We derive the complete expression of nonlocal damping in noncollinearmagnetization due to the nonuniform spin current pumped by precessionalmagnetization and incorporate it into a generalized Thiele equation to studyits effects on the dynamics of the transverse and vortex domain walls (DWs) inferromagnetic nanowires. We demonstrate that the transverse component ofnonlocal damping slows down the field-driven DW propagation and increases theWalker breakdown field whereas it is neglected in many previous works inliterature. The experimentally measured DW mobility variation with the dampingtuned by doping with heavy rare-earth elements that had discrepancy frommicromagnetic simulation are now well understood with the nonlocal damping. Ourresults suggest that the nonlocal damping should be properly included as aprerequisite for quantitative studies of current-induced torques innoncollinear magnetization.
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