{
  "abstract": "The source-free condition, $\\nabla\\cdot\\mathbf{B}_{\\mathrm{xc}}=0$, where $\\mathbf{B}_{\\mathrm{xc}}=δE_{\\mathrm{xc}}/δ\\mathbf{m}$ is the exchange-correlation (xc) magnetic field of non-collinear spin-density functional theory (SDFT) and $\\mathbf{m}$ the magnetization, is widely believed to be exact. Recent studies report that projecting the field of a parent functional onto its source-free part improves the predicted magnetic moments. We show that the condition violates the global spin-rotation symmetry of $E_{\\mathrm{xc}}$ and therefore cannot be exact. A source-free field is exact only in a transverse theory whose xc functional differs from $E_{\\mathrm{xc}}$ and is itself not invariant under spin rotations. We examine a source-free (SoF) construction, an exchange-correlation energy given by a parent SDFT functional evaluated at the transverse magnetization $\\mathbf{m}_{\\perp}$. Its field is divergence-free, remains a functional derivative and exerts local torques, but still, it breaks global spin-rotation symmetry. With the LSDA as parent we examine the \\ce{Mn2} molecule. The SoF and the locally collinear (LoC) LSDA both give too short a bond and too large a bond energy, but SoF finds a broken-symmetry antiferromagnetic solution, consistent with the experimentally observed $^{1}Σ^{+}_{g}$ ground state, with a coupling of the right sign and roughly the right size, while LoC finds a high-spin $^{11}Π_{u}$ ferromagnet and the wrong sign. The broken symmetry of SoF, however, produces severe errors in directional properties: a rigid spin rotation of the magnetization changes the energy by about $1\\,\\mathrm{eV}$, in a weak uniform field the magnetization points perpendicular to the field instead of antiparallel to it, and the molecule develops a spurious magnetic anisotropy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01533",
  "author_total": 2,
  "authors": [
    {
      "name": "Ester Livshits"
    },
    {
      "name": "Roi Baer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cvfd0krtjc0f5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01533",
  "fulltext_url": null,
  "id": "cvfd0krtjc0f5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01533",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7206202951",
  "pdf_url": "https://arxiv.org/pdf/2609.01533",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cvfd0krtjc0f5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2609.01533",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01533"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "No source-free exchange-correlation magnetic fields in non-collinear spin-density functional theory",
  "title_text": "No source-free exchange-correlation magnetic fields in non-collinear spin-density functional theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/cvfd0krtjc0f5",
  "venue": "arXiv",
  "versions": []
}