We consider electrons on a honeycomb or triangular lattice doped to the saddle point of the band structure. We assume the system parameters are such that spin density wave (SDW) order emerges below a temperature T(N) and investigate the nature of the SDW phase. We argue that at T≤T(N), the system develops a uniaxial SDW phase whose ordering pattern breaks O(3)×Z(4) symmetry and corresponds to an eight-site unit cell with nonuniform spin moments on different sites. This state is a half-metal--it preserves the full original Fermi surface, but has gapless charged excitations in one spin branch only. It allows for electrical control of spin currents and is desirable for nanoscience.