Proximity-Induced Spin-Orbit Torque in Graphene on a Trigonal CrSBr Monolayer

TL;DR

This work investigates proximity-induced spin-orbit torque (SOT) in graphene placed on a trigonal CrSBr monolayer using a combined density functional theory (DFT) and nonequilibrium Green's function (NEGF) framework. The CrSBr substrate imparts an exchange field and spin polarization to graphene, producing a current-driven self-SOT on graphene's Dirac electrons, with the even SOT component vanishing in the 2D, ballistic interface. The SOT is dominated by the odd component and exhibits strong angular phase shifts due to noncollinearity between CrSBr magnetization and proximity-induced moments in graphene; the torque magnitude is sensitive to the Fermi level and interfacial coupling. The trigonal CrSBr monolayer shows room-temperature ferromagnetism with a Curie temperature around 304 K, making graphene/CrSBr a compelling platform for room-temperature 2D spintronics and proximity-engineered spin control.

Abstract

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.

Figures (8)

• Figure 1: A Schematic view of the device composed of a central region made of graphene/CrSBr heterostructure attached to the left (L) and right (R) graphene leads for conducting unpolarized charge current into the graphene within the central region.
• Figure 2: Calculated spin-resolved band structure of CrSBr monolayer unit cell. The color scale corresponds to $\langle S_z\rangle$ spin expectation value. The Fermi level is set to zero.
• Figure 3: Temperature dependence of CrSBr monolayer magnetization obtained by Monte Carlo simulation (circles) and analytical fit (solid line) for a finite system with the linear size $L=50$. The fitted Curie temperature $T_{\rm c}(L=50) \approx 316.8\ \mathrm{K}$. The inset shows the finite-size scaling analysis of $T_{\rm c}(L)$ versus $1/L^{\nu}$ with $\nu \simeq 0.41$, yielding the critical temperature $T_{\rm c} \approx 304.4~\mathrm{K}$. The data point for $L=50$ is emphasised with a black circle.
• Figure 4: Optimized graphene/CrSBr heterostructure: (a) top view and (b) side view. The $3 \times 3$ graphene supercell matched with a $2 \times 2$ CrSBr supercell, and a uniaxial strain of approximately 3% was applied to the graphene layer to achieve lattice commensurability. The structure was fully relaxed, resulting in an interlayer distance of 3.7 Å.
• Figure 5: Calculated spin-resolved band structure of graphene/CrSBr heterostructure. Zoom shows band spin splitting topology of graphene states near the Dirac point. The color scale corresponds to $\langle S_z\rangle$ spin expectation value. The Fermi level is set to zero.