Non-equilibrium spatial distribution of Rashba spin torque in   ferromagnetic metal layer
  We study the spatial distribution of spin torque induced by a strong Rashba spin-orbit coupling (RSOC) in a ferromagnetic (FM) metal layer, using the Keldysh non-equilibrium Green's function method. In the presence of the s-d interaction between the non-equilibrium conduction electrons and the local magnetic moments, the RSOC effect induces a torque on the moments, which we term as the Rashba spin torque.   A correlation between the Rashba spin torque and the spatial spin current is presented in this work, clearly mapping the spatial distribution of Rashba Spin torque in a nano-sized ferromagnetic device. When local magnetism is turned on, the out-of-plane (Sz) Spin Hall effect (SHE) is disrupted, but rather unexpectedly an in-plane (Sy) SHE is detected. We also study the effect of Rashba strength (\alpha_R) and splitting exchange (\Delta) on the non-equilibrium Rashba spin torque averaged over the device. Rashba spin torque allows an efficient transfer of spin momentum such that a typical switching field of 20 mT can be attained with a low current density of less than 10^6 A/cm^2. 
N. L. Chung, M. B. A. Jalil and S. G. Tan
cond-mat.mes-hall