用于自旋依赖原子模拟的笛卡尔张量等变机器学习力场

中文摘要 AI 辅助

磁性材料的原子结构与自旋自由度之间存在复杂耦合，对实验相关长度和时间尺度的原子模拟构成了基础挑战。本文提出HotPP-Spin，这是HotPP（用于磁性机器学习原子间势的自旋依赖扩展版本），基于笛卡尔张量等变消息传递构建。原子磁矩被视为显式轴矢量自由度，空间反演和时间反演宇称通过张量耦合进行传播。该构造无需施加预定义的解析相互作用形式，即可统一描述以交换作用为主的相互作用和自旋轨道诱导的相互作用。标量自旋依赖势能面通过微分产生能量守恒的原子力和磁有效场。对共线磁性、非共线磁性以及自旋轨道耦合诱导的磁各向异性的基准测试表明，HotPP-Spin在同一通用框架内准确描述了磁能景、磁力和依赖磁序的能量-体积关系。对于H相单层VSe₂，使用学习到的磁有效场进行随机自旋动力学模拟，确定有限尺寸磁有序相变温度为415--435 K，与报道的实验值418.5±7.8 K数值吻合良好。这些结果确立了笛卡尔张量消息传递作为连接第一性原理磁能量学与结构和自旋耦合现象的大规模原子模拟的通用途径。

英文摘要

Magnetic materials exhibit an intricate coupling between atomic structure and spin degrees of freedom, posing a fundamental challenge for atomistic simulations across experimentally relevant length and time scales. Here we introduce HotPP-Spin, a spin-dependent extension of HotPP for magnetic machine learning interatomic potentials, built on Cartesian tensor equivariant message passing. Atomic magnetic moments are treated as explicit axial-vector degrees of freedom, while spatial-inversion and time-reversal parities are propagated through the tensor couplings. This construction provides a unified representation of exchange-dominated and spin-orbit-induced interactions without imposing predefined analytical interaction forms. A scalar spin-dependent potential energy surface yields energy-conserving atomic forces and magnetic effective fields through differentiation. Benchmarks spanning collinear magnetism, noncollinear magnetism, and spin-orbit-coupling-induced magnetic anisotropy show that HotPP-Spin accurately describes magnetic energy landscapes, magnetic forces, and magnetic-order-dependent energy-volume relations within the same general framework. For H-phase monolayer VSe\(_2\), stochastic spin-dynamics simulations using the learned magnetic effective fields locate the finite-size magnetic ordering crossover at 415--435~K, in close numerical agreement with the reported experimental value of \(418.5\pm7.8\)~K. These results establish Cartesian tensor message passing as a general route for connecting first-principles magnetic energetics with large-scale atomistic simulations of coupled structural and spin phenomena.

发表机构

• Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥综合性国家科学中心人工智能研究院）
• Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）
• Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）

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