# Exchange-correlation magnetic fields in spin-density-functional theory

## TL;DR

This paper investigates the role of exchange-correlation magnetic fields in spin-density-functional theory, highlighting their increasing importance in correlated, localized electron systems and comparing exact solutions with approximations.

## Contribution

It provides exact benchmark solutions for two-electron Hubbard lattices and analyzes the significance of xc magnetic fields and torques in noncollinear magnetic systems.

## Key findings

- xc magnetic fields become more important with increased correlation and localization
- xc torques have a minor effect on magnetization dynamics
- approximate functionals tend to favor symmetry-breaking at strong interactions

## Abstract

In spin-density-functional theory for noncollinear magnetic materials, the Kohn-Sham system features exchange-correlation (xc) scalar potentials and magnetic fields. The significance of the xc magnetic fields is not very well explored; in particular, they can give rise to local torques on the magnetization, which are absent in standard local and semilocal approximations. We obtain exact benchmark solutions for two electrons on four-site extended Hubbard lattices over a wide range of interaction strengths, and compare exact xc potentials and magnetic fields with approximations obtained from orbital-dependent xc functionals. The xc magnetic fields turn out to play an increasingly important role as systems becomes more and more correlated and the electrons begin to localize; the effects of the xc torques, however, remain relatively minor. The approximate xc functionals perform overall quite well, but tend to favor symmetry-broken solutions for strong interactions.