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arXiv · 2609.01533

No source-free exchange-correlation magnetic fields in non-collinear spin DFT

Ester Livshits·Roi Baer
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Abstract

We show that the Maxwellian equation \nabla\cdot\mathbf{B}_{\mathrm{xc}}=0, where \mathbf{B}_{\mathrm{xc}} is the exchange-correlation (xc) magnetic field, is not an exact condition of non-collinear spin density functional theory: it violates global spin-rotation symmetry, the invariance of the energy when all electron spins are rotated together. How much does this matter in practice? To find out we impose the condition in the best way we can: we modify any parent xc functional so that \mathbf{B}_{\mathrm{xc}} is its divergence-free functional derivative, stays exact for the homogeneous gas, and exerts the local torques a locally collinear functional cannot. Any non-physical result from the calculation must be due to the spurious condition, not the implementation. On \ce{Mn2} with LSDA as parent, the source-free (SoF) construction and locally collinear (LoC) LSDA both give too short a bond and too large a bond energy, but differ on the magnetic and electronic properties: SoF finds the experimentally observed ^{1}\Sigma^{+}_{g} antiferromagnet, with a coupling of the right sign and roughly the right size, while LoC finds a high-spin ^{11}\Pi_{u} ferromagnet and the wrong sign. Despite this success, breaking the symmetry has serious consequences: a rigid spin rotation of the magnetization changes E_{\mathrm{xc}} by about 1\,\mathrm{eV} (it should not change at all), the magnetization induced by a weak uniform field points perpendicular to the field (it should be antiparallel to it), and the system develops a spurious magnetic anisotropy of about 175\,\mathrm{meV} (an effect that requires spin-orbit coupling, absent here).

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Ester Livshits, Roi Baer. 2026-09-01. No source-free exchange-correlation magnetic fields in non-collinear spin DFT. https://arxiv.org/abs/2609.01533

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