  The electronic structure of the ferromagnetic semiconductor EuO is
investigated by means of spin- and angle-resolved photoemission spectroscopy
(spin-ARPES) and density functional theory. EuO exhibits unique properties of
hosting both weakly-dispersive nearly fully polarized Eu $4f$ bands, as well as
O $2p$ levels indirectly exchange-split by the interaction with Eu nearest
neighbors. Our temperature-dependent spin-ARPES data directly demonstrates the
exchange splitting in O $2p$ and its vanishing at the Curie temperature. Our
calculations with a Hubbard $U$ term reveal a complex nature of the local
exchange splitting on the oxygen site and in conduction bands. We discuss the
mechanisms of the indirect exchange in the O 2p levels by analyzing
orbital-resolved band characters in ferromagnetic and antiferromagnetic phases.
The directional effects due to spin-orbit coupling are predicted theoretically
to be significant in particular in the Eu 4f band manifold. The analysis of the
shape of spin-resolved spectra in the Eu $4f$ spectral region reveals
signatures of hybridization with O $2p$, in agreement with the theoretical
predictions. We also analyze spectral changes in the spin-integrated spectra
throughout the Curie temperature and demonstrate they derive from both the
magnetic phase transition and effects due to sample aging, unavoidable for this
highly reactive material.
