  By systematic first-principles calculations, we study the electronic
structure and magnetic property of SrCrO$_3$. Our results suggest that
SrCrO$_3$ is a weakly correlated antiferromagnetic (AF) metal, a very rare
situation in transition-metal oxides. Among various possible AF states, the
C-type spin ordering with small amount of orbital polarization (dxy orbital is
more occupied than the d_{yz/zx} orbital) is favored. The detailed mechanism to
stabilize the C-type AF state is analyzed based on the competition between the
itinerant Stoner instability and superexchange, and our results suggest that
the magnetic instability rather than the orbital or lattice instabilities plays
an important role in this system. The experimentally observed compressive
tetragonal distortion can be naturally explained from the C-type AF state. By
applying the LDA+$U$ method to study this system, we show that wrong ground
state will be obtained if $U$ is large.
