  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.
