  Recently, transition metal dichalcogenides (TMDs) have been extensively
studied for their efficient spin-orbit torque generation in TMD/ferromagnetic
bilayers, owing to their large spin-orbit coupling, variety in crystal
symmetries, and pristine interfaces. Although the TMD layer was considered
essential for the generation of the observed SOTs, recent reports show the
presence of a self-torque in single-layer ferromagnetic devices with magnitudes
comparable to TMD/ferromagnetic devices. Here, we perform second-harmonic Hall
SOT measurements on metal-organic chemical vapor deposition (MOCVD) grown
MoS$_{2}$/permalloy/Al$_{2}$O$_{3}$ devices and compare them to a single-layer
permalloy/Al$_{2}$O$_{3}$ device to accurately disentangle the role of
self-torques from contributions from the TMD layer. We report a damping-like
self-torque conductivity of opposite sign in our single-layer
permalloy/Al$_{2}$O$_{3}$ device compared to one
MoS$_{2}$/permalloy/Al$_{2}$O$_{3}$ device, and find no significant one for all
other MoS$_{2}$/permalloy/Al$_{2}$O$_{3}$ devices. This indicates a competition
between the self-torque and the torque arising from the TMD layer, which would
reduce the observed torque in these bilayers. In addition, we find a field-like
spin-torque conductivity of comparable magnitude to control
MoS$_{2}$/permalloy/Al$_{2}$O$_{3}$ devices, indicating only a minor role of
the MoS$_{2}$ layer. Finally, we find a linear dependence of the SOT
conductivity on the Hall bar leg/channel width ratio of our devices, indicating
that the Hall bar dimensions are of significant importance for the reported SOT
strength. Our results accentuate the importance of delicate details, like
device asymmetry, Hall bar dimensions, and self-torque generation, for the
correct disentanglement of the microscopic origins underlying the SOTs,
essential for future energy-efficient spintronic applications.
