The magnetic properties in the parent compounds are often intimately related to the microscopic mechanism of superconductivity. Here we report the first direct measurements on the electronic structure of a parent compound of the newly discovered iron
-based superconductor, BaFe$_2$As$_2$, which provides a foundation for further studies. We show that the energy of the spin density wave (SDW) in BaFe$_2$As$_2$ is lowered through exotic exchange splitting of the band structure, rather than Fermi surface nesting of itinerant electrons. This clearly demonstrates that a metallic SDW state could be solely induced by interactions of local magnetic moments, resembling the nature of antiferromagnetic order in cuprate parent compounds.
