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Unconventional spin-orbit torque in transition metal dichalcogenide/ferromagnet bilayers from first-principles calculations

Motivated by recent observations of unconventional out-of-plane dampinglike torque in \ch{WTe2}/Permalloy bilayer systems, we calculate the spin-orbit torque generated in two-dimensional transition metal dichalcogenide (TMD)-ferromagnet heterostructures using first-principles methods and linear response theory. Our numerical calculation of spin-orbit torques in \ch{WTe2}/Co and \ch{MoTe2}/Co heterostructures shows both conventional and novel dampinglike torkances (torque per electric field) with comparable magnitude, around $100~\hbar/2e~(\rm Ω\cdot cm)^{-1}$, for an electric field applied perpendicular to the mirror plane of the TMD layer. To gain further insight into the source of dampinglike torque, we compute the spin current flux between the TMD and Co layers and find good agreement between the two quantities. This indicates that the conventional picture of dampinglike spin-orbit torque, whereby the torque results from the spin Hall effect plus spin transfer torque, largely applies to TMD/Co bilayer systems.