Topology in Magnetism: from generation and deformation to interaction

Abstract

In magnetic materials, electron spin underlies magnetism, and collective interactions among localized spins give rise to topological magnetic structures such as domain walls, vortices, and skyrmions. These structures are promising candidates for future spintronic applications due to their nanoscale size, non-volatility, topological stability, and characteristic topology-oriented dynamics. In particular, differing topological characteristics determine the stability and dynamics of each structure, so a clear understanding of topology is essential for applications. However, it is difficult to fully adapt topological concepts to magnetic structures, since the continuum description on a discrete lattice and the narrow energetic stability regimes leave a gap. This gap allows the formation and annihilation of otherwise topologically protected magnetic structures. These transitions enable information writing and deletion, but complicate control and interpretation of dynamics and interactions. In this thesis, we employ topology as a common language to interpret magnetic structure dynamics, where formation, deformation, and interactions depend on their topological properties. In perpendicular magnetic anisotropy nanowires with interfacial Dzyaloshinskii–Moriya interaction, fields above the Walker limit drive domain wall deformation, accompanied by a topological transition that can repeatedly generate skyrmions. We identify the role of the internal wall structure in this process and provide a theoretical analysis. Based on the concept of a skyrmion bag, which contains a variable number of skyrmions in a larger skyrmion, we reconfigure the topological invariants of the magnetic structure, analyze their interactions using Thiele equations, and establish the dynamics with equations that include topological charge. There are many benefits to applying topology to magnetic structures, which simplify complex magnetization dynamics and enhance the understanding and prediction of dynamical properties. The finding of unconventional topological properties and the fundamental study of topological magnetic structures would provide a scientific breakthrough for understanding magnetic structure dynamics. Additionally, the data and analytical methods in this thesis, as well as follow-up studies on topological transitions and interactions among magnetic structures, can help bridge perspectives across different magnetic structures and unify insights from past and ongoing work.