Interplay of magnetic textures with spin-orbit coupled substrates

Magnetic textures such as skyrmions in thin films grown on substrates possess significant technological potential. Inhomogeneous magnetic structures can be described as homogeneous ferromagnetic order in the presence of anisotropic spin-orbit coupling (SOC). However, how this induced SOC stemming from the magnetic textures interplays with the SOC of the substrate remains unexplored. Here we show that these two contributions to SOC are, in general, not additive. We demonstrate this by employing a spintronics gauge theory. We further compute local currents which, when considered in the proper frame, match the spintronics gauge theory results. Finally, we analyze global transport quantities and show that they substantiate our previous results quantitatively. The implications for skyrmionics as well as topological superconductivity are discussed.