Valley-dependent spin-orbit torques in two-dimensional hexagonal crystals

Abstract

We study spin-orbit torques in two-dimensional hexagonal crystals such as graphene, silicene, germanene, and stanene. The torque possesses two components, a fieldlike term due to inverse spin galvanic effect and an antidamping torque originating from Berry curvature in mixed spin-k space. In the presence of staggered potential and exchange field, the valley degeneracy can be lifted and we obtain a valley-dependent Berry curvature, leading to a tunable antidamping torque by controlling the valley degree of freedom. The valley imbalance can be as high as 100% by tuning the bias voltage or magnetization angle. These findings open new venues for the development of current-driven spin-orbit torques by structural design.

Current‐Induced Spin–Orbit Torques for Spintronic Applications

“…Next, SOT has an intriguing feature that facilitates a wide range of spintronic materials. Various exotic materials such as topological insulators, [56,128,201,202] Weyl semimetals, [133][134][135][136][137] and other 2D materials [138][139][140][141] have been investigated as spin sources with large SOT efficiencies. For instance, the critical current for SOT switching is reported to be ≈6 × 10 5 A cm −2 for Bi 2 Se 2 /NiFe [131] and ≈3 × 10 5 A cm −2 for WTe 2 /NiFe, [129] which is orders of magnitude smaller than that for Pt/NiFe, [129] Furthermore, SOT can be applied to any type of magnetic material.…”

“…In this respect, heavy metals (HMs) such as Ta, [20,21,23,45,124] W, [22,47,48,73,125] and Pt [19,25,44,76,82,93,126,127] and their alloys [77,[95][96][97] have been extensively investigated. In addition, other exotic materials including topological insulators (TIs) [56,[128][129][130][131][132][133][134] or 2D materials [135][136][137][138][139][140][141] have been suggested as effective spin current sources. While they show a very large θ SH , these exotic materials pose critical challenges for applications, such as large area fabrication, compatibility with a FM, especially PMA materials, or applicability to the conventional Si processes.…”

Theory of Rashba Torques

“…The theoretical investigation of inverse spin galvanic effect and SOTs has been recently extended towards two dimensional hexagonal lattices such as, but not limited to, graphene, silicene, germanene, stanene, transition metal dichalcogenides etc. [100,101,102]. The parametric dependence of the torque in these materials does not significantly differ from the toy model of the Rashba two dimensional electron gas or from the richer three dimensional dilute magnetic semiconductors discussed above.…”

Tunable spin-charge conversion through topological phase transitions in zigzag nanoribbons

“…In this system, Rashba spin-orbit coupling enables the electrical generation of a nonequilibrium spin density, δS y , an effect known as the inverse spin galvanic effect [44] and studied in detail in bulk two-dimensional hexagonal crystals [31,47]. In Fig.…”