Organic magnetoresistance near saturation: mesoscopic effects in small devices

In organic light emitting diodes with small area the current may be dominated by a finite number, $N$ of sites in which the electron-hole recombination occurs. As a result, averaging over the hyperfine magnetic fields, ${\mathbf b}_h$, that are generated in these sites by the environment nuclei is incomplete. This creates a random ({\em mesoscopic}) current component, $\delta I({\mathbf B})$, at field ${\mathbf B}$ having relative magnitude $\sim N^{-1/2}$. We demonstrate that mesoscopic fluctuations develop at fields $|{\mathbf B}| \gg |{\mathbf b}_h|$, where the average magnetoresistance is near saturation. These fluctuations originate from the slow beating between $S$ and $T_{0}$ states of the recombining $e$-$h$ spin pair-partners. We identify the most relevant processes responsible for the current fluctuations as due to anomalously slow beatings that develop in sparse $e$-$h$ polaron pairs at sites for which the ${\mathbf b}_h$ projections on the external field direction almost coincide. To find the characteristic period $\Delta {\mathbf B}$ of the fluctuations, we calculate the correlator $K({\mathbf B}, \Delta {\mathbf B}) = \left<\delta I\left( {\mathbf B} - \Delta {\mathbf B} \right) \delta I\left( {\mathbf B} + \Delta {\mathbf B} \right)\right>$.