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Spin-wave-induced spin torque in Rashba spin-orbit coupling system

We study the effects of Rashba spin-orbit coupling on the spin torque induced by spin waves, which are the plane wave dynamics of magnetization. The spin torque is derived from linear response theory, and we calculate the dynamic spin torque by considering the impurity-ladder-sum vertex corrections. This dynamic spin torque is divided into three terms: a damping term, a $distortion$ term, and a correction term for the equation of motion. The $distorting$ torque describes a phenomenon unique to the Rashba spin-orbit coupling system, where the distorted motion of magnetization precession is subjected to the anisotropic force from the Rashba coupling. The oscillation mode of the precession exhibits an elliptical trajectory, and the ellipticity depends on the strength of the nesting effects, which could be reduced by decreasing the electron lifetime.