Electronic structure and magnetism in slightly doped SrB_6

Spin-polarized band calculations for supercells of SrB$_{6}$, where a La-, In- or Al- impurity or a vacancy is replacing one Sr, are performed within the local spin density approximation. Moderately large cells with 8 formula units (56 atoms) are studied for all dopings and large ones with 27 formula units (189 atoms) for the case of La-doping. The undoped system has a vanishing density-of-states (DOS) at the Fermi energy (E$_F$), while the additional La-d band makes E$_F$ to enter the bands above the gap. An Al (or In) impurity has the opposite effect, with a rigid-band like shift of E_F to below the gap. In the former case, the addition of a d-electron makes a local, impurity-like modification of the electronic structure close to the La atom. As has been shown in a previous publication, it can lead to a weak ferromagnetic state. This result is shown to persist at even lower doping, by the 189-atom cell calculations, with a moment of the order 0.1 $\mu_B$ per La impurity. An addition of a p-electron, by an In-impurity, makes no similar effect. The magnetic state can be understood from a charge transfer and an additional gain in potential energy, as a spin-splitting is imposed. Different models with modified localization of the La-band are made in order to show the correlation between charge transfer and the size of the magnetic moment.