Inefficiency of orbital Hall effect on the spin torque in transition metal/ferromagnet bilayers

Current induced spin torque is essential and crucial in spintronics. In this work, we systematically investigate the spin torque in transition metal(TM)/ferromagnet(FM) bilayers by using first-principles calculations and taking into account the phonon scattering at room temperature. To examine the spin and orbital Hall contribution, the studied transition metals include 5d heavy metals Pt, W, Au as well as 3d light metals Ti, V, Cr, Cu etc. We found that in TM/CoFe bilayers with typical 3d and 5d transition metals, the spin torque on CoFe mainly originates from spin Hall mechanism with the magnitude and sign of damping like torque efficiency consistent with the spin Hall conductivity. In TM/Ni bilayers, the spin torque is contributed by three mechanisms including spin and orbital Hall current in TM, as well as self-torque in Ni. The orbital Hall contribution in TM is accompanied by noteworthy opposite self spin torque in Ni, which leads to inapparent torque efficiency in Ti/Ni and V/Ni bilayers. For TM(5d heavy metal)/Ni bilayers, the spin torque induced by orbital Hall and self-torque in Ni nearly cancel each other, which makes the spin torque on Ni still align with that of the spin Hall effect in TM. Our work reveals much less efficient contribution of orbital Hall than spin Hall effect on the spin torque in transition metal/ferromagnet bilayers.