Density Functional Theory of Magnetic Systems Revisited
  The Hohenberg-Kohn theorem of density functional theory (DFT) for the case of electrons interacting with an external magnetic field (that couples to spin only) is examined in more detail than previously. A unexpected generalization is obtained: in certain cases (which include half metallic ferromagnets and magnetic insulators) the ground state, and hence the spin density matrix, is invariant for some non-zero range of a shift in uniform magnetic field. In such cases the ground state energy is not a functional of the spin density matrix alone. The energy gap in an insulator or a half metal is shown to be a ground state property of the N-electron system in magnetic DFT. 
H. Eschrig and W. E. Pickett