Spin-dependent trap-assisted tunneling in magnetic tunnel junctions: A Monte Carlo study

Spin-dependent resonant tunneling is responsible for the large resistance modulation with magnetic fields observed in three-terminal spin accumulation experiments [1]; however, the expression for the magnetoresistance dependence was questioned [2]. To resolve the controversy, we developed a numerical Monte Carlo approach for the trap-assisted spin tunneling in tunnel junctions. In contrast to spinindependent tunneling [3,4], the transition rates depend on the magnetic field B and the magnetization M direction of the electrodes. In the case, when an electron can jump from a normal electrode to the trap with the rate ΓNN and from the trap to the ferromagnetic electrode (characterized by the polarization vector pp = Γ+−Γ− 2ΓF MM |MM| ) with the rates Γ± = ΓOO(1 ± |pp|) for the spin parallel (anti-parallel) to M (Fig.1), the trap occupation n depends on the electron spin s [5]: