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The spin density wave (SDW) state of the uniform electron gas is investigatedin the exact exchange approximation of noncollinear spin density functionaltheory (DFT). Unlike in Hartree-Fock theory, where the uniform paramagneticstate of the electron gas is unstable against formation of the spin densitywave for all densities, in exact-exchange spin-DFT this instability occurs onlyfor densities lower than a critical value. It is also shown that, although in asuitable density range it is possible to find a non-interacting SDW groundstate Slater determinant with energy lower than the corresponding paramagneticstate, this Slater determinant is not a self-consistent solution of theOptimized Effective Potential (OEP) integral equations of noncollinearspin-DFT. A selfconsistent solution of the OEP equations which gives an evenlower energy can be found using an excited-state Slater determinant where onlyorbitals with single-particle energies in the lower of two bands are occupiedwhile orbitals in the second band remain unoccupied even if their energies arebelow the Fermi energy.

Overhauser's spin-density wave in exact-exchange spin density functional theory