Abstract
The textures of the spin fields in geometrically confined systems such as, quantum dots and quantum rings are introduced in this chapter. Analogous to the topological soliton skyrmion, the topological charge of the spin fields in real space are given by the winding numbers and Pontryagin indices. The trivial and non-trivial patterns of the spin fields are discussed. Spin-orbit couplings, inhomogeneous magnetic fields, and density-related effects, such as Coulomb interaction and impurity, make the spin textures vary in style and topologically non-trivial. Different topological charges can be considered to represent information in real devices, thus the manipulation of the topological charge in the quantum dots and rings by external conditions may be useful in spintronics and information techniques.
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