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Spin-transfer torque (STT) provides key mechanisms for current-inducedphenomena in ferromagnets. While it is widely accepted that STT involves bothadiabatic and non-adiabatic contributions, their underlying physics and rangeof validity are quite controversial. By computing microscopically the responseof conduction electron spins to a time varying and spatially inhomogeneousmagnetic background, we derive the adiabatic and non-adiabatic STT in a unifiedfashion. Our result confirms the macroscopic theory [Phys. Rev. Lett.\textbf{93},~127204 (2004)] with all coefficients matched exactly. Ourderivation also reveals a benchmark on the validity of the result, which isused to explain three recent measurements of the non-adiabatic STT in quitedifferent settings.

Microscopic derivation of Spin-transfer torques in ferromagnets