We report measurements of the optical gap in a GdN film at temperatures from 300 to 6K, covering both the paramagnetic and ferromagnetic phases. The gap is 1.31eV in the paramagnetic phase and red-shifts to 0.9eV in the spin-split bands below the Curie temperature. The paramagnetic gap is larger than was suggested by very early experiments, and has permitted us to refine a (LSDA+U)-computed band structure. The band structure was computed in the full translation symmetry of the ferromagnetic ground state, assigning the paramagnetic-state gap as the average of the majority- and minority-spin gaps in the ferromagnetic state. That procedure has been further tested by a band structure in a 32-atom supercell with randomly-oriented spins. After fitting only the paramagnetic gap the refined band structure then reproduces our measured gaps in both phases by direct transitions at the X point.
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