# Non-local field-like spin-orbit torques in Rashba systems: an ab-initio study of Ag$_{2}$Bi/Ag/Fe film

## TL;DR

This study uses first-principles calculations to reveal long-range, non-local field-like spin-orbit torques in Ag$_{2}$Bi/Ag/Fe films, influenced by disorder and Bi vacancies, challenging traditional spin Hall effect explanations.

## Contribution

It demonstrates the non-local origin of SOT in Rashba systems and shows how disorder and vacancies can tune the torque, providing new insights into spin transfer mechanisms.

## Key findings

- Large SOT from Ag$_{2}$Bi layer far from Fe
- SOT can be engineered via Bi vacancies
- SOT strongly depends on disorder type

## Abstract

We investigate from first principles the field-like spin-orbit torques (SOTs) in a Ag$_{2}$Bi-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 Ag$_{2}$Bi 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 non-local 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 Ag$_{2}$Bi 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.