4f levels of rare-earth hexaborides: A simple approach based on a modified orthogonalized-plane-wave method and a self-consistent-field atomic-structure calculation.

Abstract

The electronic structures of trivalent and divalent rare-earth hexaborides R${\mathrm{B}}_{6}$ are calculated by using the modified orthogonalized-plane-wave method within the framework of the muffin-tin-potential approximation based on the self-consistent-field atomic-structure calculations. By regarding the 4f state as a partially filled corelike state and for the transition between 4f and 5d states, and adopting the transition state introduced by Slater which includes the effect of the screening of 4f states by 5d electrons, an attempt is made to understand the x-ray-photoemission spectroscopy (XPS) experiments and bremsstrahlung isochromat spectra (BIS). It is shown that the calculated results of the 4f levels relative to the Fermi level generally agree with the experimental ones obtained from the XPS for ${\mathrm{CeB}}_{6}$, ${\mathrm{PrB}}_{6}$, ${\mathrm{NdB}}_{6}$, ${\mathrm{SmB}}_{6}$, ${\mathrm{GdB}}_{6}$, and ${\mathrm{YbB}}_{6}$ and the BIS for ${\mathrm{GdB}}_{6}$, ${\mathrm{TbB}}_{6}$, and ${\mathrm{DyB}}_{6}$, but there is a considerable difference between the calculations and experiments for the XPS for ${\mathrm{TbB}}_{6}$, ${\mathrm{DyB}}_{6}$, and ${\mathrm{HoB}}_{6}$ and the BIS for ${\mathrm{LaB}}_{6}$, ${\mathrm{CeB}}_{6}$, and ${\mathrm{PrB}}_{6}$. The reason for this disagreement is mainly attributed to the effect of 4f multiplets which is not taken into account in the present study.