动力学和电流诱导的Dzyaloshinskiii-Moriya相互作用：非共线磁体中阻尼、旋磁和电流诱导转矩的作用
Dynamical and current-induced Dzyaloshinskii-Moriya interaction: Role for damping, gyromagnetism, and current-induced torques in noncollinear magnets
摘要：
外加电流和磁化动力学都改变了Dzyaloshinskiii-Moriya相互作用（Dzyaloshinskiii-Moriya interaction，简称Dzyaloshinskii-Moriya interaction），我们分别称之为电流诱导Dzyaloshinskii-Moriya相互作用（CIDMI）和动态Dzyaloshinski-Moriya相互作用（Dzyaloshinski-Moriya interaction，简称Dzyaloshinski-Moriya interaction）。我们报告了一个CIDMI理论和DALK理论。CIDMI的逆包括通过随时间变化的磁化梯度$\partial^2 M(r,t)/\partial r\partial t$的电荷泵浦，而DIMMI的逆描述了由$\partial^2 M(r,t)/\partial r\partial t$产生的转矩。在非共线磁体中，CIDMI和DIMI取决于局部磁化方向。由此产生的空间梯度对应的扭矩，需要包括到吉尔伯特阻尼，回转磁，电流感应扭矩（CITS）的理论，以满足Onsager互易关系。CIDMI与磁化动力学引起的轨道磁性的改变有关，我们称之为动态轨道磁性（DOM），DOM的空间梯度有助于电荷泵。我们目前的应用程序，这种形式主义的CITS和转矩转矩相关的纹理Rashba铁磁体。
英文摘要：
Both applied electric currents and magnetization dynamics modify the Dzyaloshinskii-Moriya interaction (DMI), which we call current-induced DMI (CIDMI) and dynamical DMI (DDMI), respectively. We report a theory of CIDMI and DDMI. The inverse of CIDMI consists in charge pumping by a time-dependent gradient of magnetization $\partial^2 M(r,t)/\partial r\partial t$, while the inverse of DDMI describes the torque generated by $\partial^2 M(r,t)/\partial r\partial t$. In noncollinear magnets CIDMI and DDMI depend on the local magnetization direction. The resulting spatial gradients correspond to torques that need to be included into the theories of Gilbert damping, gyromagnetism, and current-induced torques (CITs) in order to satisfy the Onsager reciprocity relations. CIDMI is related to the modification of orbital magnetism induced by magnetization dynamics, which we call dynamical orbital magnetism (DOM), and spatial gradients of DOM contribute to charge pumping. We present applications of this formalism to the CITs and to the torque-torque correlation in textured Rashba ferromagnets.
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