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We investigate Gilbert damping, spectroscopic gyromagnetic ratio andcurrent-induced torques in the one-dimensional Rashba model with an additionalnoncollinear magnetic exchange field. We find that the Gilbert damping differsbetween left-handed and right-handed N\'eel-type magnetic domain walls due tothe combination of spatial inversion asymmetry and spin-orbit interaction(SOI), consistent with recent experimental observations of chiral damping.Additionally, we find that also the spectroscopic $g$ factor differs betweenleft-handed and right-handed N\'eel-type domain walls, which we call chiralgyromagnetism. We also investigate the gyromagnetic ratio in the Rashba modelwith collinear magnetization, where we find that scattering corrections to the$g$ factor vanish for zero SOI, become important for finite spin-orbitcoupling, and tend to stabilize the gyromagnetic ratio close to itsnonrelativistic value.

Chiral damping, chiral gyromagnetism and current-induced torques in textured one-dimensional Rashba ferromagnets