  In order to enhance the magnitude of spin-orbit torque (SOT), considerable
experimental works have been devoted to studying the thickness dependence of
the different layers in multilayers consisting of heavy metal (HM), ferromagnet
(FM) and capping layers. Here we present a theoretical model based on the
spin-drift-diffusion (SDD) formalism to investigate the effect of the capping
layer properties such as its thickness on the SOT observed in experiments. It
is found that the spin Hall-induced SOT can be significantly enhanced by
incorporating a capping layer with opposite spin Hall angle to that of the HM
layer. The spin Hall torque can be maximized by tuning the capping layer
thickness. However, in the absence of the spin Hall effect (SHE) in the capping
layer, the torque decreases monotonically with capping layer thickness.
Conversely, the spin Hall torque is found to decrease monotonically with the FM
layer thickness, irrespective of the presence or absence of SHE in the capping
layer. All these trends are in correspondence with experimental observations.
Finally, our model suggests that capping layers with long spin diffusion length
and high resistivity would also enhance the spin Hall torque.
