AI 中文总结
研究针对磁势能面建模难题，提出自旋张量等变势（STEP）。该方法将磁矩视为连续自由度并嵌入等变表示，通过特定耦合引入物理偏差。实验表明其数据效率高，在多基准测试中精度有竞争力，能高保真再现多种物理特性，是有效建模框架。
AI 中文摘要
准确且高效地对磁势能面进行建模仍然具有挑战性，因为对各种非共线自旋晶格构型进行自旋极化第一性原理计算在计算上要求很高。本文引入了自旋张量等变势（STEP），这是一种磁机器学习原子间势，将矢量磁矩视为连续几何自由度并将其嵌入等变表示中。通过中心 - 环境张量积将中心自旋表示与其局部自旋晶格环境耦合，STEP引入了物理信息偏差，同时保持平移不变性和$\mathrm{SO}(3)$等变性，并支持特征级时间反演对称化。对单层CrI$_3$的学习曲线分析表明，STEP实现了显著的数据效率，高阶张量通道和迭代中心 - 环境耦合导致能量、力和磁力误差的陡峭学习曲线。在公共的FeAl、CrN和Fe基准上，与最近的磁机器学习势相比，STEP实现了有竞争力或更高的精度。使用紧凑但有代表性的CrI$_3$数据集，STEP以高保真度再现了声子色散和磁振子谱，捕捉了微妙的各向异性磁相互作用。对于Fe$_2$Mo$_3$O$_8$，STEP进一步提供了磁振子 - 声子杂化的定量描述并再现了其特征磁振子极化子色散。最后，由STEP驱动的自旋动力学模拟得出的单层CrI$_3$和体心立方Fe的居里温度与实验结果吻合良好。这些结果确立了STEP作为用于建模自旋 - 晶格耦合、磁激发和有限温度磁行为的物理信息丰富、数据高效且可扩展的框架。
英文摘要
Accurate and efficient modeling of magnetic potential energy surfaces remains challenging because spin-polarized first-principles calculations for diverse non-collinear spin-lattice configurations are computationally demanding. Here we introduce the Spin Tensor Equivariant Potential (STEP), a magnetic machine-learning interatomic potential that treats vector magnetic moments as continuous geometric degrees of freedom and embeds them in an equivariant representation. By coupling the central spin representation to its local spin-lattice environment through a Center-Environment Tensor Product, STEP introduces a physics-informed bias while preserving translational invariance and $\mathrm{SO}(3)$ equivariance and supporting feature-level time-reversal symmetrization. Learning-curve analysis on monolayer CrI$_3$ shows that STEP achieves pronounced data efficiency, with higher-order tensor channels and iterative center-environment couplings leading to steep learning curves for energy, force, and magnetic force errors. On public FeAl, CrN, and Fe benchmarks, STEP achieves competitive or improved accuracy compared with recent magnetic machine-learning potentials. Using a compact but representative CrI$_3$ dataset, STEP reproduces phonon dispersions and magnon spectra with high fidelity, capturing subtle anisotropic magnetic interactions. For Fe$_2$Mo$_3$O$_8$, STEP further provides a quantitative description of magnon--phonon hybridization and reproduces its characteristic magnon polaron dispersion. Finally, spin dynamics simulations driven by STEP yield Curie temperatures for monolayer CrI$_3$ and bcc Fe in good agreement with experiments. These results establish STEP as a physically informed, data-efficient, and scalable framework for modeling spin-lattice coupling, magnetic excitations, and finite-temperature magnetic behavior.
