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Effects of spin-orbit interaction on magnetic and electronic structures in antiferromagnetic LaFeAsO

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.