Spin-orbit torque and inverse spin-orbit torque effects in monolayer Fe₃GeTe₂

In ferromagnetic systems lacking inversion symmetry, an applied electric field can drive the magnetization dynamics through the spin-orbit torque effect while an effective magnetic field can also induce charge current through the inverse spin-orbit torque effect. These two phenomena are reciprocal and connected by the Onsager reciprocal relations. To illustrate these two reciprocal effects, we use first-principles calculations to study the spin-orbit torque and ensuing magnetic dynamics in the monolayer Fe₃GeTe₂ that lacks inversion symmetry. By expanding the torque versus magnetization direction as a series of vector spherical harmonics, we find that higher order terms (up to $ell=4$) are significant and play important roles in magnetic dynamics. They give rise to deterministic, magnetic field-free electrical switching of perpendicular magnetization. We also discuss the inverse spin-orbit torque effect in the monolayer Fe₃GeTe₂ using the reciprocal relations. We compute the time-symmetry signatures of these two effects and note that they differ from those of related torques in bilayer systems.