  Half-metallicity (full spin polarization of the Fermi surface) usually occurs
in strongly correlated electron systems. We demonstrate that doping a
spin-density wave insulator in the weak-coupling regime may also stabilize
half-metallic states. The undoped spin-density wave is formed by four nested
bands [i.e., each band is characterized by charge (electron/hole) and spin
(up/down) labels]. Of these four bands only two accumulate the doped carriers,
forming a half-metallic two-valley Fermi surface. Depending on parameters, the
spin polarizations of the electron-like and hole-like valleys may be (i)
parallel or (ii) antiparallel. The Fermi surface of (i) is fully spin-polarized
(similar to usual half-metals). Case (ii), referred to as "a spin-valley
half-metal", corresponds to complete polarization with respect to the
spin-valley operator. The properties of these states are discussed.
