Bipolaron Mechanism for Organic Magnetoresistance

We present a mechanism for the recently discovered magnetoresistance in disordered $\pi$-conjugated materials, based on hopping of polarons and bipolaron formation, in the presence of the random hyperfine fields of the hydrogen nuclei and an external magnetic field. Within a simple model we describe the magnetic field dependence of the bipolaron density. Monte Carlo simulations including on-site and longer-range Coulomb repulsion show how this leads to positive and negative magnetoresistance. Depending on the branching ratio between bipolaron formation or dissociation and hopping rates, two different line shapes in excellent agreement with experiment are obtained.

Figure 1

Hyperfine field average of the function $f(B)$ of Eq. (2), determining the bipolaron probability, for various branching ratios $b=r_{\alpha \to \beta }/r_{\alpha \to e}$. The lower three thick lines show Lorentzian fits, the upper three fits to the non-Lorentzian empirical law. Inset: model as described in the main text, with the black arrow indicating the spin of a polaron present at $\beta$ (arbitrarily chosen opposite to the local magnetic field) and the gray arrows the spin of a possible additional polaron.

Figure 2

Symbols: ○, simulated magnetoconductance traces for a particular choice of parameters. □, bipolaron formation and dissociation rates multiplied by $b^{\prime }=10$. Solid lines: fits through □ and ○ with the empirical laws $\propto B^2/(|B|+B_0{)}^2$ ($B_0\approx 2.75B_{\mathrm{hf}}$) and $\propto B^2/(B^2+B_0^2)$ ($B_0\approx 3.5B_{\mathrm{hf}}$), respectively.

Figure 3

Simulated magnetoconductance for $B/B_{\mathrm{hf}}=100$ and $kT/\sigma =0.1$ as a function of the bipolaron energy $U$ for (a) $eEa/\sigma =0.3$ and (b) $eEa/\sigma =0.6$ for several choices of the Fermi level, $E_{\mathrm{F}}$. The model parameters are assigned.

Figure 4

Simulated magnetoconductance for $B/B_{\mathrm{hf}}=100$ as a function of $\sigma /kT$ for several choices of the model parameters. The model parameters are assigned.

Figure 5

(a) Simulated magnetoconductance for $B/B_{\mathrm{hf}}=100$ as a function of the long-range Coulomb repulsion strength $V$ for several choices of the model parameters. (b) Magnetic field induced change, $\Delta P/P$, in polaron population, $P$, as a function of $V$. The inset shows $P$ vs $V$. The model parameters are assigned.