Cartesian tensor equivariant machine-learning force field for spin-dependent atomistic simulations
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
Funders: National Natural Science Foundation of China, Ministry of Education of the People's Republic of China, China Postdoctoral Science Foundation, Nanjing University, Collaborative Innovation Center of Advanced Microstructures, National Science and Technology Major Project, Fundamental Research Funds for the Central Universities, Science Challenge Project
OpenAlex ID: W7204895200