Anomalous Magnetoresistance beyond the Julli\`ere Model for Spin Selectivity in Chiral Molecules

The issue of anomalous high magnetoresistance, beyond the Julli\`ere model, observed in nonmagnetic electrode-chiral molecular-ferromagnetic electrode devices has puzzled the community for a long time. Here, by considering the magnetic proximity effect which shifts the nonmagnetic-ferromagnetic interface toward chiral molecules, we show the anomalous high magnetoresistance beyond the spin polarization in ferromagnetic electrodes even in the very weak spin-orbit coupling. Our results are in excellent agreement with the experiments, demonstrating that the spin-orbit coupling plays a fundamental role in chiral-induced spin selectivity and the magnetic proximity effect can dramatically enhance the magnetoresistance. These results elucidate the interaction between chiral molecules and ferromagnetic electrodes and facilitate the design of chiral-based spintronic devices.