Abstract
From all-electron fixed-spin-moment calculations we show that ferromagnetic and checkerboard antiferromagnetic ordering in LaFeAsO are not stable and the stripe antiferromagnetic configuration with is the only stable ground state. The main exchange interactions between Fe ions are large, antiferromagnetic, and frustrated. The magnetic stripe phase breaks the tetragonal symmetry, removes the frustration, and causes a structural distortion. These results successfully explain the magnetic and structural phase transitions in LaFeAsO recently observed by neutron scattering. The presence of competing strong antiferromagnetic exchange interactions suggests that magnetism and superconductivity in doped LaFeAsO may be strongly coupled, much like in the high- cuprates.