Ferromagnetic redshift of the optical gap in GdN

Abstract

We report measurements of the optical gap in a GdN film at temperatures from $300\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, covering both the paramagnetic and ferromagnetic phases. The gap is $1.31\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ in the paramagnetic phase and redshifts to $0.9\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ 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 $(\mathrm{LSDA}+U)$-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.