Evaluation of spin-flip scattering in chirality-induced spin selectivity using the Riccati equation

The chirality-induced spin selectivity (CISS) in layers of helical molecules has gained considerable attention in the emerging field of spintronics, because the effect enables spin-filter devices under ambient conditions. Several theoretical studies have been carried out to explain this effect on a microscopic scale, but the origin of the effect is still controversial. In particular, the role of spin-flip scattering during electron transport is an open issue. In this study, we describe the electron and spin transport by macroscopic rate equations including spin-dependent losses and spin-flip scattering. We reduce the problem to the solution of the Riccati differential equation to obtain analytical expressions. The results allow the strength and scalability of CISS based spin-filters to be determined and interpreted from experimental data or quantum mechanical models. For the helical systems studied experimentally so far, it turns out that spin-flip scattering plays a minor role.