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. An 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. 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. Its relation to the gap in the Kohn–Sham eigenvalue spectrum is analyzed.