Topological solitons in two-dimensional chiral magnets

手性天幕是发生在手性对称性破碎的磁体中的拓扑场构型。这些新颖的磁性纳米结构以孤立的孤子或排列在规则的晶格中出现，这相当于超导涡旋状态风格的新磁秩序。早在25年前，人们就根据一个非常简单的能量泛函理论预测了手性天空。关键效应是手性诱导的Dzyaloshinskii-Moriya相互作用，这是海森堡交换的反对称对应物，用螺旋型泛函表示。最近在各种材料体系中意外发现的手性粒子的实验结果，极大地激发了人们的兴趣和活动，并为物理学开辟了一个新的方向。由于其优异的稳定性和对电流的有效动态耦合，手性粒子成为未来自旋电子器件中有前途的信息载体。该项目关注的是在空间二维环境中由手性相互作用引起的拓扑模式的形成、结构和动力学。我们将用全局变分演算的方法讨论手性磁体模型中天元结构的发生和稳定性。我们将遇到的一个主要挑战是对控制相图的全面理解。目前的理论预测主要是基于能量泛函的数值最小化或特定Ansatz的特别优化。因此，需要一种全面的数学方法来严格表征关键领域。随着对孤立手性粒子的能量学和内部结构的进一步了解，我们的目标是研究由Landau-Lifshitz-Gilbert方程耦合自旋-扭矩效应引起的动态稳定性和有效动力学。我们期望在这个项目中获得的数学见解和开发的方法也将有助于探索手性天子物理学的新方面，并有助于寻找稳定磁性拓扑孤子的新机制。

Chiral skyrmions are topological field configurations occurring in magnets of broken chiral symmetry. These novel magnetic nanostructures emerge as isolated solitons or arranged in regular lattices, which amounts to a new magnetic order in the style of the vortex state in superconductivity. Chiral skyrmions have been predicted theoretically about 25 years ago on the basis of a remarkably simple energy functional. The key effect is chirality induced Dzyaloshinskii-Moriya interaction, which is the anti-symmetric counterpart of Heisenberg exchange and expressed in terms of helicity type functionals. The unexpected recent experimental discovery of chiral skyrmions in a variety of material systems has boosted the interest and activity and opened a new direction in physics. Owing to their outstanding stability properties and efficient dynamic coupling to electric currents, chiral skyrmions became a promising candidate as information carrier in future spintronic devices.The project is concerned with the formation, structure and dynamics of topological patterns arising from chiral interaction in the spatially two-dimensional context. We shall address the occurrence and stability of skyrmionic structures in models of chiral magnets by means of global variational calculus. A major challenge we shall meet is the comprehensive understanding of the governing phase diagram. The current theoretical prediction is mainly based on numerical minimization of the energy functional or ad-hoc optimization of a specific Ansatz. Therefore a global mathematical approach to rigorously characterize critical fields would be desirable. With improved knowledge on the energetics and internal structure of isolated chiral skyrmions, we aim to examine the dynamic stability and effective dynamics arising from the Landau-Lifshitz-Gilbert equation coupled to spin- torque effects. We expect that the mathematical insight achieved and methods developed within this project will also contribute to the exploration of new aspects in the physics of chiral skyrmions and to the search of new mechanisms to stabilize topological solitons in magnetism.