Ultraviolet reflectance and electronic states of layered nickel halides studied with synchrotron radiation

The real (${\epsilon }_1$) and imaginary (${\epsilon }_2$) parts of the dielectric function, together with the energy-loss function, $-\mathrm{Im}\left[\frac{1}{\hat{\epsilon }\mathrm{}\left(E\right)\mathrm{}}\right]$, of freshly cleaved crystals of Ni${\mathrm{Cl}}_2$, Ni${\mathrm{Br}}_2$, and Ni${\mathrm{I}}_2$ have been obtained in the region 2-31 eV by Kramers-Kronig analysis of near-normal-incidence reflectance spectra. The spectra of Ni${\mathrm{I}}_2$ have been obtained over the entire region at 300 and 30 K, and those of Ni${\mathrm{Cl}}_2$ and Ni${\mathrm{Br}}_2$ have been measured at 30 K only from 2 to 11 eV. The results can be described in terms of charge-transfer transitions, interband transitions, and plasma oscillations. The low-temperature spectra of the materials reveal the presence of exciton structures. Plasma resonance effects have been identified in the high-energy region (15-20 eV). The optical spectra of $\mathrm{Ni}{X}_2 (X=\mathrm{C}\mathrm{l},\mathrm{B}\mathrm{r},\mathrm{I})$ were analyzed in terms of the known band structures of Ni${\mathrm{Cl}}_2$ and Ni${\mathrm{Br}}_2$. Nearly all of the main spectral features beyond the energy gap can be identified in terms of direct interband transitions at the symmetry points $\Gamma$, $Z$, $F$, and $L$ and along symmetry lines of the Brillouin zone. The energy gap is assigned to ${\Gamma }_3^{-}\to {\Gamma }_1^{+}$ transitions in Ni${\mathrm{Cl}}_2$ (8.72 eV), Ni${\mathrm{Br}}_2$ (7.90 eV), and Ni${\mathrm{I}}_2$ (6.26 eV). Finally, the interpretation of the satellite exciton at 5.65 eV in Ni${\mathrm{I}}_2$ (30 K) and at 6.50 eV in Ni${\mathrm{Br}}_2$ (30 K) is discussed in terms of the triplet exciton state predicted by Onodera and Toyozawa.