Enhanced Shot Noise as a Signature of Trap-Assisted Tunneling in Magnetic Tunnel Junctions: a Monte Carlo Approach

A numerical Monte Carlo approach to evaluate transport due to spin-dependent trap-assisted tunneling in magnetic tunnel junctions has been developed. The current and the low frequency current noise is calculated. It is shown that the shot noise at spin-dependent hopping is significantly enhanced due to the Pauli spin blockade. This provides an additional characteristic for identifying spin-dependent trap-assisted tunneling as a cause of large magnetoresistance observed in three-terminal spin accumulation experiments. Introduction With magnetic tunnel junctions scaling down, many interesting phenomena due to the correlated charge transport are anticipated. The Coulomb interaction leads to a strong repulsion on a trap a Coulomb blockade and results in pronounced charge transport correlations, when electrons are transferred through the trap [1]. Indeed, an electron from a contact cannot jump on the trap before the electron from the trap escapes to a lead. The Pauli exclusion principle forbidding two electrons with the same spins to occupy the same quantum state on the trap results in yet another correlation effect during the transport through quantum dots and traps [2]. Spin correlations are responsible for large magnetoresistance and magnetoluminescence effects observed at room temperature in organic semiconductors and in organic light-emitting diods [3]. Spin-dependent resonant tunneling is also believed to be responsible for the large resistance modulation with the magnetic field [4] observed in three-terminal spin accumulation experiments [5]. However, the phenomenon remains puzzling [6], and even the expression for the magnetoresistance dependence obtained in [4] was recetly challenged [7]. To resolve the controversy, we present a numerical Monte Carlo approach capable of evaluating the current due to trap-assisted tunneling. We also calculate the shot noise at spin-dependent hopping and demonstrate that, due to the Pauli spin blockade in a magnetic field parallel to the magnetization of the ferromagnetic contacts, the Fano factor is significantly enhanced relative to the direct tunneling case. This provides an additional characteristic for distinguishing spin-dependent trap-assisted tunneling as a possible cause of the large magnetoresistance [5] in spin accumulation experiments. 1. Method and Results To describe the spin-independent hopping it is sufficient to provide the transition rates to/from a trap, and the stationary current and its low-frequency fluctuations can then be evaluated by a Monte Carlo algorithm [8, 9]. In contrast to spin-independent tunneling, the transition rates with spin depend on the magnetic field and the magnetization direction of the electrodes. In the case when an electron tunnels from a normal electrode to the trap with the rate ΓN and from a trap to the ferromagnetic electrode characterized by the polarization vector p = (Γ++Γ−)/(2ΓF )M/M with the rates Γ± for the spin parallel (anti-parallel) to the magnetization M (Fig.1), the trap occupation 0 ≤ n ≤ 1 dynamics depends on the electron spin s [10]: dn dt = ΓN (1− n)− ΓFn− ΓFps (1) ds dt = −ΓF s − pΓFn+ [s× ω]. (2) Here ω = eB mc is the Larmor frequency vector pointing in the direction of the external field B. The escape probability P (t) = 1 − n(t) from the trap is determined by the matrix differential equation resolved for n(t):