In this work, we study the motion of skyrmions in a ferromagnetic waveguide using a time-dependent non-equilibrium Green’s function formalism implemented on a real space tight-binding model. We analyze the perturbation induced by this motion and look at the time-dependent distribution of the non-equilibrium charge, spin densities and then discuss the topological Hall effect. The current pumped during this motion is analyzed and shown to have an influence on the torque applied on the whole texture with a signature unveiled in the renormalization of the damping parameter. A cooperative effect due to the collective motion of skyrmions is proposed in order to enhance the skyrmion's velocity. The stationary regime is analyzed as a function of the different parameters of the system and explained using the formalism of electronic pumping. A simple formula for the current is provided. We propose this cooperative electronic pumping to enhance the collective skyrmion mobility in racetracks.
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