  Magnetic and electronic structures in LaFeAsO in the single-stripe-type
antiferromagnetic (AFM) phase are studied using first-principles
density-functional calculations including the spin-orbit interaction. We show
that the longitudinal ordering (LO) where Fe magnetic moments are parallel or
anti-parallel with the in-plane AFM ordering vector is lower in energy than
transverse orderings (TOs), in good agreement with neutron diffraction
experiments. Calculated energy difference between LO and TOs is about 0.1 meV
per Fe atom, indicating that LO will prevail at temperature below about 1 K. We
also show that the spin-orbit interaction splits degenerate bands at some
high-symmetry points in the Brillouin zone by about 60 meV, depending on
spatial directions of the Fe magnetic moments.
