Domain wall motion driven by spin transfer torque from spin-polarized current

Together with the spinor Boltzmann equation (SBE) satisfied by conduction electrons, we solve the Landau–Lifshitz–Gilbert–Slonczewski (LLGS) equation to study the domain wall (DW) motion driven by the spin-polarized current. The SBE and LLGS equation are coupled together by the spin transfer torque (STT) induced by the s–d exchange interaction between the conduction electrons and the local magnet of DW. Based on the spin diffusion equation derived from SBE, we obtain a generalized STT originated from the inhomogeneity of spin current density, which can be divided into adiabatic and nonadiabatic parts but with somewhat different terms from the previous works. We illustrate this by an example of DW motion in a ferromagnet metal under an external electric field, the spin accumulation, and spin current density of conduction electrons and the DW dynamics are presented. We find that the nonadiabatic STT has a comparable contribution to the total STT within the spin-flip relaxation time, which can play an important role in the nonequilibrium DW dynamics. We also estimate the velocity of DW $$\sim 100$$ ∼ 100 m/s when an $$10^6$$ 10 6 V/m electric field is applied.