Direct Observation of Momentum-Dependent Exchange Interaction in a Heisenberg Ferromagnet

We measured the temperature-dependent three-dimensional angle-resolved photoemission spectra of EuO (100) thin film, a typical Heisenberg ferromagnetic semiconductor, to investigate the essential origin of the ferromagnetic transition. We observed sizable energy dispersion and large binding-energy shift of the Eu 4f state below the Curie temperature only near the r and X points, despite the expected Heisenberg-type local magnetism. The band dispersion and temperature dependence of the Eu 4f state indicates that the indirect exchange and superexchange interactions have strong momentum dependence. The observed temperature-dependent energy shift of the 4f state is the essential origin of the magnetism of EuO.