Topologically Driven Spin-Orbit Torque in Dirac Matter

Abstract

We unveil novel spin-orbit torque mechanisms driven by topological edge states in magnetic graphene-based devices. Within the energy gap, a damping-like torque plateau emerges within the quantum anomalous Hall phase upon breaking particle-hole symmetry, while for energies at the spin-split Dirac points located within the bands, a large damping-like torque develops as a result of a vanishing Fermi contour. Such torques are tunable by the degree of spin-pseudospin entanglement dictated by proximity-induced spin-orbit coupling terms.

Figures (2)

• Figure 1: (a) Band structure exhibiting spin-split Dirac cones at energies $\mp J_\text{ex} / 2$ along the out-of-plane axis $\hat{\boldsymbol{z}}$, and a band gap at charge neutrality (yellow highlight), with $J_\text{ex} = 40 \,\text{meV}$ and $\lambda_\text{KM} = \lambda_\text{R} = 4 \,\text{meV}$(b) Spin texture of the valence band, showing a sharp quenching at the band edge (yellow highlight) due to Kane-Mele SOC. (c) Damping-like non-equilibrium spin texture (arbitrary units) of the valence band, showing a source of DL torque at the band edge and at the Dirac point.
• Figure 2: $S_\text{DL}$ with (solid black curve) and without (dashed grey curve) Kane-Mele SOC, with $J_\text{ex} = 40 \,\text{meV}$ and $\lambda_\text{R} = 4 \, \text{meV}$. A SOT plateau is observed throughout the band gap at charge neutrality enabled by $\lambda_\text{KM}$ (yellow highlight). At the Dirac points (red and blue highlights) a sharp valley in $S_\text{DL}$ is observed due to spin-pseudospin entanglement, which can be reverted into a sharp peak by $\lambda_\text{KM}$. Left inset: $S_\text{FL}$, is insensitive to $\lambda_\text{KM}$. Right inset: $S_\text{DL}$ at the gap (yellow), spin majority Dirac point (red), and spin minority Dirac cone (blue) as a function of $\lambda_\text{KM}$.