Rashba-induced spin electromagnetic fields in the strong sd coupling regime

Spin electromagnetic fields driven by the Rashba spin–orbit interaction, or Rashba-induced spin Berry's phase, in ferromagnetic metals are theoretically studied using the Keldysh Green's function method. Considering the limit of strong sd coupling without spin relaxation (adiabatic limit), the spin electric and magnetic fields are determined by calculating transport properties. The spin electromagnetic fields can be expressed in terms of a Rashba-induced effective vector potential, and thus they satisfy Maxwell's equation. In contrast to the conventional spin Berry's phase, the Rashba-induced one is linear in the gradient of magnetization profile, and thus can be extremely large even for slowly varying structures. We show that the Rashba-induced spin Berry's phase exerts a Lorentz force on spin resulting in a giant spin Hall effect in magnetic thin films in the presence of magnetization structures. A Rashba-induced spin magnetic field would be useful to distinguish between topologically equivalent magnetic structures. We propose experimental setups where a Rashba-induced spin magnetic field is identified.