Temperature, electric-field, and carrier-density dependence of hopping magnetoresistivity in disordered organic semiconductors

Based on the extended variable range hopping mechanism in a disordered energy landscape with a Gaussian density of states, we determine the dependence of the magnetoresistivity on temperature, carrier density, magnetic field, and electric field. Experimental electric-field and temperature characteristics in device based on organic semiconductors are excellently reproduced with this unified description of the magnetoresistivity. We further show that the spin transport indeed can be explained by the fact that magnetic field will decrease the density of transport states and similar to the decrease of carrier density without it. We finally demonstrate that magnetoresistivity is strongly dependent on the carrier density; by changing the carrier density in the hopping system, the magnetoresistivity can increase more than 500 times.

Figure 1

(a) Three types of transport mode in organic spintronic devices, such as spin exchange, polaron hopping, and bipolaron hopping. (b) Diagram of variable range hopping (VRH) transport with the density of states under the effect of electric and magnetic field, where the current is carried by the hopping of polarons or bipolarons.

Figure 2

Magnetic field dependence of magnetoresistance (MR) at various voltages. Symbols: experimental data from Ref. [37]. Lines: fits using the theoretical model given by Eq. (9).

Figure 3

Electric-field dependence of MR for a larger localization length of $a^{-1}=5\AA$. Inset: for a smaller localization length of $a^{-1}=1\AA$.

Figure 4

Temperature dependence of MR. Symbol: experimental data from Ref. [41]. Solid line: fits using the theoretical model given by Eq. (9). Inset: temperature dependence of magnetic resistivity.

Figure 5

Carrier-density dependence of MR for different temperatures and magnetic field.

Figure 6

MR as a function of Hubbard energy for different disorder parametric in the normalized Fermi level $E_f/\sigma$.

Figure 7

Schematic explanation for carrier-density dependence of MR.