Spin-orbit coupling in organic spintronics

I will talk about spin-orbit coupling (SOC) in $\pi$-conjugated organicmaterials and its effects on spin characteristics including the spin-relaxation time, spin-diffusion length, and $g$ factor [1]. While $\pi$ electrons are responsible for low-energy electrical and optical processes in $\pi$-conjugated organic solids, $\sigma$ electrons must be explicitly included to properly describe the SOC. The SOC mixes up- and down-spin states and, in the context of spintronics, can be quantified by an admixture parameter in the electron and hole polaron states in $\pi$-conjugated organics. Molecular geometry fluctuations such as ring torsion, which are common in soft organic materials and may depend on sample preparation, are found to have a strong effect on the spin mixing. The SOC-induced spin mixing leads to spin flips as polarons hop from one molecule to another, giving rise to spin relaxation and diffusion. The spin-relaxation rate is found to be proportional to the carrier hopping rate. The spin-diffusion length depends on the spin mixing and hopping distance but is insensitive to the carrier mobility. The SOC influences the $g$ factor of the polaron state and makes it deviate from the free-electron value. The SOC strengths in common organics are quantified based on first-principles calculations and their values in tris-(8-hydroxyquinoline) aluminum (Alq$_3$) and in copper phthalocyanine (CuPc) are particularly strong, due to the orthogonal arrangement of the three ligands in the former and Cu $3d$ orbitals in the latter. The theory quantitatively explains the recent measured spin-diffusion lengths in Alq$_3$ from muon spin rotation and in CuPc from spin-polarized two-photon photoemission. \\[4pt] [1] Z. G. Yu, Phys. Rev. Lett. {\bf 106}, 106602 (2011); Phys. Rev. B {\bf 85}, 115201 (2012).