We investigate the magnetization relaxation of a one-dimensional helimagnetic system coupled to interacting itinerant electrons. The relaxation is assumed to result from the emission of plasmons, the elementary excitations of the one-dimensional interacting electron system, caused by slow changes of the magnetization profile. This dissipation mechanism leads to a highly nonlocal form of magnetization damping that is strongly dependent on the electron-electron interaction. Forward scattering processes lead to a spatially constant damping kernel, while backscattering processes produce a spatially oscillating contribution. Due to the nonlocal damping, the thermal fluctuations become spatially correlated over the entire system. We estimate the characteristic magnetization relaxation times for magnetic quantum wires and nuclear helimagnets.
Gilbert damping in metallic ferromagnets from Schwinger-Keldysh field theory: Intrinsically nonlocal and nonuniform, and made anisotropic by spin-orbit coupling
Nonlocal damping of spin waves in a magnetic insulator induced by normal, heavy, or altermagnetic metallic overlayer: A Schwinger-Keldysh field theory approach
Annihilation of topological solitons in magnetism with spin wave burst finale: The role of nonequilibrium electrons causing nonlocal damping and spin pumping over ultrabroadband frequency range
Reply to the Comment on "Negative Landau damping in bilayer graphene"
在这里，我们解决了Svintsov和Ryzhii [arXiv：1812.03764]对我们关于石墨烯中的负朗道阻尼的文章[Phys. Rev. Lett. 119，133901（2017）]。我们证明，由于动力学和正则动量之间的差异，漂移电流偏置的石墨烯的导电性是由一个伽利略变换时，电子-电子相互作用占主导地位，并迫使电子气以恒定的速度移动，类似于一个移动的介质。此外，它表明，在石墨烯的非局部效应既不排除一个负的朗道阻尼，也没有出现在石墨烯平台的不稳定性。
偏离平衡位置的共线磁化的进动和阻尼由Landau-Lifshitz-Gilbert方程描述。对于非共线磁化，不知道如何描述阻尼。我们利用第一性原理散射理论研究了重要铁磁合金Ni $_{80}$ Fe $_{20}$的一维横向畴壁的阻尼，并用唯象模型解释了结果.阻尼被发现不仅取决于磁化织构，但也对特定的动力学模式的布洛赫和Néel DW。即使在高度无序的Ni $_{80}$ Fe $_{20}$合金中，也发现阻尼是显著非局部的。
