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We analyze spin density wave (SDW) order in iron-based superconductors andelectronic structure in the SDW phase. We consider an itinerant model forFe-pnictides with two hole bands centered at $(0,0)$ and two electron bandscentered at $(0,\pi)$ and $(\pi,0)$ in the unfolded BZ. A SDW order in such amodel is generally a combination of two components with momenta $(0,\pi)$ and$(\pi,0)$, both yield $(\pi,\pi)$ order in the folded zone. Neutronexperiments, however, indicate that only one component is present. We show that$(0,\pi)$ or $(\pi,0)$ order is selected if we assume that only one hole bandis involved in the SDW mixing with electron bands. A SDW order in such 3-bandmodel is highly degenerate for a perfect nesting and hole-electron interactiononly, but we show that ellipticity of electron pockets and interactions betweenelectron bands break the degeneracy and favor the desired $(0,\pi)$ or$(\pi,0)$ order. We further show that stripe-ordered system remains a metal forarbitrary coupling. We analyze electronic structure for parameters relevant tothe pnictides and argue that the resulting electronic structure is in goodagreement with ARPES experiments. We discuss the differences between our modeland $J_1-J_2$ model of localized spins.

Magnetic degeneracy and hidden metallicity of the spin density wave state in ferropnictides