  We report a first-principles study of the magnetic properties, site disorder
and magneto-structural coupling in multiferroic gallium ferrite (GFO) using
local spin density approximation (LSDA+U) of density functional theory. The
calculations of the ground state A-type antiferromagnetic structure predict
magnetic moments consistent with the experiments whilst consideration of
spin-orbit coupling yields a net orbital moment of ~ 0.025 Bohr magneton/Fe
site also in good accordance with the experiments. We find that though site
disorder is not spontaneous in the ground state, interchange between Fe2 and
Ga2 sites is most favored in the disordered state. The results show that
ferrimagnetism in GFO is due to Ga-Fe site disordering such that Fe spins at
Ga1 and Ga2 sites are antiferromagnetically aligned while maintaining
ferromagnetic coupling between Fe spins at Ga1 and Fe1 sites as well as between
Fe spins at Ga2 and Fe2 sites. The effect of spin configuration on the
structural distortion clearly indicates presence of magneto-structural coupling
in GFO.
