi energy changes. Furthermore, the evolution of the $\textbf{k}$-dependent transport and overlap properties is shown with respect to thickness variations demonstrating rich tuning potential. Conversely, multiple calculations modifying the skyrmion-radius, -shape, and -density demonstrate the topological invariance of the topological spin Hall effect. Overall, the topological spin Hall effect is an interesting phenomenon with rich application possibilities. Foremost, it facilitates the discovery of the so far undetected antiferromagnetic skyrmions, but also might provide efficient spin-current generation as required in spintronic applications. Alternatively, it could serve as read-out mechanism of more complex devices like antiferromagnetic, skyrmion-based racetrack memory. Hence, the developed versatile and readily applicable computational scheme is a great addition for future antiferromagnetics kyrmion studies