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The stochastic Liouville equation is applied to the field of organic magnetoresistance to perform detailed microscopic calculations on the different proposed models. By adapting this equation, the influence of a magnetic field on the current in bipolaron, electron-hole pair, and triplet models is calculated. The simplicity and wide applicability of the stochastic Liouville equation makes it a powerful tool for interpreting experimental results on magnetoresistance measurements in organic semiconductors. New insights are gained on the influence of hopping rates and disorder on the magnetoresistance.

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Fringe fields emanating from magnetic domain structures can give rise to magnetoresistance in organic semiconductors. In this article, we explain these magnetic-field effects in terms of a B mechanism. This mechanism describes how variations in magnetic-field strength between two polaron hopping sites can induce a difference in precessional motion of the polaron spins, leading to mixing of their spin states. In order to experimentally explore the fringe-field effects, polymer thin-film devices on top of a rough in-plane magnetized cobalt layer are investigated. The cobalt layer can be described by a distribution of out-of-plane magnetic anisotropies, most likely induced by thickness variations in the cobalt. With a magnetic field perpendicular to the cobalt layer, fringe fields are created because some domains are magnetized out of plane whereas the magnetization of other domains remains approximately in plane. By varying the distance between the polymer layer and the cobalt layer, we find that the magnetoresistance arising from these fringe fields reduces with the gradient in the fringe fields, in agreement with the B mechanism.