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Spin-Split Conduction band in \eb\ and Tuning of Half-Metallicity with External Stimuli

We report 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 inter-site 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, the RIXS data suggest that EuB6 at low temperature can be consistently described with a semi-metallic electronic structure with incomplete spin-polarization. We propose routes to achieve half-metallicity in EuB6, which utilize the strong tunability of the electronic structure against gate voltage, strain, and magnetic field.