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

TL;DR

This paper theoretically investigates Rashba-induced spin electromagnetic fields in ferromagnetic metals, revealing their large magnitude and potential to generate significant spin Hall effects, with implications for magnetic structure analysis.

Contribution

It introduces a theoretical framework for Rashba-induced spin electromagnetic fields in the strong sd coupling regime, highlighting their linear dependence on magnetization gradients and large effects.

Findings

Spin electromagnetic fields are expressed via an effective vector potential.

Rashba-induced spin Berry's phase is linear in magnetization gradient.

Large spin Hall effect is predicted in magnetic thin films.

Abstract

Spin electromagnetic fields driven by the Rashba spin-orbit interaction, or Rashba-induced spin Berry's phase, in ferromagnetic metals is theoretically studied based on the Keldysh Green's function method. Considering a 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 turn out to be expressed in terms of a Rashba-induced effective vector potential, and thus they satisfy the 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 the Lorentz force on spin resulting in a giant spin Hall effect in magnetic thin films in the presence of magnetization structures. Rashba-induced spin magnetic field would be useful to distinguish between topologically equivalent magnetic structures.