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 electron-hole ($e$-h) recombination occurs. As a result, averaging over the hyperfine magnetic fields, ${\mathit{b}}_h$, that are generated in these sites by the environment nuclei is incomplete. This creates a random (mesoscopic) current component, $\delta I\left(\mathit{B}\right)$, at field $\mathit{B}$ having relative magnitude $\sim$$N^{-1/2}$. To quantify the statistical properties of $\delta I\left(\mathit{B}\right)$ we calculate the correlator $K(\mathit{B},\Delta \mathit{B})=\langle \delta I(\mathit{B}-\frac{\Delta \mathit{B}}{2})\delta I(\mathit{B}+\frac{\Delta \mathit{B}}{2})\rangle$ for parallel, $\Delta \mathit{B}\parallel \mathit{B}$, and perpendicular, $\Delta \mathit{B}\perp \mathit{B}$ orientations of $\Delta \mathit{B}$. We demonstrate that mesoscopic fluctuations develop at fields $\left|\mathit{B}\right|\gg |{\mathit{b}}_h|$, where the average magnetoresistance is near saturation. These fluctuations originate from the slow beating between the singlet ($S$) and triplet ($T_0$) states of the recombining $e$-h spin-pair partners. We identify the most relevant processes responsible for the current fluctuations as being due to anomalously slow beatings that develop in sparse $e$-h polaron pairs at sites for which the ${\mathit{b}}_h$ projections on the external field direction almost coincide.

Figure 1

The dependence $I\left(B\right)$ of the device current on the applied magnetic field is shown schematically in the strong-field limit $B\gg b_0$. Enlargement illustrates mesoscopic fluctuations emerging in a small sample. Two insets are the correlators of the mesoscopic fluctuations for $\Delta \mathit{B}\parallel \mathit{B}$ and $\Delta \mathit{B}\perp \mathit{B}$ plotted from Eqs. (13) and (15), respectively.

Figure 2

In a strongly inhomogeneous device with $W\gg L$ the current passage is dominated by the most conductive channels, $I={\sum }_n{I}_n$. Each current component is limited by the most resistive junction, illustrated schematically. The current through this junction is sensitive to the spin dynamics of the constituting PP. “Slow” pairs, shown in the enlargement, are those in which the $z$ projections of their hyperfine fields coincide accidentally. The inset shows ${\sum }_{n=1}^N{I}_n$ calculated for two realizations of $N=1\times {10}^4$ random hyperfine fields with rms $b_0={10}^2{\zeta }^{-1}$.

Figure 3

Schematic representation of the PP population dynamics in the strong-field domain. For variants of cycle I (IV) the pair is assembled and, subsequently, disassembled in the $T_{+}$ ($T_{-}$) state. For variants II (III) the pair is assembled in the $S$ ($T_0$) state, in which it undergoes slow dynamics prior to disassembly. In the course of the slow dynamics the pair can recombine; recombination is possible only from $S$. Since the transport is unidirectional, current is passed through a junction upon completion of each cycle variant.