Sliding conductivity of a magnetic kink crystal in a chiral helimagnet

We derive a current-driven sliding conductivity of the magnetic kink crystal (MKC) in chiral helimagnet under weak magnetic field applied perpendicular to the helical axis. For this purpose, we discuss the correlated dynamics of quantum-mechanical itinerant spins and the MKC which are coupled via the sd exchange interaction. The itinerant spins are treated as fully quantum-mechanical operators whereas the dynamics of the MKC is considered within classical Lagrangian formalism. By appropriately treating elementary excitations around the MKC state, we construct coupled equations of motion for the collective coordinates (the center-of-mass position and quasi-zero-mode coordinate) associated with the sliding motion of the MKC. By solving them, we demonstrate that the correlated dynamics is understood through a hierarchy of two time scales: Boltzmann relaxation time ${\ensuremath{\tau}}_{\text{el}}$, when a nonadiabatic spin-transfer torque appears, and Gilbert damping time ${\ensuremath{\tau}}_{\text{MKC}}$, when adiabatic spin-transfer torque comes up. As a notable consequence, we found that the terminal velocity of the sliding motion reverses its sign depending on the band-filling ratio of the conduction electron system.