Spin transport with dispersive traps: Narrowing of the Hanle curve

We study theoretically the spin transport in a device in which the active layer is an organic film with numerous deep and widely dispersed in energy in-gap levels serving as traps. A carrier, diffusing between a magnetized injector and detector, spends a considerable portion of time on the traps. This feature of transport does not affect the giant magnetoresistance, which is sensitive only to the mutual orientation of magnetizations of the injector and detector. By contrast, the presence of traps strongly affects the sensitivity of the spin transport to an external magnetic field perpendicular to the magnetizations of the electrodes (the Hanle effect). Namely, the Hanle curve narrows dramatically and develops a flat background. The origin of such a narrowing is that the spin precession takes place during the entire time of the carrier motion between the electrodes, while the spin relaxation takes place only during diffusive motion between the subsequent traps. If the resulting width of the Hanle curve is smaller than the measurement resolution, observation of the Hanle peak becomes impossible. This would explain why the Hanle effect is missing in experiments on organic spin valves, where the giant magnetoresistance is unambiguously detected.

Figure 1

Carrier transport between the magnetized electrodes in the presence of deep traps is illustrated schematically in (a) coordinate and (b) energy spaces. An injected spin-up carrier relaxes the spin while visiting the sites numbered as 1, 3, 4, and 5, but preserves the spin while visiting the traps numbered as 2 and 6.

Figure 2

A cartoon model of a two-step transport between the magnetized electrodes. The intermediate states are a trap $\mathcal{T}$, with a long waiting time and no local field, and a site $\mathcal{S}$, which hosts the field ${\mathit{B}}_{\mathcal{S}}$. The trap dominates the Hanle response in external field ${\mathit{\omega }}_L$ while the site fully controls the value of GMR.

Figure 3

Evolution of the Hanle response $R_H\left({\omega }_L\right)$ with the density of traps $\mathcal{N}$ measured in the units ${\left(D{\tau }_0\right)}^{-1/2}$, is plotted from Eqs. (15), (19), and (20). Three curves correspond to $\mathcal{N}=0$ (black), $\mathcal{N}={(2/D{\tau }_0)}^{1/2}$ (blue), and $\mathcal{N}=2{(2/D{\tau }_0)}^{1/2}$ (green). The characteristic density ${\left(D{\tau }_0\right)}^{-1/2}$ corresponds to one trap per diffusion displacement during the trapping time.