Topological solitons in two-dimensional chiral magnets

手征Skyrmions是出现在手征对称性破缺的磁体中的拓扑场组态。这些新颖的磁性纳米结构以孤立的孤立子或排列在规则晶格中的形式出现，从而形成了超导中涡旋态的新磁序。大约25年前，在一个非常简单的能量泛函的基础上，从理论上预测了手性Skyrmions。关键效应是手性诱导的Dzyaloshinskii-Moriya相互作用，它是反对称的Heisenberg交换，用螺旋度类型泛函表示。最近在各种材料体系中发现的手性Skyrmions的意外实验发现，激发了人们的兴趣和活力，并开辟了物理学的新方向。手性Skirmions由于其优异的稳定性和对电流的有效动态耦合，成为未来自旋电子器件中最有希望的信息载体。该项目致力于在空间二维背景下研究手性相互作用产生的拓扑图的形成、结构和动力学。我们将用整体变分的方法讨论手性磁体模型中天子结构的发生和稳定性。我们将迎接的一项重大挑战是全面了解管理相图。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，需要一种全球数学方法来严格描述关键领域。随着对孤立手征Skyrmions的能量学和内部结构的进一步了解，我们的目标是研究由耦合了自旋-扭矩效应的Landau-Lifshitz-Gilbert方程产生的动力学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发展的方法也将有助于探索手征天空微子物理的新方面，并有助于寻找稳定磁中拓扑孤子的新机制。

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.