Spin-transfer torque (STT) provides key mechanisms for current-induced phenomena in ferromagnets. While it is widely accepted that STT involves both adiabatic and non-adiabatic 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 non-adiabatic STT in a unified fashion. Our result confirms the macroscopic theory [Phys. Rev. Lett. \textbf{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 non-adiabatic STT in quite different settings.
@article{arxiv.1212.1964,
title = {Microscopic derivation of Spin-transfer torques in ferromagnets},
author = {Ran Cheng and Qian Niu},
journal= {arXiv preprint arXiv:1212.1964},
year = {2013}
}