Semiclassical theory of magnetoresistance in positionally-disordered organic semiconductors

A recently introduced percolative theory of unipolar organic magnetoresistance is generalized by treating the hyperfine interaction semiclassically for an arbitrary hopping rate. Compact analytic results for the magnetoresistance are achievable when carrier hopping occurs much more frequently than the hyperfine field precession period. In other regimes, the magnetoresistance can be straightforwardly evaluated numerically. Slow and fast hopping magnetoresistance are found to be uniquely characterized by their lineshapes. We find that the threshold hopping distance is analogous a phenomenological two-site model's branching parameter, and that the distinction between slow and fast hopping is contingent on the threshold hopping distance.