{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30338",
  "author_total": 8,
  "authors": [
    {
      "name": "Junjie Wang"
    },
    {
      "name": "Yijie Zhu"
    },
    {
      "name": "Zhongwei Zhang"
    },
    {
      "name": "Zhiyue Guo"
    },
    {
      "name": "Xudong Zhu"
    },
    {
      "name": "Lixin He"
    },
    {
      "name": "Chi Ding"
    },
    {
      "name": "Jian Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ckh14crjqgbsx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30338",
  "fulltext_url": null,
  "id": "ckh14crjqgbsx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30338",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "2505|Machine Learning in Materials Science"
    ]
  ],
  "openalex": "W7204895200",
  "pdf_url": "https://arxiv.org/pdf/2608.30338",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ckh14crjqgbsx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.30338",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30338"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Cartesian tensor equivariant machine-learning force field for spin-dependent atomistic simulations",
  "title_text": "Cartesian tensor equivariant machine-learning force field for spin-dependent atomistic simulations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/ckh14crjqgbsx",
  "venue": "arXiv",
  "versions": []
}