Analytical Skyrmion Solutions of the Non-Linear Sigma Model
S. Trimper
Institute of Physics, Martin-Luther-University, Halle, Germany
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Motivated by studying quantum topological states we analyze the mesoscopic non-linear sigma model in two dimensions. We find systematically analytical solutions for the spatially depending magnetization density for arbitrary winding number under the constraint of topological protection. The methods allows also to get analytical expressions for other alignments such as a quadrupolar one. The inhomogeneous energy and skyrmion densities are calculated. Using a formulation of the local magnetization density in terms of a two component complex spinor field we get the related vector potential playing the role of the Berry curvature. The related magnetic field offers a spatial dependence which is completely different from electrodynamics. The dynamical stability of the solutions are discussed.

DOI:10.12693/APhysPolA.135.1275
topics: magnetism, non-linear sigma model, topological states, skyrmions