We report an Eu L3-edge resonant inelastic x-ray scattering (RIXS) investigation of the electronic structure of EuB6. We observe that the RIXS spectral weight around 1.1 eV increases dramatically when the system is cooled below the ferromagnetic ordering temperature and follows the magnetic order parameter. This spectral feature is attributed to the intersite excitation from the local 4f orbital to the spin-split 5d orbital on the neighboring site, illustrating the essential role of exchange splitting of the conducting electrons. Based on our density functional theory calculations and the RIXS data, EuB6 at low temperature can be consistently described with a semimetallic electronic structure with incomplete spin polarization. We propose that half-metallicity in EuB 6 can be achieved utilizing the strong tunability of the electronic structure against gate voltage, strain, and magnetic field.
