The Inner Topological Structure And Defect Control Of Magnetic Skyrmions

The creation and annihilation of individual magnetic skyrmion demonstrates the potential for topological charge in future informat ion-storage concepts. Skyrmions are promising candi-dates as information carriers for future information-processing devices due to their character,such as small nanometres size, stability in topological structure, and easily be written or deleted,etc., it has become a focus of current research. In a few years, the nanoscale skvyrmions have been observed in laboratory, and the creation and annihilation of single skyrmion have been achieved.In this article, we research skyrmions by virtue of (?)-mapping topological current theory,and understand skyrmions by using Wu-Yang potential and projecting again. We reveal the relation of skyrmions and winding number and explain the creation and annihilation of magnetic skyrmions. With the help of Duan's decomposition theory of gauge potential and (?)-mapping topological current theory, we reveal topological property of skyrmions and prove its topological property can be characterized by Hopf index ?i and Brouwer degree ?i.At first, in viewpoint of potential we understand skyrmions again. By definition of skyrmion-s, we obtain another formula of skyrmions. Then we introduce Wu-Yang potential and prove that the integral kernel of skyrmions can be expressed as curvature tensor of Wu-Yang potential,then prove that the Wu-Yang potential is U(1) gauge potential.Next, we find a smooth vector field, and regard the projection of the normalized magneti-zation vector as .(?)(x1,x2), on the 2-dimensional smooth surface ?. We decompose Wu - Yang Gauge Potential. Then, we obtain a valid formula of winding number, illustrate the relation of skyrmions and winding number.Finally, we reveal the Inner structure of skyrmions and prove that the topological charge of skyrmions is one half of the winding number of the vector field (?)(x1,x2) at single zero point.We expound in theory how to control the creation and annihilation of skyrmions. The Landau-Lifshitz-Gilbert(LLG) equation tell one the changing law of the direction of magnetization vector,so one can control the direction of magnetization vector to obtain one single skyrmion with positive or opposite charge in experiment by using external local electronic or magnetic field.Our theory, which is based on Duan's decomposition theory of gauge potential, is not only to give a theory itself, but also be able to guide experiment.