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arXiv · 2608.30338

Cartesian tensor equivariant machine-learning force field for spin-dependent atomistic simulations

Junjie Wang·Yijie Zhu·Zhongwei Zhang·Zhiyue Guo·Xudong Zhu·Lixin He·Chi Ding·Jian Sun
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Abstract

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.

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Junjie Wang, Yijie Zhu, Zhongwei Zhang, Zhiyue Guo, Xudong Zhu, Lixin He, Chi Ding, Jian Sun. 2026-08-31. Cartesian tensor equivariant machine-learning force field for spin-dependent atomistic simulations. https://arxiv.org/abs/2608.30338

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