# Thermally Driven Topology in Chiral Magnets

## Abstract

Magnetism is an old field in condensed matter physics, but it is still vibrant and full of excitement. Regardless of deep fundamental physics therein, it also has broad application in engineering technology, modern hard disk drive as an example. Magnetic skyrmion, a vortex-like structure in two-dimensional magnetic systems, has been discovered in various magnetic materials, among which chiral magnets are a family of candidates. The skyrmions are characterized by nonzero topological charges. The vortex-like structure of skyrmions makes skyrmion materials good candidates of new generation of data storage device. So understanding the transport properties of the skyrmion materials is important for the possible application in the future. The Hall effect is a key aspect of electron transports. The topological Hall effect, which is one component in the total Hall effect, only depends on the magnetic structures, and the topological Hall conductivity is proportional to the topological charge. It thus serves as the transport signature of magnetic skyrmions. The major mission of this thesis is to investigate the topological charge distribution in realistic models and uncover the relationship between the existence of skyrmions and other chiral excitations. The organization of the thesis is the following. The first chapter is the introduction. A historical survey about magnetic skyrmions and chiral magnets is presented firstly. The magnetic skyrmion is identified by the topological charge. Further, the relationship between the topological hall effect and topological charge is described by the emergent electrodynamics. The importance of the topological charge in chiral magnets is explained in this part. Following the importance of the topological charge, the investigation of topological charge in two-dimensional chiral magnets is presented in the second chapter. The Monte Carlo simulation is employed to calculate the topological charge on a square lattice. The results show that the nonzero topological charge is not necessarily correlated to the existence of skyrmions in chiral magnets. To understand the numerical results, simple analysis based on the physical picture of a triangle on the square lattice is performed. Then we calculate the topological charge in continuum model of chiral magnets. At the high temperature limit, the numerical results, picture analysis and the analytic result are consistent. Then, in this chapter, there is a description of the recent experimental work on thin film SrRuO3 which confirmed our theoretical prediction. A discussion on spin chirality, topological charge and Hall conductivity is presented in the end. However, no experiment on chiral magnets has been on a perfect monolayer system. So we extend the investigation of topological charge into three-dimensional situation. This work is introduced in the third chapter. The Monte Carlo simulation and the analytical calculation are presented firstly. A special issue in three-dimensional chiral magnets is the thickness dependence. The Monte Carlo simulation is used to address this issue. A combination of analytical calculation and physical picture of magnons is used to explain the numerical results well. Similar as the second chapter, the experiment on finite thickness SrRuO3 is described. Because the effective Dzyaloshinskii—Moriya interaction is due to the interface effect which cannot be used to judge our numerical results based on homogenous chiral magnets. The Heisenberg interaction in the system described in the previous two chapters is ferromagnetic interaction. More physical results with antiferromagnetic interaction are expected in different magnetic system. In the fourth chapter, a review of the work on a frustrated magnet with hexagonal lattice is introduced. The direction of the DM interaction of the hexagonal lattice is perpendicular to the bonds of nearest magnetic atoms. The topological charge is calculated numerically. A similar thermally driven topology as found in chiral magnets is achieved by investigating the topological charge. Following that, the system with staggered DM interaction is discussed. The study of the topological charge in this system not only gives the evolution of thermally driven topology of the system, but also distinguishes the topological charge and spin chirality based on the antiferromagnetic interaction. Not only thermally driven topology in chiral magnets but also the driven motion of skyrmions are interesting to us. Inspired by the similarity of the vortex state in the Type-II superconductor and skyrmion crystal phase, we investigate the proximity effect between the skyrmion material and non-centrosymmetric s-wave superconductor. The method is to calculate the effective interaction between the Cooper pairs and skyrmions. A field-theoretical approach is employed to this end.