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We introduce a multiscale framework which combines time-dependentnonequilibrium Green function (TD-NEGF) algorithms, scaling linearly in thenumber of time steps and describing quantum-mechanically conduction electronsin the presence of time-dependent fields of arbitrary strength or frequency,with classical time evolution of localized magnetic moments described by theLandau-Lifshitz-Gilbert (LLG) equation. The TD-NEGF+LLG framework can beapplied to a variety of problems where current-driven spin torque inducesdynamics of magnetic moments as the key resource for next generationspintronics. Using magnetic domain wall (DW) as an example, we predict that itsmotion will pump time-dependent spin and charge currents (on the top ofunpolarized DC charge current injected through normal metal leads to drive theDW motion). The conversion of AC components of spin current, whose amplitudeincreases (decreases) as the DW approaches (distances from) the normal metallead, into AC voltage via the inverse spin Hall effect offers a tool toprecisely track the DW position along magnetic nanowire. We also quantify theDW transient inertial displacement due to its acceleration and deceleration bypulse current and the entailed spin and charge pumping. Finally, TD-NEGF+LLG asa nonperturbative (i.e., numerically exact) framework allows us to establishthe limits of validity of the so-called spin-motive force (SMF) theory forpumped charge current by time-dependent magnetic textures---the perturbativeanalytical formula of SMF theory becomes inapplicable for large frequencies(but unrealistic in magnetic system) and, more importantly, for increasingnoncollinearity when the angles between neighboring magnetic moments exceed$\simeq 10^\circ$.

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Spin and charge pumping by steady or pulse current-driven magnetic  domain wall: A self-consistent multiscale  time-dependent-quantum/time-dependent-classical approach