Optical anisotropy and electronic structures of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Cd</mml:mi><mml:mi mathvariant="normal">Mo</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Cd</mml:mi><mml:mi mathvariant="normal">W</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>crystals: Polarized reflection measurements, x-ray photoelectron spectroscopy, and electronic structure calculations

The polarized reflectivity spectra of $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_{4}$ single crystals with a scheelite structure and of $\mathrm{Cd}\mathrm{W}{\mathrm{O}}_{4}$ with a wolframite structure are measured in the $3--30\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ range by using synchrotron radiation. The spectra of optical constants for the crystallographic axes are derived by a Kramers--Kronig analysis. X-ray photoelectron spectroscopy (XPS) and the calculation of the electronic structure by using a discrete variational $X\ensuremath{\alpha}$ method are performed for $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_{4}$. The calculation shows that the $\mathrm{Cd}\phantom{\rule{0.2em}{0ex}}4d$ state is localized at the bottom region of the $\mathrm{O}\phantom{\rule{0.2em}{0ex}}2p$ valence band, and the $\mathrm{Cd}\phantom{\rule{0.2em}{0ex}}5s$ state has a significant contribution to the bottom of the conduction band, composed of the $\mathrm{Mo}\phantom{\rule{0.2em}{0ex}}4d$ state. The XPS spectrum of $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_{4}$ resembles that of $\mathrm{Cd}\mathrm{W}{\mathrm{O}}_{4}$. Unlike the XPS spectrum, the optical spectra of $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_{4}$ resemble those of scheelite $\mathrm{Ca}\mathrm{Mo}{\mathrm{O}}_{4}$ rather than $\mathrm{Cd}\mathrm{W}{\mathrm{O}}_{4}$. An excitonic transition is observed as a weak shoulderlike structure in $\mathrm{Cd}\mathrm{W}{\mathrm{O}}_{4}$, while it is not appreciable in $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_{4}$. These experimental results are discussed in comparison with the theoretical calculation of electronic structures. The remarkable anisotropy of the optical spectra in $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_{4}$ is explained by taking into account the presence of the $\mathrm{Cd}\phantom{\rule{0.2em}{0ex}}5s$ state at the bottom of the conduction band. The dichroism of $\mathrm{Cd}\mathrm{W}{\mathrm{O}}_{4}$ is discussed in terms of the chain structure of $\mathrm{W}\mathrm{O}_{6}{}^{6\ensuremath{-}}$ octahedra in wolframite crystals. The present study indicates that the Cd metal states play a crucial role in the optical properties near the fundamental absorption edge in both $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_{4}$ and $\mathrm{Cd}\mathrm{W}{\mathrm{O}}_{4}$.