  Electronic structure calculations using quantum Monte Carlo (QMC) methods
conclusively show that pure CaB$_6$ is a narrow-gap semiconductor with an
$X$-point gap $\sim 1.3$ eV. This should put to rest controversies as to
whether the compound is a semimetal or a semiconductor, as also theories
suggesting it to be an excitonic insulator. Our extensive Hartree-Fock (HF) and
density functional theory (DFT) calculations support the view that the
hexaboride ferromagnetism can be induced by contamination with magnetic element
atoms like Fe and that presence of La is not essential for this. La impurity,
however, gives rise to a metallic state with a small electron-like Fermi
surface as seen in ARPES experiments.
