Hyperfine-induced spin relaxation of a diffusively moving carrier in low dimensions: implications for spin transport in organic semiconductors

摘要

The hyperfine coupling between the spin of a charge carrier and the nuclearspin bath is a predominant channel for the carrier spin relaxation in manyorganic semiconductors. We theoretically investigate the hyperfine-induced spinrelaxation of a carrier performing a random walk on a d-dimensional regularlattice, in a transport regime typical for organic semiconductors. We show thatin d=1 and d=2 the time dependence of the space-integrated spin polarization,P(t), is dominated by a superexponential decay, crossing over to a stretchedexponential tail at long times. The faster decay is attributed to multipleself-intersections (returns) of the random walk trajectories, which occur moreoften in lower dimensions. We also show, analytically and numerically, that thereturns lead to sensitivity of P(t) to external electric and magnetic fields,and this sensitivity strongly depends on dimensionality of the system (d=1 vs.d=3). Furthermore, we investigate in detail the coordinate dependence of thetime-integrated spin polarization, $\sigma(r)$, which can be probed in the spintransport experiments with spin-polarized electrodes. We demonstrate that,while $\sigma(r)$ is essentially exponential, the effect of multipleself-intersections can be identified in transport measurements from the strongdependence of the spin decay length on the external magnetic and electricfields.