Spin-orbit torques (SOTs) in heavy-metal/ferromagnetic heterostructures have become a promising tool to achieve efficiently magnetization reversal using electrical current pulses . SOTs have also been instrumental for current-induced magnetization switching in antiferromagnets (AFMs) with reduced symmetry . It is generally accepted that the microscopic origin of SOTs is the relativistic spin-orbit coupling (SOC) of the heavy metal that provides charge-to-spin conversion, but the precise microscopic origins of SOTs are still being debated, with the spin Hall effect (SHE) due to nonlocal spin currents and the spin Rashba-Edelstein effect (SREE) due to local spin polarization at the interface being the primary candidates.
We employ first-principles calculations to investigate computationally the electrically induced out-of-equilibrium spin and orbital polarizations in symmetry-broken anti-ferromagnets CuMnAs and Mn2Au  as well as in Pt/3d-metal (Co, Ni, Cu) bilayer films and pure 3d-metal films . We use linear-response theory to compute the full spin and orbital conductivity tensors and the induced spin and orbital polarizations. For the symmetry-broken AFMs we find that the dominant effect is the locally induced orbital polarization, i.e., an orbital Rashba-Edelstein effect (OREE) that is about 50x larger than the SREE. The OREE moreover does not require SOC and, because of symmetry, the induced orbital polarizations always exhibit (staggered) Rashba symmetry whereas the SREE, generated from the OREE through SOC, can exhibit Dresselhaus or Rashba symmetry.
For the Pt/3d-metal bilayer systems we compute similarly that the electrically induced transverse orbital polarization is exceedingly larger (~100 x) than the induced spin polarization and present even without SOC, in contrast to the spin polarization. This pin-points that also in the Pt/3d-metal bilayers the electrically induced orbital polarization due to the OREE and the orbital Hall effect (OHE)  are the primary responses, whereas the SREE and SHE are induced from these through SOC. We further compute atom-resolved response quantities that allow us to identify the induced spin-polarizations that lead to fieldlike (FL) SOTs and dampinglike (DL) SOTs and compare their relative magnitude, dependence on the magnetization direction, as well as their Pt-layer thickness dependence. We find that the DL SOT component is due to the magnetic SHE at the Pt/Co and Pt/Ni interfaces. Lastly, we calculate the electrically induced orbital polarization in non-magnetic metal films and show that it has a profile across the film that is distinctly different from that of the induced spin polarization.
 I.M. Miron, K. Garello, G. Gaudin, et al., Nature 476, 189 (2011)
 P. Wadley, B. Howells, J. Železný, et al., Science 351, 587 (2016)
 L. Salemi, M. Berritta, et al., Nat. Commun. 10, 5381 (2019)
 L. Salemi, M. Berritta, and P.M. Oppeneer, Phys. Rev. Mater. 5, 074407 (2021)
 D. Go, D. Jo, Ch. Kim, and H.-W. Lee, Phys. Rev. Lett. 121, 086602 (2018)