  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.
