Abstract
Spin-transfer torque (STT) provides key mechanisms for current-induced phenomena in ferromagnets. While it is widely accepted that STT involves both adiabatic and nonadiabatic contributions, their underlying physics and range of validity are quite controversial. By computing microscopically the response of conduction electron spins to a time varying and spatially inhomogeneous magnetic background, we derive the adiabatic and nonadiabatic STT in a unified fashion. Our result confirms the macroscopic theory [Phys. Rev. Lett. 93, 127204 (2004)] with all coefficients matched exactly. Our derivation also reveals a benchmark on the validity of the result, which is used to explain three recent measurements of the nonadiabatic STT in quite different settings.
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