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

Abstract

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 Gamma 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.

Electronic transport through EuO spin-filter tunnel junctions

“…The splitting between the majority-and minority-spin conduction bands is calculated to be about 0.6 eV, in agreement with previous theoretical studies 26,[32][33][34][35][36] and with recent experiments using three-dimensional (3D) angle-resolved photoemission spectroscopy. 37,38 The Eu-6s states show a spin splitting similar to the Eu-5d states, namely, 0.4 eV.…”

Effect of non-uniform exchange field in ferromagnetic graphene

“…In [6], the momentum dependence of exchange coupling is experimentally demonstrated. Our next goal is to choose a specific choice for the momentum dependence, which may produce some impressive results.…”

“…The exchange vector may be a function of coordinate, momentum or time. The authors in [6], have experimentally demonstrated that the exchange coupling in case of the deposition of ferromagnetic insulators may be momentum dependent. On the other hand the spin lens is described in [7] with the help of space dependent exchange field.…”

“…In this context, the charge and spin Hall effect [15][16][17][18] in spin chiral ferromagnetic graphene is discussed in [5]. The exchange interaction thus induced can be non uniform [6,7] as well. The exchange vector may be a function of coordinate, momentum or time.…”

“…In this spin chiral configuration, the authors in [5] demonstrate a different type of Hall effect from the spin Hall mechanism in the extended Drude model approach. The Hall effect that is generated by the spin Hall mechanism in graphene via the spin-orbit dynamics of the carriers can be well explored through non uniform exchange interaction [6][7][8]. As the gauge theory can be applied in describing transport in graphene [9,10], the role of momentum space and real space Berry curvature for a system with finite spin-orbit coupling is also worth studying.…”