The aim of this paper is to present a rigorous mathematical proof of the dynamical laws for the topological solitons( magnetic vortices) in ferromagnets and anti-ferromagnets. It is achieved through the conservation l...The aim of this paper is to present a rigorous mathematical proof of the dynamical laws for the topological solitons( magnetic vortices) in ferromagnets and anti-ferromagnets. It is achieved through the conservation laws for the topological vorticity and the weak convergence methods.展开更多
Two kinds of topological soliton （skyrmion and magnetic vortex ring） in ferromagnets are studied. They have the common topological origin, a tensor Hαβ = n→·（δαn→×βδn→）, which describes the non-...Two kinds of topological soliton （skyrmion and magnetic vortex ring） in ferromagnets are studied. They have the common topological origin, a tensor Hαβ = n→·（δαn→×βδn→）, which describes the non-trivial distribution of local orientation of magnetization n→ at large distances in space. The topological stability of skyrmion is protected by the winding number. Knot-like topological defect as magnetic vortex rings is also studied. On the assumption that magnetic vortex rings are geometric lines, we present their δ-function distribution in ferromagnetic materials. Furthermore, it is briefly shown that Hopf invariant is a proper topological invariant to describe the topology of magnetic vortex rings.展开更多
文摘The aim of this paper is to present a rigorous mathematical proof of the dynamical laws for the topological solitons( magnetic vortices) in ferromagnets and anti-ferromagnets. It is achieved through the conservation laws for the topological vorticity and the weak convergence methods.
基金National Natural Science Foundation of China under Grant No.10275030
文摘Two kinds of topological soliton （skyrmion and magnetic vortex ring） in ferromagnets are studied. They have the common topological origin, a tensor Hαβ = n→·（δαn→×βδn→）, which describes the non-trivial distribution of local orientation of magnetization n→ at large distances in space. The topological stability of skyrmion is protected by the winding number. Knot-like topological defect as magnetic vortex rings is also studied. On the assumption that magnetic vortex rings are geometric lines, we present their δ-function distribution in ferromagnetic materials. Furthermore, it is briefly shown that Hopf invariant is a proper topological invariant to describe the topology of magnetic vortex rings.
