A phenomenology of magnetic chiral damping is proposed in the context of magnetic materials lacking inversion symmetry breaking. We show that the magnetic damping tensor adopts a general form that accounts for a component linear in magnetization grad
ient in the form of Lifshitz invariants. We propose different microscopic mechanisms that can produce such a damping in ferromagnetic metals, among which spin pumping in the presence of anomalous Hall effect and an effective $s$-$d$ Dzyaloshinskii-Moriya antisymmetric exchange. The implication of this chiral damping in terms of domain wall motion is investigated in the flow and creep regimes. These predictions have major importance in the context of field- and current-driven texture motion in noncentrosymmetric (ferro-, ferri-, antiferro-)magnets, not limited to metals.
Current-induced domain wall (DW) displacements in an array of ultrathin Pt/Co/AlOx wires with perpendicular magnetic anisotropy have been directly observed by wide field Kerr microscopy. DWs in all wires in the array were driven simultaneously and th
eir displacement on the micrometer-scale was controlled by the current pulse amplitude and duration. At the lower current densities where DW displacements were observed (j less than or equal to 1.5 x 10^12 A/m^2), the DW motion obeys a creep law. At higher current density (j = 1.8 x 10^12 A/m^2), zero-field average DW velocities up to 130 +/- 10 m/s were recorded.
