Optical and magneto-optical properties and electronic structures of single-crystalline $R{\mathrm{Al}}_2$ $(R=\mathrm{Y}$, La, Ce, Pr, and Lu)

The diagonal optical conductivity spectra of single crystals of $R{\mathrm{Al}}_2$ $(R=\mathrm{Y},$ La, Ce, Pr, and Lu) were measured at room temperature by spectroscopic ellipsometry in the $1.5–5.6-\mathrm{eV}$ range. All the compounds exhibit two strong interband absorption peaks at about 1.8 and 3.6 eV for ${\mathrm{YAl}}_2$ and ${\mathrm{LuAl}}_2,$ and at about 2.0 and 3.0 eV for ${\mathrm{LaAl}}_2,$ ${\mathrm{CeAl}}_2,$ and ${\mathrm{PrAl}}_2.$ Such differences in the second peak position appear in the theoretical optical conductivity spectra calculated from their band structures obtained by the tight-binding linear-muffin-tin-orbitals method. Most of the contributions to the two peaks in ${\mathrm{LaAl}}_2$ are from the p and d states, i.e., $\overrightarrow{p}d$ and $\overrightarrow{d}p$ transitions, while those involving f states are negligible. These results suggest that f character near $E_F$ for ${\mathrm{LaAl}}_2,$ ${\mathrm{CeAl}}_2,$ and ${\mathrm{PrAl}}_2$ distorts their conduction bands significantly through hybridization, leading to different optical spectra compared to those of ${\mathrm{YAl}}_2$ and ${\mathrm{LuAl}}_2.$ The magneto-optical properties of ${\mathrm{CeAl}}_2$ and ${\mathrm{PrAl}}_2$ were measured at low temperatures. The Kerr rotation $\left({\Theta }_K\right)$ and ellipticity $\left({\epsilon }_K\right)$ for both compounds show similar spectral variations with maximum ${\Theta }_K$ of $0.35°$ and $0.55°$ at about 2.1 eV for ${\mathrm{CeAl}}_2$ and ${\mathrm{PrAl}}_2,$ respectively. The evaluated off-diagonal conductivity spectra of the two compounds are also similar, with two structures at about 2.1 and 3.8 eV for ${\mathrm{CeAl}}_2$ and 2.1 and 3.4 eV for ${\mathrm{PrAl}}_2.$ The energy difference in the second structures is interpreted as due to the different conduction-band structures of the two compounds caused by different hybridization strengths of their f states with conduction bands, because of the difference in their degree of localization.