  Magnetic skyrmions, topologically protected vortex-like configurations in
spin textures, are of wide conceptual and practical appeal for quantum
information technologies, notably in relation to the making of so-called
race-track memory devices. Skyrmions can be created, steered and destroyed with
magnetic fields and/or (spin) currents. Here we focus on the latter mechanism,
analyzed via a microscopic treatment of the skyrmion-current interaction. The
system we consider is an isolated skyrmion in a square-lattice cluster,
interacting with electrons spins in a current-carrying quantum wire. For the
theoretical description, we employ a quantum formulation of spin-dependent
currents via nonequilibrium Green's functions (NEGF) within the generalized
Kadanoff-Baym ansatz (GKBA). This is combined with a treatment of skyrmions
based on classical localized spins, with the skyrmion motion described via
Ehrenfest dynamics. With our mixed quantum-classical scheme, we assess how
time-dependent currents can affect the skyrmion dynamics, and how this in turn
depends on electron-electron and spin-orbit interactions in the wire. Our study
shows the usefulness of a quantum-classical treatment of skyrmion steering via
currents, as a way for example to validate/extract an effective,
classical-only, description of skyrmion dynamics from a microscopic quantum
modeling of the skyrmion-current interaction.
