Microscopic Spin-Orbit Torque in 3d-5d Transition Metal Bilayers Based on Tight-Binding Model

Transition metal has attracted much attention both from fundamental physics and practical applications due to either the magnetization of 3d transition metals or strong spin-orbit coupling of 5d ones. Their combination at the interface of 3d-5d transition metal thin films leads to a variety of intriguing emergent phenomena, which are, however, not yet clearly understood. To give a realistic but strongly tunable description of these systems, we theoretically study the electronic structure of 3d and 5d transition-metal thin films by using first-principles' calculation and construct the corresponding tight-binding Hamiltonian on the basis of s, d, and p_z orbitals by employing two-center approximation based on Slater-Koster table. Non-linear least square fitting is employed to determine the tight-binding parameters. Based on this microscopic model, we further study the spin-orbit torque at the 3d-5d transition-metal bilayers by non-equilibrium Green's function method.