Spin Hall Effect in Disordered Organic Solids.

We study the spin Hall effect (SHE) in disordered π-conjugated organic solids, where individual molecules are oriented randomly and electrical conduction is via carrier hopping. The SHE, which arises from interference between direct (i→j) and indirect (i→k→j) hoppings in a triad consisting of three molecules i, j, and k, is found to be proportional to λ(n(i)×n(j)+n(j)×n(k)+n(k)×n(i)), where λ is the spin admixture of π electrons due to the spin-orbit coupling and n(i) is the orientation vector of molecule i. Electrical conductivity σ(qq) (q=x,y,z) and spin Hall conductivity σ(sh) are computed by numerically solving the master equations of a system containing 32×32×32 molecules and summing over contributions from all triads in the system. The obtained value of the spin Hall angle Θ(sh) is consistent with experimental data in PEDOT: PSS, with a predicted temperature dependence of logΘ(sh)∼T(-1/4).