Ground and excited state properties of CaB$_{6}$ determined byLDA and screened--exchange LDA investigations

CaB$_6$ has recently attracted great interest because it exhibits weak high-temperature ferromagnetism when lightly doped by La and could possibly be useful in room temperature spintronic devices. In pure CaB$_6$, its semiconductor nature has now been established experimentally\footnote{B.K. Cho, et.al., PRB 69, 113202 (2004) and references therein.}. Questions about its theoretical description are centered about the fact that first principles LDA calculations underestimate band gaps and in CaB$_6$ results in a semi-metal with a 0.3 eV overlap at the X point. Here we use the full-potential linearized augmented plane wave method (FLAPW)\footnote{Wimmer, Krakauer, Weinert and Freeman, PRB 24, 864(1981)} within both the LDA and the screened--exchange LDA (sX--LDA) to determine the ground and excited state properties of CaB$_6$. First, we did the geometry optimization with LDA and used this optimized structure in sX--LDA calculations. We find that CaB$_6$ is a semiconductor with a gap of 0.68 eV at X in agreement with the recent experimental results. We also calculated the optical properties with spin--orbit coupling and full matrix elements. Finally, results of similar calculations for Eu and La doped CaB$_6$ will be reported.