基于符号回归方法探索磁性斯格明子结构近似解析式

Exploring approximate analytical expression for magnetic skyrmion structure based on symbolic regression method

磁性斯格明子是一种非平庸的拓扑磁结构,它能够在具有Dzyaloshinskii-Moriya(DM)相互作用的手性磁体中稳定存在,其静态以及动态特性与其结构特征息息相关.然而,一般情况下斯格明子结构解析式并不存在.因此,许多研究者给出了近似解析式.本文介绍了使用符号回归算法探索磁性斯格明子结构解析式的新方法,在考虑DM相互作用和外部磁场对磁性斯格明子结构的影响下,使用符号回归算法得到了两个较为合适的近似解析式,其适用范围与占主导地位的相互作用有关.研究结果验证了符号回归算法在探索磁性斯格明子结构解析式的强大能力,为磁结构的解析式探索提供了新思路.

Magnetic skyrmion is a kind of nontrivial topological magnetic structure,which can exist stably in chiral magnet with Dzyaloshinskii-Moriya(DM) interaction,and its static and dynamic properties are closely related to its structural characteristics.However,there are no general analytical expressions for skyrmion profiles.Therefore,many researchers have provided approximate solutions.In this paper,a new approach to exploring magnetic skyrmion structures is introduced by using a symbolic regression approach.Considering the influence of DM interaction and external magnetic field on magnetic skyrmion structure,two suitable approximate expressions are obtained through symbolic regression algorithms.The applicability of these expressions depends on the dominant interaction.The research results in this work validate the powerful capability of symbolic regression algorithms in exploring the magnetic skyrmion profiles.So,the present study provides a new method for finding the analytical expressions for magnetic structure.