Influence of nonlocal damping on the field-driven domain wall motion

We derive the complete expression of nonlocal damping in noncollinear magnetization due to the nonuniform spin current pumped by precessional magnetization and incorporate it into a generalized Thiele equation to study its effects on the dynamics of the transverse and vortex domain walls (DWs) in ferromagnetic nanowires. We demonstrate that the transverse component of nonlocal damping slows down the field-driven DW propagation and increases the Walker breakdown field whereas it is neglected in many previous works in literature. The experimentally measured DW mobility variation with the damping tuned by doping with heavy rare-earth elements that had discrepancy from micromagnetic simulation are now well understood with the nonlocal damping. Our results suggest that the nonlocal damping should be properly included as a prerequisite for quantitative studies of current-induced torques in noncollinear magnetization.