Date of this Version
PHYSICAL REVIEW B 101, 020407(R) (2020)
The thickness dependence of spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers is studied using the ﬁrst-principles nonequilibrium Green’s function formalism combined with the Anderson disorder model. A systematic expansion in orthogonal vector spherical harmonics is used for the angular dependence of the torque. The dampinglike torque in Co/Pt and Co/Au bilayers can be described as a sum of the spin-Hall contribution, which increases with thickness in agreement with the spin-diffusion model, and a comparable interfacial contribution. The magnetoconductance in the plane perpendicular to the current in Co/Pt bilayers is of the order of a conductance quantum per interfacial atom, exceeding the prediction of the spin-Hall model by more than an order of magnitude. This suggests that the “spin-Hall magnetoresistance,” similarly to the dampinglike torque, has a large interfacial contribution unrelated to the spin-Hall effect.