Motivated by recent progress in employing two key classes of two-dimensional materials—topological insulators and transition-metal dichalcogenides (TMDCs)—as spin sources for generating spin-orbit torque (SOT), we investigate current-induced spin polarization and the resulting SOT in bilayers composed of a TMDC (${\mathrm{WSe}}_2$ or ${\mathrm{MoSe}}_2$) and ferromagnetic chromium iodide (${\mathrm{CrI}}_3$), beyond the linear response regime. Using the steady-state Boltzmann equation, we find that intraband transitions yield a strong fieldlike torque on the ${\mathrm{CrI}}_3$ layer, while interband transitions give rise to a comparatively weaker dampinglike torque in the ${\mathrm{WSe}}_2/{\mathrm{CrI}}_3$ system. Remarkably, the dampinglike component is enhanced by up to three orders of magnitude in $n$-doped ${\mathrm{MoSe}}_2$, reaching a strength comparable to the fieldlike torque, which itself is an order of magnitude larger than that in the ${\mathrm{WSe}}_2$-based bilayer. Both torque components exhibit strong asymmetry between $n$- and $p$-type doping in ${\mathrm{WSe}}_2$ and ${\mathrm{MoSe}}_2$ systems. Furthermore, we demonstrate that the twist angle plays a crucial role: depending on the TMDC and chemical potential, twisting can reverse the sign of the SOT and significantly modulate its magnitude. Finally, we show that a transverse gate electric field enables substantial tunability of the SOT, by nearly one order of magnitude, and induces a sign reversal at a twist angle of $10.{16}^{\circ }$.

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• Spin-orbit torque
• Spintronics
• Twistronics
• Transition metal dichalcogenides
• Twisted heterostructures
• Boltzmann theory