稳态或脉冲电流驱动的磁畴壁对自旋和电荷的抽运：一种自洽的多尺度含时量子/含时经典方法
Spin and charge pumping by steady or pulse current-driven magnetic domain wall: A self-consistent multiscale time-dependent-quantum/time-dependent-classical approach
摘要：
我们引入了一个多尺度框架，它结合了时间相关的非平衡格林函数（TD-NEGF）算法，线性缩放的时间步长的数量和描述量子力学传导电子的存在下，随时间变化的字段的任意强度或频率，经典的时间演化的本地化磁矩描述的Landau-Lifshitz-Gilbert（LLG）方程。TD-NEGF+LLG框架可以应用于各种问题，其中电流驱动的自旋力矩诱导磁矩的动力学作为下一代自旋电子学的关键资源。以磁畴壁（DW）为例，我们预测其运动将泵送与时间相关的自旋和电荷电流（在通过正常金属引线注入的未极化DC电荷电流的顶部驱动DW运动）。通过逆自旋霍尔效应将自旋电流的AC分量（其幅度随着DW接近（远离）正常金属引线而增大（减小））转换为AC电压提供了一种精确跟踪DW沿磁性纳米线的位置的工具。我们还量化了DW瞬态惯性位移，由于其加速和减速的脉冲电流和所需的自旋和电荷泵。最后，TD-NEGF+LLG作为非微扰（即，数值精确）框架允许我们建立所谓的自旋动力（SMF）理论的有效性的限制泵的电荷电流的时间相关的磁纹理-SMF理论的微扰解析公式变得不适用于大的频率（但不现实的磁系统），更重要的是，增加非共线性时，相邻的磁矩之间的角度超过$\simeq 10^\circ$。
英文摘要：
We introduce a multiscale framework which combines time-dependent nonequilibrium Green function (TD-NEGF) algorithms, scaling linearly in the number of time steps and describing quantum-mechanically conduction electrons in the presence of time-dependent fields of arbitrary strength or frequency, with classical time evolution of localized magnetic moments described by the Landau-Lifshitz-Gilbert (LLG) equation. The TD-NEGF+LLG framework can be applied to a variety of problems where current-driven spin torque induces dynamics of magnetic moments as the key resource for next generation spintronics. Using magnetic domain wall (DW) as an example, we predict that its motion will pump time-dependent spin and charge currents (on the top of unpolarized DC charge current injected through normal metal leads to drive the DW motion). The conversion of AC components of spin current, whose amplitude increases (decreases) as the DW approaches (distances from) the normal metal lead, into AC voltage via the inverse spin Hall effect offers a tool to precisely track the DW position along magnetic nanowire. We also quantify the DW transient inertial displacement due to its acceleration and deceleration by pulse current and the entailed spin and charge pumping. Finally, TD-NEGF+LLG as a nonperturbative (i.e., numerically exact) framework allows us to establish the limits of validity of the so-called spin-motive force (SMF) theory for pumped charge current by time-dependent magnetic textures---the perturbative analytical formula of SMF theory becomes inapplicable for large frequencies (but unrealistic in magnetic system) and, more importantly, for increasing noncollinearity when the angles between neighboring magnetic moments exceed $\simeq 10^\circ$.
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