Mixed Quantum-Classical Approaches to Spin Current and Polarization Dynamics in Chiral Molecular Junctions

Chiral molecular junctions offer a promising platform for realizing chiral-induced spin selectivity (CISS), where spin filtering occurs without external magnetic fields. Here, we investigate spin transport in such junctions by combining quantum master equation (QME) methods for purely electronic dynamics with surface hopping (SH) and mean-field Ehrenfest (MF) approaches to incorporate electron-phonon coupling. To the best of our knowledge, this is the first study employing the SH method to investigate spin dynamics in molecular junctions. For low-frequency nuclear vibrations and weak molecule-lead coupling, the SH method is particularly suitable and outperforms MF. Our results show that transient spin polarization emerges but eventually vanishes. Bias, molecular length, and SOC govern the dynamics─higher bias enhances current but reduces polarization, while longer molecules and stronger SOC amplify it. Electron-phonon coupling modifies current-voltage responses, enhancing currents at moderate bias and suppressing them at high bias. However, the extent to which electronic and vibrational effects interplay in influencing CISS remains unclear, highlighting the need for further investigation. These findings underscore the complex relationship between electronic and vibrational interactions in CISS and suggest directions for future research in molecular spintronics.