Circuit-model analysis for spintronic devices with chiral molecules as spin injectors

Recent research discovered that charge-transfer processes in chiral molecules can be spin-selective, and the effect was named chiral-induced spin selectivity (CISS). Follow-up work studied hybrid spintronic devices with conventional electronic materials and chiral (bio)molecules. However, a theoretical foundation for the CISS effect is still in development, and the spintronic signals were not evaluated quantitatively. We present a circuit-model approach that can provide quantitative evaluations. Our analysis assumes the scheme of a recent experiment that used photosystem I (PSI) as spin injectors, for which we find that the experimentally observed signals are, under any reasonable assumptions on relevant PSI timescales, too high to be fully due to the CISS effect. We also show that the CISS effect can in principle be detected using the same type of solid-state device, and by replacing silver with graphene, the signals due to spin generation can be enlarged four orders of magnitude. Our approach thus provides a generic framework for analyzing these types of experiments and advancing the understanding of the CISS effect.

Figure 1

Electron transfer chain of PSI and the geometry of the solid-state device used in Ref. [26]. The device was a stack of 150 nm of nickel, 0.5 nm of ${\mathrm{AlO}}_x$, and 50 nm of silver. PSI was immobilized on top of the silver layer, and the voltage difference between the silver and the nickel was measured. PSI is represented by the green area on which the structure of a part that contains the PSI electron transfer chain is overlaid. The structure highlights key cofactors such as ${\mathrm{Fe}}_{\text{4}}{\mathrm{S}}_{\text{4}}$ clusters ($F_B$, $F_A$, and $F_X$), primary electron acceptors ($A_1$ and $A_0$), the reaction center (P700), and the chiral (helical) structural surroundings. Here PSI is in the $up$ orientation, with P700 close to silver, and the ${\mathrm{Fe}}_{\text{4}}{\mathrm{S}}_{\text{4}}$ clusters at the far end. Red labelings mark the light-induced electron transfer process, including the photon ($h\nu$) and the electron ($e$), the photoexcitation pathway (solid arrows), and the unknown relaxation pathway (dashed arrow). The protein structure is taken from the RCSB Protein Data Bank (PDB ID 1JB0) [37].

Figure 2

PSI modeled as a spin-current source. (a) PSI compared to a pure spin-current source with a spin relaxation pathway. It creates spin accumulation in the silver layer upon light illumination. Spin-up electrons (red) are transferred from silver to PSI, while spin-down electrons (blue) are transferred back to silver. No charge current flows through PSI, but a spin-down accumulation is created in silver. (b) The model of panel (a), reduced to its net spin-injection effect. The contribution from each component in the dashed box in (a) cannot be clearly distinguished, therefore we treat them together as an ideal spin-current source $I_s$ with a parallel resistance $R$. Since the total impedance in PSI is much larger than that of silver, we consider $R\to \infty$. The net effect of this reduced model is to inject a spin current $I_s$ into the silver layer. Here we show the drawing for one PSI unit, but the spin currents ($I_{\text{PSI}},I_s$) concern the values for the entire PSI ensemble on the device.

Figure 3

Two-current circuit model for the spintronic device of Ref. [26] (symbols introduced in the main text). Different parts of the device are separated by dashed lines. Spin-up and spin-down current channels are distinguished by color. PSI is represented by a pure spin-current source as introduced in Fig. 2. The spin relaxation in silver is modeled as a pathway with spin-flip resistance $R_{\text{sf-Ag}}$ connecting the two spin-current channels.

Figure 4

Electron transfer process and corresponding timescales in PSI, here depicted in a manner where the vertical placements of states reflect their energy levels. Here the PSI unit is in the $up$ orientation. The excitation process is labeled by the black arrows with corresponding timescales marked. However, the relaxation process is unknown (dashed arrow). The blue scale shows the spatial distance between different parts of the electron transfer chain.

Figure 5

A circuit model considering the spin injection in a nonmagnetic conducting material. Spin-up and spin-down components are separated into red and blue channels. A pure spin current $I_{\uparrow \downarrow }$ is sourced between the two channels. Spin relaxation is modeled as a spin-flip resistance $R_{\text{sf}}$. The spin accumulation is measured as the signal $V_{\uparrow \downarrow }$ from a voltage meter that has fully spin-selective contacts.