Weak–strong uniqueness for the Landau–Lifshitz–Gilbert equation in micromagnetics

We consider the time-dependent Landau–Lifshitz–Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time. Unlike available results in the literature, our analysis also includes the physically relevant lower-order terms like Zeeman contribution, anisotropy, stray field, and the Dzyaloshinskii–Moriya interaction (which accounts for the emergence of magnetic Skyrmions). Moreover, our proof gives a template on how to approach weak–strong uniqueness for even more complicated problems, where LLG is (nonlinearly) coupled to other (nonlinear) PDE systems.     

具有Dzyaloshinskii-Moriya相互作用的二维spin-Peierls模型的基态行为

在平均场理论基础上,研究了具有DzyaloshinskiiMoriya(缩写为DM)相互作用的二维spinPeierls模型以及DM相互作用对二聚化的影响.研究表明,随模型参量的不同,DM相互作用能加强或削弱二聚化位移.另外,发现DM相互作用对二聚化位移的依赖程度参量λ存在一个特殊点λc,当λ=λc时,DM相互作用对二聚化没有影响.随晶格弹性系数的增加,λc将增大,而链间耦合将使λc减小 关键词： 二维spinPeierls模型 DM相互作用     

Fast current-induced motion of a transverse domain wall induced by interfacial Dzyaloshinskii–Moriya interaction

Based on a theoretical study, we show that the interfacial Dzyaloshinskii–Moriya interaction results in very efficient current-induced manipulation of a transverse domain wall in magnetic nanowires. The efficient domain wall motion is caused by combined effects of the domain wall distortion induced by the interfacial Dzyaloshinskii–Moriya interaction and the damping-like spin–orbit spin transfer torque. We find that with reasonable parameters, the domain wall velocity reaches a few hundreds m/s at the current density of 10⁷ A/cm², which has never been achieved before. Our result will be beneficial for low-power operation of domain wall devices.     

Control of Quantum-Memory Induced by Generated Thermal XYZ-Heisenberg Entanglement: y-Component DM Interaction

This study explores the thermal quantum-memory-assisted entropic uncertainty relation (QM-EUR) and entanglement in a general two-qubit XYZ-Heisenberg spin chain model in the presence of the Dzyaloshinskii–Moriya (DM) interaction. The characterization of y-component DM and spin–spin interactions are particularly focused. It is found that the DM and spin–spin interaction strengths highly regulate the flow behavior and the initial final levels of QM-EUR and entanglement. In comparison, the spin–spin interaction strength in the z-direction remains useful in both ferromagnetic and anti-ferromagnetic regimes for entropic uncertainty suppression and entanglement generation. Additionally, the negative and the positive $y\mathrm{-}$directed DM values can usefully turn classical states into resourceful quantum states. The dynamics of thermal QM-EUR and entanglement-of-formation have symmetric behaviors only with respect to y-component DM and z-component spin–spin interaction. Finally, different critical points of temperature, $y\mathrm{-}$component DM as well as spin–spin interaction are encountered, which should be opted to preserve quantum correlations and degrade uncertainty.