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 γ². This mixing effects spin flips as polarons hop from one molecule to another. The spin relaxation time is τsf=R̄²/(16γ²D), and the spin diffusion length is Lₛ=R̄/4|γ|, where R̄ is the mean polaron hopping distance and D the carrier diffusion constant. The SOC in tris-(8-hydroxyquinoline) aluminum (Alq₃) is particularly strong due to the orthogonal arrangement of the three ligands. The theory quantitatively explains the temperature-dependent spin diffusion in Alq₃ from recent muon measurements.