发表机构
Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem（希伯来大学化学研究所弗里茨·哈伯分子动力学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究指出非共线自旋DFT中无源自xc磁场条件违背自旋旋转对称性，通过构造SoF泛函计算Mn₂，发现其能得到实验观测的反铁磁体，但存在磁化旋转改变能量等非物理问题。
AI 中文摘要
我们证明，麦克斯韦方程∇·𝐁ₓc=0（其中𝐁ₓc为交换关联（xc）磁场）并非非共线自旋密度泛函理论的精确条件：它违背了整体自旋旋转对称性，该对称性用于翻转电子自旋。这在实际中有多重要？为了弄清这一点，我们尽可能以最优方式强行施加该条件：修改任意父级xc泛函，使得Kohn-Sham过程产生无散度的𝐁ₓc，该场为泛函导数，对均匀气体保持精确，且能施加局域共线泛函无法实现的局域力矩。计算得出的任何非物理结果都必须归因于该虚假条件，而非实现方式。以采用LSDA作为父级泛函的Mn₂为例，无源自（SoF）构造与局域共线（LoC）LSDA均给出过短的键长和过大的键能，但在磁交换耦合及态本身方面存在差异：SoF构造得到实验观测到的¹Σ⁺ᵍ反铁磁体，其耦合符号正确且大小大致合理，而LoC构造得到高自旋¹¹Πᵤ铁磁体，符号错误。尽管SoF构造看似成功，但破坏对称性会产生严重后果：磁化强度的刚性自旋旋转会使Eₓc改变约1 eV（本应完全不变），且弱均匀场诱导的磁化强度垂直于该场（本应与场反平行）。
英文摘要
The source-free condition, $\nabla\cdot\mathbf{B}_{xc}=0$, where $\mathbf{B}_{xc}$ is the exchange-correlation (xc) magnetic field in non-collinear spin-density functional theory, is widely believed to be exact. Recent studies report that when the field of a parent functional is made source-free by projection - a posteriori, rather than by construction - the predicted magnetic moments improve. We show that the condition violates global spin-rotation symmetry of the xc energy functional $E_{xc}$ and therefore cannot be exact. It has nonetheless been found useful, so we examine the errors it introduces. We first implement the condition variationally, using any parent $E_{xc}$ functional: the resulting source-free (SoF) field is divergence-free, remains a functional derivative, and exerts local torques. With the LSDA as the parent functional, we examine Mn$_2$. SoF and the locally collinear (LoC) LSDA both give too short a bond and too large a bond energy, but they differ on the magnetic and electronic properties: SoF finds the experimentally observed $^1Σ_g^+$ antiferromagnet, with a coupling of the right sign and, extrapolated to the experimental bond length, roughly the right size, while LoC finds a high-spin $^{11}Π_u$ ferromagnet and the wrong sign. But breaking the symmetry produces severe errors in every directional property. A rigid spin rotation of the magnetization changes $E_{xc}$ by about 1 eV (it should not change at all); in a weak uniform external field the magnetization points perpendicular to the field (it should be antiparallel to it); and the system develops a spurious magnetic anisotropy of about 175 meV (an effect that requires spin-orbit coupling, which is absent here).
