Nonlocal Fieldlike Spin-Orbit Torques In Rashba Systems: Ab Initio Study Of A Ag2bi-Terminated Ag(111) Film Grown On A Ferromagnetic Fe(110) Substrate

We investigate from first principles the fieldlike spin-orbit torques (SOTs) in a Ag2Bi-terminated Ag(111) film grown on ferromagnetic Fe(110). We find that a large part of the SOT arises from the spin-orbit interaction (SOI) in the Ag2Bi layer far away from the Fe layers. These results clearly hint at a long-range spin transfer in the direction perpendicular to the film that does not originate in the spin Hall effect. In order to bring evidence of the nonlocal character of the computed SOT, we show that the torque acting on the Fe layers can be engineered by the introduction of Bi vacancies in the Ag2Bi layer. Overall, we find a drastic dependence of the SOT on the disorder type, which we explain by a complex interplay of different contributions to the SOT in the Brillouin zone.