  We have studied the newly found superconductor compound LaO$_{1-x}$F$_x$FeAs
through the first-principles density functional theory calculations. We find
that the parent compound LaOFeAs is a quasi-2-dimensional antiferromgnetic
semimetal with most carriers being electrons and with a magnetic moment of
$2.3\mu_B$ located around each Fe atom on the Fe-Fe square lattice. Furthermore
this is a commensurate antiferromagnetic spin density wave due to the Fermi
surface nesting, which is robust against the F-doping. The observed
superconduction happens on the Fe-Fe antiferromagnetic layer, suggesting a new
superconductivity mechanism, mediated by the spin fluctuations. An abrupt
change on the Hall measurement is further predicted for the parent compound
LaOFeAs.
