  Using ab initio thermodynamics we compile a phase diagram for the surface of
Fe3O4(001) as a function of temperature and oxygen pressures. A hitherto
ignored polar termination with octahedral iron and oxygen forming a wave-like
structure along the [110]-direction is identified as the lowest energy
configuration over a broad range of oxygen gas-phase conditions. This novel
geometry is confirmed in a x-ray diffraction analysis. The stabilization of the
Fe3O4(001)-surface goes together with dramatic changes in the electronic and
magnetic properties, e.g., a halfmetal-to-metal transition.
