用机器学习构建磁性力场，模拟复杂自旋结构演化
Machine Learning Force-Field Approach for Itinerant Electron Magnets
- 基于对称性不变表示的机器学习力场框架
- 成功复现三角晶格模型中的120°、自旋晶体等非共线态
- 适合研究自旋电子学中复杂磁序的动力学演化
我们综述了近期用于巡游电子磁体朗道-利夫希茨-吉尔伯特（LLG）动力学模拟的机器学习（ML）力场框架进展，重点聚焦于自旋构型的对称性不变表征的通用理论与实现。此类磁性描述符必须满足关于自旋旋转的可微性，以及对晶格点群对称性和内部自旋旋转对称性的不变性。我们提出一种基于参考不可约表示的高效实现方法，源自群论幂谱和双谱方法。该ML框架在广泛应用于自旋电子学研究的s-d模型上得到验证。结果表明，基于训练后ML模型预测的局域场进行的LLG模拟，能成功重现代表性非共线自旋结构，包括三角晶格s-d模型中的120°、四面体及自旋子晶体有序。基于ML模型的大规模热淬火模拟进一步揭示了有趣的冻结动力学和由自旋子与双子组成的玻璃态条纹相。本工作凸显了机器学习力场方法在巡游电子磁体复杂自旋序动力学建模中的价值。
原文摘要 · Abstract (English)
We review the recent development of machine-learning (ML) force-field frameworks for Landau-Lifshitz-Gilbert (LLG) dynamics simulations of itinerant electron magnets, focusing on the general theory and implementations of symmetry-invariant representations of spin configurations. The crucial properties that such magnetic descriptors must satisfy are differentiability with respect to spin rotations and invariance to both lattice point-group symmetry and internal spin rotation symmetry. We propose an efficient implementation based on the concept of reference irreducible representations, modified from the group-theoretical power-spectrum and bispectrum methods. The ML framework is demonstrated using the s-d models, which are widely applied in spintronics research. We show that LLG simulations based on local fields predicted by the trained ML models successfully reproduce representative non-collinear spin structures, including 120$^\circ$, tetrahedral, and skyrmion crystal orders of the triangular-lattice s-d models. Large-scale thermal quench simulations enabled by ML models further reveal intriguing freezing dynamics and glassy stripe states consisting of skyrmions and bi-merons. Our work highlights the utility of ML force-field approach to dynamical modeling of complex spin orders in itinerant electron magnets.
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