Transition metal dichalcogenides (TMDs) are promising materials for efficient generation of current-induced spin-orbit torques on an adjacent ferromagnetic layer. Numerous effects, both interfacial and bulk, have been put forward to explain the different torques previously observed. Thus far, however, there is no clear consensus on the microscopic origin underlying the spin-orbit torques observed in these TMD/ferromagnet bilayers. To shine light on the microscopic mechanisms at play, here we perform thickness dependent spin-orbit torque measurements on the semiconducting WSe$_{2}$/permalloy bilayer with various WSe$_{2}$ layer thickness, down to the monolayer limit. We observe a large out-of-plane field-like torque with spin-torque conductivities up to $1times10^4 ({hbar}/2e) ({Omega}m)^{-1}$. For some devices, we also observe a smaller in-plane antidamping-like torque, with spin-torque conductivities up to $4times10^{3} ({hbar}/2e) ({Omega}m)^{-1}$, comparable to other TMD-based systems. Both torques show no clear dependence on the WSe$_{2}$ thickness, as expected for a Rashba system. Unexpectedly, we observe a strong in-plane magnetic anisotropy - up to about $6.6times10^{4} erg/cm^{3}$ - induced in permalloy by the underlying hexagonal WSe$_{2}$ crystal. Using scanning transmission electron microscopy, we confirm that the easy axis of the magnetic anisotropy is aligned to the armchair direction of the WSe$_{2}$. Our results indicate a strong interplay between the ferromagnet and TMD, and unveil the nature of the spin-orbit torques in TMD-based devices. These findings open new avenues for possible methods for optimizing the torques and the interaction with interfaced magnets, important for future non-volatile magnetic devices for data processing and storage.
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