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Magnetoresistance in organic spintronic devices: the role of nonlinear effects

We derive kinetic equations describing injection and transport of spin polarized carriers in organic semiconductors with hopping conductivity via an impurity level. The model predicts a strongly voltage dependent magnetoresistance, defined as resistance variation between devices with parallel and antiparallel electrode magnetizations (spin valve effect). The voltage dependence of the magnetoresistance splits into three distinct regimes. The first regime matches well known inorganic spintronic regimes, corresponding to barrier controlled spin injection or the well known conductivity mismatch case. The second regime at intermediate voltages corresponds to strongly suppressed magnetoresistance. The third regime develops at higher voltages and accounts for a novel paradigm. It is promoted by the strong non-linearity in the charge transport which strength is characterized by the dimensionless parameter $eU/k_BT$. This nonlinearity, depending on device conditions, can lead to both significant enhancement or to exponential suppression of the spin valve effect in organic devices. We believe that these predictions are valid beyond the case of organic semiconductors and should be considered for any material characterized by strongly non-linear charge transport.