Proximity-induced spin-orbit torque in graphene on a trigonal CrSBr monolayer

We present a first-principles and quantum transport study of proximity-induced spin-orbit torque (SOT) in graphene on a trigonal CrSBr monolayer. Density functional theory combined with nonequilibrium Green's function calculations shows that the CrSBr substrate induces spin polarization and a sizable exchange splitting in the graphene Dirac states. The resulting current-driven spin density in graphene generates a self-SOT on the Dirac electrons. The proximity-induced exchange field breaks time-reversal symmetry and gives rise to a purely odd SOT component, while the even contribution vanishes. The torque magnitude exhibits a strong angular dependence with phase shifts arising from the noncollinearity between the CrSBr magnetization and the induced magnetic moments in graphene. Monte Carlo simulations based on the calculated exchange parameters predict a Curie temperature of approximately 304 K, confirming the robustness of ferromagnetism in the trigonal CrSBr monolayer. These results identify graphene/CrSBr heterostructures as a promising platform for room-temperature two-dimensional spintronics.