Spin–orbit coupling and spin relaxation rate in singly charged π-conjugated polymer chains

In inorganic semiconductor spintronics the spin-diffusion length is usually limited by spin–orbit coupling. Here we examine the effect of spin–orbit coupling in organic spintronics. We consider singly charged π-conjugated polymer chains. We show that the diagonal matrix elements for spin–orbit coupling are zero. Even the off-diagonal matrix elements are zero or negligibly small unless a twisted, non-planar polymer chain is considered. We calculate these matrix elements as a function of twist angle using tight-binding wavefunctions. We show that time reversal symmetry prevents spin–orbit induced spin-precession and propose a phonon-assisted spin-flip process.