  The emergent induction of spiral magnets that was proposed [Jpn. J. Appl.
Phys. 58, 120909 (2019)] and recently demonstrated [Nature 586, 232 (2020)] is
shown to be further extended by a comprehensive treatment of the Rashba
spin-orbit coupling and the electron spin relaxation that affect the underlying
processes of spin-transfer torque and spinmotive force. Within adiabatic
approximation, we show that the output voltages are widely altered
intrinsically via the Rashba effect whereas extrinsically via the nonadiabatic
correction due to the spin relaxation and sample disorder. The findings
respectively clarify the origins for the amplitude modulation and sign change
of the emergent inductance with tunability by electrical gating and careful
sample preparation.
