In the search for low power operation of microelectronic devices, spin-based solutions have attracted undeniable increasing interest due to their intrinsic magnetic nonvolatility. The ability to electrically manipulate the magnetic order using spin-orbit interaction, associated with the recent emergence of topological spintronics with its promise of highly efficient charge-to-spin conversion in solid state, offer alluring opportunities in terms of system design. Although the related technology is still at its infancy, this thesis intends to contribute to this engaging field by investigating the nature of the charge and spin transport in spin-orbit coupled and topological systems using quantum transport methods. We identified three promising building blocks for next-generation technology, three classes of systems that possibly enhance the spin and charge transport efficiency: (i)- topological insulators, (ii)- spin-orbit coupled magnonic systems, (iii)- topological magnetic textures (skyrmions and 3Q magnetic state). Chapter 2 reviews the basics and essential concepts used throughout the thesis: the spin-orbit coupling, the mathematical notion of topology and its importance in condensed matter physics, then topological magnetism and a zest of magnonics. In Chapter 3, we study the spin-orbit torques at the magnetized interfaces of 3D topological insulators. We demonstrated that their peculiar form, compared to other spin-orbit torques, have important repercussions in terms of magnetization reversal, charge pumping and anisotropic damping. In Chapter 4, we showed that the interplay between magnon current jm and magnetization m in homogeneous ferromagnets with Dzyaloshinskii-Moriya (DM) interaction, produces a field-like torque as well as a damping-like torque. These DM torques mediated by spin wave can tilt the imeaveraged magnetization direction and are similar to Rashba torques for electronic systems. Moreover, the DM torque is more efficient when magnons are thermally driven. Chapters 5 and 6 carry throughout tight-binding studies on the topological charge-spin transport in two-dimensional lattices with ferromagnetic skyrmions and 3Q magnetic structure. We use the Landauer-Buttiker formalism and evaluate the robustness of the topological signals. For the 3Q state, a spin-polarized quantum anomalous Hall state with chiral edge modes, unaffected by deformation and disorder, is reachable in zero net magnetization. We finish with concluding remarks and perspectives.
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