Charge pumping with strong spin-orbit coupling: Fermi surface breathing, Berry curvature, and higher harmonic generation

Spin and charge pumping induced by a precessing magnetization has been instrumental to the development of spintronics. Nonetheless, most theoretical studies so far treat the spin-orbit coupling as a perturbation, which disregards the competition between exchange and spin-orbit fields. In this work, based on Keldysh formalism and Wigner expansion, we develop an adiabatic theory of spin and charge pumping adapted to systems with arbitrary spin-orbit coupling. We apply this theory to the magnetic Rashba gas and magnetic graphene cases and discuss the pumped ac and dc current. We show that the pumped current possesses both intrinsic (Berry curvature-driven) and extrinsic (Fermi surface breathing-driven) contributions, akin to magnetic damping. In addition, we find that higher harmonics can be generated under large-angle precession and we propose a couple of experimental setups where such an effect can be experimentally observed.