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The process of topological phase transition in a chiral magnetic materialfrom skyrmion lattice phase to helical phase has been investigated numericallyand experimentally, yet the analytical expression of the evolution of skyrmionnumber and emergent magnetic monopole charge during the process is stillwaiting to be explored. In this letter, by utilizing the topological currenttheory, we show that the change of skyrmion number of a layer in the system isequal to the net monopole charges that flows through the layer. Based on thisrelation, with the help of statistical argument, we derive the analyticalexpressions of the skyrmion number and the monopole charge as functions of theexternal magnetic field. We find that the evolution of the skyrmion number isexactly the logistic growth function, and the evolution of the monopole chargeis proportional to the derivative of the skyrmion number of the system. ouranalytical results are in good agreement with the numerical simulations in\cite{2013SCIENCE}. The goodness of data fitting goes up to 99.94\%.

Logistic growth of skyrmions in 3D chiral magnets