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Magnetic skyrmions hold great promise for realizing compact and stable memorydevices that can be manipulated at very low energy costs via electronic currentdensities. In this work, we extend a recently introduced method to describeclassical skyrmion textures coupled to dynamical itinerant electrons. In thisscheme, the electron dynamics is described via nonequilibrium Green's functions(NEGF) within the generalized Kadanoff-Baym ansatz, and the classical spins aretreated via the Landau-Lifshitz-Gilbert equation. The framework is hereextended to open systems, by the introduction of a non-interactingapproximation to the collision integral of NEGF. This, in turn, allows us toperform computations of the real-time response of skyrmions to electroniccurrents in large quantum systems coupled to electronic reservoirs, whichexhibit a linear scaling in the number of time steps. We use this approach toinvestigate how electronic spin currents and dilute spin disorder affectsskyrmion transport and the skyrmion Hall drift. Our results show that theskyrmion dynamics is sensitive to the specific form of spin disorder, such thatdifferent disorder configurations leads to qualitatively different skyrmiontrajectories for the same applied bias. This sensitivity arises from the localspin dynamics around the magnetic impurities, a feature that is expected not tobe well captured by phenomenological or spin-only descriptions. At the sametime, our findings illustrate the potential of engineering microscopic impuritypatterns to steer skyrmion trajectories.

Microscopic theory of current-induced skyrmion transport and its application in disordered spin textures