|
The angular dependence of spin-orbit torque in disordered ferromagnet/heavy-metal bilayers is calculated using a first-principles nonequilibrium Green's function formalism with an explicit supercell disorder averaging. We consider Co/Pt, Co/Au, and Co/Pd bilayers with varying thicknesses and disorder strengths. In addition to the usual dampinglike and fieldlike terms, the odd torque contains a sizable planar Hall-like term (m⋅E)m×(z×m) whose contribution to current-induced damping is consistent with experimental observations. The dampinglike torquance depends weakly on disorder strength, suggesting that it is dominated by the intrinsic mechanism. The fieldlike torquance declines with increasing disorder, consistent with the inverse spin-galvanic effect being dominant. It is found that the torques that contribute to damping are almost entirely due to spin-orbit coupling on the Pt atoms, but the fieldlike torque does not require it. The calculated thickness dependence suggests that the dampinglike torque has a bulk-like contribution due to the spin-Hall effect and an interfacial contribution of a comparable magnitude.
|
