No source-free exchange-correlation magnetic fields in non-collinear spin-density functional theory
Abstract
The source-free condition, ∇·Bxc=0, where Bxc=δExc/δm is the exchange-correlation (xc) magnetic field of non-collinear spin-density functional theory (SDFT) and 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 Exc and therefore cannot be exact. A source-free field is exact only in a transverse theory whose xc functional differs from Exc 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 m⊥. 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 1Σ+g ground state, with a coupling of the right sign and roughly the right size, while LoC finds a high-spin 11Πu 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 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.
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BibTeX
@misc{livshits2026sourcefree,
title = {{No source-free exchange-correlation magnetic fields in non-collinear spin-density functional theory}},
author = {Ester Livshits and Roi Baer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.01533},
eprint = {2609.01533},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01533},
}
RIS
TY - UNPB
TI - No source-free exchange-correlation magnetic fields in non-collinear spin-density functional theory
AU - Ester Livshits
AU - Roi Baer
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2609.01533
UR - https://arxiv.org/abs/2609.01533
AB - The source-free condition, ∇·B_xc=0, where B_xc=δE_xc/δm is the exchange-correlation (xc) magnetic field of non-collinear spin-density functional theory (SDFT) and 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_xc and therefore cannot be exact. A source-free field is exact only in a transverse theory whose xc functional differs from E_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 m_⊥. 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 ^1Σ^+_g ground state, with a coupling of the right sign and roughly the right size, while LoC finds a high-spin ^11Π_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 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.
ER -