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Anatomy of spin-orbit torques in monolayer and : Insights from atomistic and momentum-space decompositions
Phys. Rev. B 114, 204424 – Published 22 October, 2026
DOI: https://doi.org/10.1103/1v68-qwcl
Abstract
We present a systematic first-principles study of the spin-orbit torques in the ferromagnetic monolayers (FGT) and (FGaT). Despite sharing the same crystal structure (point group ) and predominantly Fe spin-polarized bands, the two materials exhibit markedly different current-induced torques. We reveal these differences by computing the full angular dependence of the torkance—the torque per unit applied electric field—using linear-response theory with symmetry-adapted spin-orbit-coupled Wannier functions. FGaT may be viewed as a hole-doped analog of FGT, since Ga contributes one valence electron fewer than Ge. Although the work functions differ by only about 28 meV, the band filling near and changes substantially: The density of states at is reduced by a factor of 3 and its spin polarization reverses from minority in FGT to majority in FGaT. These electronic changes are reflected in the torques resolved by time-reversal parity, sublattice, and momentum. In particular, we identify pronounced hidden torques in FGaT and relate the suppression of its fourth-harmonic Fermi-sea component to the evolution of momentum-space pockets. Finally, we discuss the emergence of such self-torques, which are not captured by the conventional picture of current-induced spin accumulation, within a symmetry-based phenomenological framework. Our results provide microscopic insight into current-induced torques in two-dimensional ferromagnets and offer guidance for defect and van der Waals engineering of layered magnetic materials.