Duan's Topological Current Theory, Duan-Ge's U(1) Gauge Potential Decomposition Theory And Their Applications In Ferromagnets And Spin Hall Effects

In this dissertation,we use Duan's topological current theory and Duan-Ge's decomposition theory of gauge potential proposed by Prof.Yi-Shi Duan to study the topological properties of ferromagnets and spin Hall effects.The topological defects of these systems are characterized by the topological numbers of Duan's topological current theory-the Hopf indices and the Brouwer degrees.Their locations and motions also can be rigorously determined by Duan's topological current theory.Firstly,we give an introduction of Duan's topological current theory and its branch theory,we also introduce the SO(2) decomposition theory of gauge potential and the Duan-Ge's U(1) decomposition theory of gauge potential.Secondly,by making use of Duan's topological current theory and Duan-Ge's decomposition theory of gauge potential,we investigate the topological defects of ferromagnets.We point out that the "magnetic vorticity"Ω~αis the common topological origin of these defects in planar ferromagnets and three-dimensional ferromagnets.We study the two-dimensional skyrmions in planar ferromagnets and discuss the branch processes of them and the generation and annihilation of skyrmion-antiskyrmion pairs.We also study the three-dimensional skyrmions and magnetic vortex rings in(3+1)-dimensional isotropic ferromagnets,and we point out that the Hopf invariant Q is a proper topological invariant to describe the topology of these knot-like magnetic vortex rings.Finally,we investigate the spin Hall effect in neutral atomic systems,it is induced by two external light fields.We study the skyrmion excitations from the rotation of spin current density in this kind of spin Hall effect and we find out that these skyrmions can generate or annihilate at the limit points and they encounter,split,or merge at the bifurcation points. The meaning of our theoretical investigations is that we point out the important topological meaning of magnetic vorticity in ferromagnets,and from it we get the topological excitations in planar ferromagnets and three-dimensional ferromagnets.So we clarify the origin of the topological defects in ferromagnets. When we study the spin Hall effect induced by optical fields in neutral atomic systems,we give qualitative analyses for its skyrmion excitations,and these may give a good guidance for those experts to find this kind of excitations in these systems in experiments.