  Efficient manipulation of magnetic order with electric current pulses is
desirable for achieving fast spintronic devices. The Rashba-Edelstein effect,
wherein a spin polarization is electrically induced in noncentrosymmetric
systems, provides a mean to achieve current-induced staggered spin-orbit
torques. Initially predicted for spin, the orbital counterpart of this effect
has been disregarded up to now. Here, we present a generalized Rashba-Edelstein
effect, which generates not only spin polarization but also orbital
polarization, which we find to be far from being negligible and could play a
crucial role in the magnetization dynamics. We show that the orbital
Rashba-Edelstein effect does not require spin-orbit coupling to exist. We
present first-principles calculations of the frequency-dependent spin and
orbital Rashba-Edelstein susceptibility tensors for the noncentrosymmetric
antiferromagnets CuMnAs and Mn2Au. We show that the electrically induced local
magnetization has both staggered in-plane components and non-staggered
out-of-plane components, and can exhibit Rashba-like or Dresselhaus-like
symmetries, depending on the magnetic configuration. Furthermore, there is an
induced local magnetization on the nonmagnetic atoms as well, that is smaller
in Mn2Au than in CuMnAs. We compute sizable induced magnetizations at optical
frequencies, which suggest that electric-field driven switching could be
achieved at much higher frequencies.
