The emergent induction of spiral magnets that was proposed [N. Nagaosa, Jpn. J. Appl. Phys. 58, 120909 (2019)] and recently demonstrated [T. Yokouchi et al., Nature (London) 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.

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• Helicoidal magnetic texture
• Spin dynamics
• Spin torque
• Spin transfer torque
• Spintronics