Theory of Rashba spin-orbit coupling in magnetic metals is worked out from microscopic Hamiltonian describing d-orbitals. When structural inversion symmetry is broken, electron hopping between $d$-orbitals generates chiral ordering of orbital angular momentum, which combines with atomic spin-orbit coupling to result in the Rashba interaction. Rashba parameter characterizing the interaction is band-specific, even reversing its sign from band to band. Large enhancement of the Rashba parameter found in recent experiments is attributed to the orbital mixing of 3d magnetic atoms with non-magnetic heavy elements as we demonstrate by first-principles and tight-binding calculations.
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