First-principles investigation of transient spin transfer torque in magnetic multilayer systems

Abstract

By employing the nonequilibrium Green's function (NEGF) method, the transient current and the transient behavior of the spin transfer torque (STT) of the magnetic layered system are investigated within the framework of density functional theory (DFT). To reduce the huge computational cost of the transient calculation, especially when the dense mesh of $k$ sampling is present for layered systems, the complex absorbing potential (CAP) and the Pad\'e spectrum decomposition are used so that the energy integrals in calculating transient current and STT can be performed analytically using residue theorem, which dramatically reduces the computational complexity of the first-principles calculation of transient behavior. As an application of the NEGF-DFT-CAP formalism, the transient current and current-induced STT of the Co/Cu/Co trilayer system are studied under an upward bias pulse for different angles of magnetization direction between two leads. The transient current shows a damped oscillatory behavior with the oscillation frequency proportional to the applied bias, leading to a relaxation time of hundreds of femtoseconds. The time-dependent STTs show roughly the same profile for systems with different rotating angles. The oscillation behavior is also observed as the transient STT approaches the steady state value. Such oscillations can be attributed to the interface resonant states.