Optical band gap hierarchy in a magnetic oxide: Electronic structure of NiFe${}_2$O${}_4$

We combined first-principles calculations with optical spectroscopy and variable-temperature film growth techniques to comprehensively investigate the electronic structure of NiFe${}_2$O${}_4$. We find this system to be an indirect-gap material in the minority channel, with two higher-energy direct-gap structures in the minority and majority channels, respectively. An analysis of states near the band edge simultaneously exposes both the charge transfer and Mott limits of the Zaanen-Sawatzky-Allen classification scheme. The gap hierarchy is well suited for spintronics applications.

Figure 1

Density of states of NiFe${}_2$O${}_4$ calculated according to (a) the LSDA + $U$ and (b) the screened hybrid functional HSE06 methods. The enhanced gap in the latter method is clearly seen. (c) HSE06 energy bands along $\Gamma$-$X$-$W$ for majority (left) and minority (right) channels. The minority channel exhibits an indirect gap between $X$ and $\Gamma$. In both channels, the lowest conduction band is nearly flat over a wide region, possibly leading to many nearly degenerate transitions (both direct and indirect). (d) Dielectric constant ${\varepsilon }_2\left(E\right)$ as a function of energy. Red curve: experimental spectrum; green curve: theoretical result in the $\mathit{ab}$ plane; blue curve: theoretical result in the $c$ direction. The agreement between calculated and experimental responses is reasonable. The inset shows the effective number of electrons $n_{\mathrm{eff}}$ as a function of energy. The various gaps are indicated.

Figure 2

The 300 K absorption spectrum of NiFe${}_2$O${}_4$. The top left inset shows the optical band gap analysis for the film grown at 690 ${}^{\circ }$C. The bottom left inset shows the rendered color[36] for the film grown at 690 ${}^{\circ }$C compared to a photograph of the same film. The right inset shows the dependence of the direct and indirect optical band gaps on growth temperature.