Logistic growth of skyrmions in 3D chiral magnets

TL;DR

This paper derives an analytical model showing that the skyrmion number in 3D chiral magnets follows a logistic growth pattern during topological phase transitions, validated by numerical simulations.

Contribution

It introduces an analytical expression for skyrmion number evolution based on topological current theory, linking it to monopole charge flow during phase transition.

Findings

Skyrmion number follows a logistic growth function.

Monopole charge evolution is proportional to the derivative of skyrmion number.

Analytical results match numerical simulations with 99.94% accuracy.

Abstract

The process of topological phase transition in a chiral magnetic material from skyrmion lattice phase to helical phase has been investigated numerically and experimentally, yet the analytical expression of the evolution of skyrmion number and emergent magnetic monopole charge during the process is still waiting to be explored. In this letter, by utilizing the topological current theory, we show that the change of skyrmion number of a layer in the system is equal to the net monopole charges that flows through the layer. Based on this relation, with the help of statistical argument, we derive the analytical expressions of the skyrmion number and the monopole charge as functions of the external magnetic field. We find that the evolution of the skyrmion number is exactly the logistic growth function, and the evolution of the monopole charge is proportional to the derivative of the skyrmion number of the system. our analytical results are in good agreement with the numerical simulations in \cite{2013SCIENCE}. The goodness of data fitting goes up to 99.94\%.