Anomalous Magnetoresistance beyond the Jullière Model for Spin Selectivity in Chiral Molecules

Abstract

The issue of anomalous high magnetoresistance, beyond the Jullière 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.

Figures (4)

• Figure 1: Schematic of chiral molecular model and the corresponding spin polarization. (a) Schematic of a N-chiral molecule-FM (or N) device. The right electrode is set to be nonmagnetic to study the spin polarization $P_s$ for electron propagation through chiral molecules, or to be ferromagnetic to study the MR. In the presence of MPE induced by the FM electrode, the rightmost site of chiral molecules becomes magnetized. (b) Schematic diagram of two-pathway interference. (c) and (d) are conductances $G_\uparrow$, $G_\downarrow$ and spin polarization $P_s$ versus the energy $E$ in N-chiral molecule-N device at extremely weak SOC $s_1=0.01t_1$. Here, $E$ is the Fermi energy, $t_1$ is the intrachain hopping integral and $G_0=e^2/h$ is the quantum conductance.
• Figure 2: Conductance and MR in the N-molecule-FM device. (a) and (b) respectively show conductances $G_{+M}$, $G_{-M}$ and MR, $P_s P_{FM}$ versus Fermi energy $E$ in the device without MPE. Here $MR\le P_s P_{FM}<P_{FM}$ implies the validity of the Jullière model. (c) Conductances $G_{+M}$ and $G_{-M}$ versus $E$ by considering the MPE ($M=-\varepsilon_{FM}=t_1$). (d) MR in the presence of MPE for different MPE parameters, in which MR can be larger than $P_{FM}=30\%$, implying the invalidity of the Jullière model. In (a-d), the SOC strength $s_1=0.01t_1$.
• Figure 3: MR vs. parameters of the MPE and the physical mechanism for $MR>P_{FM}$. (a) 2D plot of MR versus the parameters $M$ and $\varepsilon_{FM}$ of the MPE at the Fermi level $E=-0.16t_1$. The dashed-white line represents $MR=P_{FM}=30\%$. (b) $P_s{\widetilde{P}}_{FM}$ as a function of $M$ and $\varepsilon_{FM}$. Here the $P_s{\widetilde{P}}_{FM}$ is almost identical to MR in (a). (c) and (d) Modified spin-up (blue line) and spin-down (red line) DOSs versus the energy $E$ for $M=-\varepsilon_{FM}=t_1$ (c) and $M=\varepsilon_{FM}=t_1$ (d). The green-dashed-vertical lines show $E=-0.16t_1$, the value of which is used in (a,b).
• Figure 4: I-V results for finite bias. (a) Current of the device versus the voltage $V$ with the right FM electrode under positive and negative magnetizations for $\Gamma_L=0.1t_1$. (b) MR versus the voltage $V$ for different $\Gamma_L$. The green dashed line is $P_{FM}=30\%$. In (a) and (b), the SOC strength $s_1=0.01t_1$, $E=-0.16t_1$ and $M={-\varepsilon}_{FM}=t_1$, and $I_0=e t_1/h$ is the current unit.