Source-Free Exchange-Correlation Magnetic Fields in Density Functional Theory

Spin-dependent exchange-correlation energy functionals in use today depend on the charge density and the magnetization density: E_xc[ρ, m]. However, it is also correct to define the functional in terms of the curl of m for physical external fields: E_xc[ρ, ∇ × m]. The exchange-correlation magnetic field, B_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. This source-free method is simple to implement in all existing density functional theory codes.