Anomalous and spin Hall effect in tunnel junctions with spin orbit interaction

Considering a tight binding model in Keldysh formalism we describe the anomalous and spin Hall effect in tunnel junctions in the presence of Rashba spin orbit coupling. Two types of structures are considered, conventional magnetic tunnel junctions (normal metal - insulator - ferromagnet) and spin filter tunnel junctions (normal metal - magnetic insulator - ferromagnet). We show that the magnitudes of the anomalous and spin Hall effects are enhanced in the presence of magnetic insulators. In both types of structures the angular dependence exhibit a cosine and sine behavior.