Complementary angle-resolved photoemission and bulk-sensitive k-resolved resonant inelastic x-ray scattering of divalent hexaborides reveal a >1 eV X-point gap between the valence and conduction bands, in contradiction to the band overlap assumed in several models of their novel ferromagnetism. This semiconducting gap implies that carriers detected in transport measurements arise from defects, and the measured location of the bulk Fermi level at the bottom of the conduction band implicates boron vacancies as the origin of the excess electrons. The measured band structure and X-point gap in CaB_6 additionally provide a stringent test case for proper inclusion of many-body effects in quasi-particle band calculations.
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