Ferromagnetic redshift of the optical gap in GdN

We report measurements of the optical gap in a GdN film at temperatures from $300\text{to}6\mathrm{K}$, covering both the paramagnetic and ferromagnetic phases. The gap is $1.31\mathrm{eV}$ in the paramagnetic phase and redshifts to $0.9\mathrm{eV}$ 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.

Figure 1

(Color online) Transmission through a $200\mathrm{nm}$ $\mathrm{Gd}\mathrm{N}∕\sim 200\mathrm{nm}$ GaN film deposited on sapphire. The $300\mathrm{K}$ data were collected with the sample in vacuum, and for the 6 and $75\mathrm{K}$ data there were additional four polythene windows in the path which sacrificed intensity above $1.5\mathrm{eV}$ and across a gap near $0.9\mathrm{eV}$. The edge at $1.3\mathrm{eV}$ is clearly visible in 75 and $300\mathrm{K}$ data, as is the tail of reduced intensity below that threshold at $6\mathrm{K}$. The inset shows the transmission reduction in the ferromagnetic phase, with a clear indication of an interband edge at a lower energy than in the paramagnetic phase.

Figure 2

(Color online) Absorption coefficient $\left(\eta \right)$ implied by the data of Fig. 1 in paramagnetic and ferromagnetic phases.

Figure 3

(Color online) The band structure of GdN calculated with the value of $U_d=8.0\mathrm{eV}$ determined from the paramagnetic and ferromagnetic gaps reported in this paper. The solid lines represent majority-spin bands, and dashed lines minority.

Figure 4

(Color online) Energy bands of GdN in a $2\times 2\times 1$ supercell of the cubic fcc cell (containing 32 atoms) from $\Gamma =(0,0,0)$ to $X=(\frac{\pi }{2a},0,0)$ with randomly chosen spin directions on the Gd sites. The bands are colored according to spin content, with red for majority and blue for minority spin.