# Source-free exchange-correlation magnetic fields in density functional theory

## TL;DR

This paper introduces a source-free formulation of exchange-correlation magnetic fields in density functional theory, improving magnetic moment predictions and spatial field geometries across various materials, including pnictides.

## Contribution

It presents a novel source-free approach to exchange-correlation functionals, enhancing accuracy of magnetic properties in DFT calculations.

## Key findings

- Improved total magnetic moments for a wide range of materials.
- Good agreement with experimental moments in pnictides.
- Significant differences in spatial geometry of ${f B}_{
m xc}$ for pnictides.

## Abstract

Spin-dependent exchange-correlation energy functionals in use today depend on the charge density and the magnetization density: $E_{\rm xc}[\rho,{\bf m}]$. However, it is also correct to define the functional in terms of the curl of ${\bf m}$ for physical external fields: $E_{\rm xc}[\rho,\nabla\times{\bf m}]$. The exchange-correlation magnetic field, ${\bf B}_{\rm xc}$, then becomes source-free. We study this variation of the theory by uniquely removing the source term from local and generalized gradient approximations to the functional. By doing so, the total Kohn-Sham moments are improved for a wide range of materials for both functionals. Significantly, the moments for the pnictides are now in good agreement with experiment. We also predict dramatic differences in the spatial geometry of ${\bf B}_{\rm xc}$ for the pnictides. Our source-free method is simple to implement in all existing density functional theory codes.