  The introduction of a strong Rashba spin orbit coupling (SOC) had been
predicted to enhance the spin motive force (SMF) [see Phys. Rev. Lett. {\bf
108}, 217202 (2012)]. In this work, we predict further enhancement of the SMF
by time modulation of the Rashba coupling $\alpha_R$, which induces an
additional electric field $E^R_d={\dot \alpha_R} m_e/e\hbar({\hat z}\times
{\mathbf m})$. When the modulation frequency is higher than the magnetization
precessing frequency, the amplitude of this field is significantly larger than
previously predicted results. Correspondingly, the spin torque on the
magnetization is also effectively enhanced. Additionally, the nature of SOC
induced spin torque in the system can be transformed from damping to
antidamping-like by modulating ${\dot \alpha_R}$. We also suggest a biasing
scheme to achieve rectification of SMF, {\it i.e.}, by application of a square
wave voltage at the resonant frequency. Finally, we numerically estimate the
resulting spin torque field arising from a Gaussian pulse time modulation of
$\alpha_R$.
