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 \(\sim 100\) m/s when an \(10^6\) V/m electric field is applied.

连同传导电子满足的自旋玻尔兹曼方程 (SBE)，我们求解 Landau-Lifshitz-Gilbert-Slonczewski (LLGS) 方程以研究由自旋极化电流驱动的畴壁 (DW) 运动。SBE 和 LLGS 方程通过由传导电子和 DW 的局部磁体之间的 s-d 交换相互作用引起的自旋转移矩 (STT) 耦合在一起。基于由SBE导出的自旋扩散方程，我们得到了源于自旋电流密度不均匀性的广义STT，它可以分为绝热和非绝热部分，但与以前的工作有些不同。我们通过外部电场下铁磁金属中 DW 运动的一个例子来说明这一点，自旋积累，以及传导电子的自旋电流密度和 DW 动力学。我们发现非绝热 STT 在自旋翻转弛豫时间内对总 STT 具有相当的贡献，这可以在非平衡 DW 动力学中发挥重要作用。我们还估计了 DW 的速度\(\sim 100\) m/s 当施加\(10^6\) V/m 电场时。