First Principles Study of Spin-Orbit Torque in Pt/Co and Pd/Co Bilayers

Spin-orbit torque (SOT) induced by spin Hall and interfacial effects in heavy metal(HM)/ferromagnetic(FM) bilayers has recently been employed to switch the magnetization direction using in-plane current injection. In this work, using the Keldysh Green's function approach and first principles electronic structure calculations we determine the Field-Like (FL) and Damping-Like (DL) components of the SOT for the HM/Co (HM = Pt, Pd) bilayers. We investigate the effects of HM and FM thicknesses, srain, oxidation as well as rigid shift of the chemical potential on the SOTs. We compare the HM thickness dependence and also efect of oxigen in the FM with the experimental results where we see an overall good agreement. The dependence of the SOT on the position of the Fermi level suggests that the DL-SOT dominated by the Spin Hall effect of the bulk HM.