Spin-Orbit Coupling, Spin Relaxation, and Spin Diffusion in Organic Solids

We develop a systematic approach of quantifying spin-orbit coupling (SOC) and a rigorous theory of carrier spin relaxation caused by the SOC in disordered organic solids. The SOC mixes up and down spin in the polaron states and can be characterized by an admixture parameter gamma(2). This mixing effects spin flips as polarons hop from one molecule to another. The spin relaxation time is tau(sf) = (R) over bar (2)/(16 gamma(2)D), and the spin diffusion length is L(s) = (R) over bar /4 vertical bar gamma vertical bar, where (R) over bar is the mean polaron hopping distance and D the carrier diffusion constant. The SOC in tris-(8-hydroxyquinoline) aluminum (Alq(3)) is particularly strong due to the orthogonal arrangement of the three ligands. The theory quantitatively explains the temperature-dependent spin diffusion in Alq(3) from recent muon measurements.