Circuit-Model Analysis for Spintronic Devices with Chiral Molecules as Spin Injectors

Xu Yang,∗ Tom Bosma, Bart J. van Wees, and Caspar H. van der WalZernike Institute for Advanced Materials, University of Groningen, NL-9747AG Groningen, The Netherlands

(Dated: June 10, 2019)

Recent research discovered that charge transfer processes in chiral molecules can be spin selectiveand named the effect chiral-induced spin selectivity (CISS). Follow-up work studied hybrid spintronicdevices with conventional electronic materials and chiral (bio)molecules. However, a theoreticalfoundation for the CISS effect is still in development and the spintronic signals were not evaluatedquantitatively. We present a circuit-model approach that can provide quantitative evaluations. Ouranalysis 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 assumptionson relevant PSI time scales, too high to be fully due to the CISS effect. We also show that the CISSeffect can in principle be detected using the same type of solid-state device, and by replacing silverwith graphene, the signals due to spin generation can be enlarged four orders of magnitude. Ourapproach thus provides a generic framework for analyzing this type of experiments and advancingthe understanding of the CISS effect.

Electronic spin lies at the heart of spintronics due toits capability to convey digital information. In contrast,this quantum mechanical concept has found few applica-tions in chemistry and biology as the energy states associ-ated with opposite spin orientations are often degenerate.Molecular chirality, on the other hand, is thoroughly dis-cussed in chemistry and biology but rarely concerned inspintronics. In the past decade, the two concepts havebeen increasingly linked together thanks to the discoveryof the chiral-induced spin selectivity (CISS) effect, whichdescribes that the electron transfer in chiral moleculesis spin dependent.1–11 This discovery not only providesnew approaches to controlling chiral molecules12 and un-derstanding their interactions,13 but also opens up thepossibility of small, flexible, and fully organic spintronicdevices. Previously, organic materials were incorporatedin spintronic devices as spin transport channels and spin-charge converters, but the conversion efficiency remainedlow.14–22 Building on CISS, hybrid devices with efficientmolecular spin injectors and detectors were realized.23–32

However, a full understanding of the signals produced bythese devices is still lacking, and thereby the understand-ing of CISS largely hindered.

We present here a circuit-model approach to quantita-tively evaluating the spin signals measured from hybridsolid-state devices designed for studying the CISS effect.Similar approaches have been used for the analyses ofspintronic devices with metallic and semiconducting ma-terials.33–35 They provided accurate descriptions of ex-perimental results and have been extended to a widerange of device geometries. We apply here such mod-eling to devices with adsorbed molecular active layersinstead of metal contacts. While generally applicable,we take the device reported in Ref. 26 as a case studyfor demonstrating our approach. In comparison to ourrecent analysis using electron-transmission modeling,36

the circuit-model approach is more suited for including arole for optically driven chiral molecules, and for electrontransport outside the linear-response regime.

In the work of Ref. 26, cyanobacterial photosystem I

P700 A0

A1

FX

FA

FB

V

Ni

Ag

AlOx

𝑒

𝑒

𝑒

ℎ𝜐

PSI

FIG. 1. Electron transfer chain of PSI and the geometry ofthe solid-state device used in Ref. 26. The device was a stackof 150 nm of nickel, 0.5 nm of AlOx, and 50 nm of silver. PSIwas immobilized on top of the silver layer, and the voltagedifference between the silver and the nickel was measured. PSIis represented by the green area, on which the structure of apart that contains the PSI electron transfer chain is overlaid.The structure highlights key cofactors such as Fe4S4 clusters(FB, FA and FX), primary electron acceptors (A1 and A0),the reaction center (P700), and the chiral (helical) structuralsurroundings. Here PSI is in the up orientation, with P700close to silver, and the Fe4S4 clusters at the far end. Redlabellings mark the light induced electron transfer process,including the photon (hν) and the electron (e), the photo-excitation pathway (solid arrows) and the unknown relaxationpathway (dashed arrow). The protein structure is taken fromthe RCSB Protein Data Bank (PDB ID 1JB0).37

(PSI) protein complexes were self-assembled on a silver-AlOx-nickel junction and the orientation of PSI (up ordown) was controlled by mutations and linker molecules.Figure 1 shows a device with PSI in the up orientation.Here, P700, the reaction center of PSI, was located adja-cent to the silver layer. In P700, charge separation took

arX

iv:1

904.

0314

2v2

[co

nd-m

at.m

es-h

all]

7 J

un 2

019

2

V

Ni

Ag

AlOx

𝐼𝑃𝑆𝐼

𝑒

𝑒 𝑒 𝑒 𝑒 𝑒

𝑒

PSI A)

Ni

Ag

AlOx

𝐼𝑆

B)

𝑅 → ∞

𝑅𝑠𝑓−𝑃𝑆𝐼

𝑅𝑐𝑃𝑆𝐼↓ 𝑅𝑐𝑃𝑆𝐼↑

V

FIG. 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 toPSI, while spin-down electrons (blue) are transferred back to silver. No charge current flows through PSI but a spin-downaccumulation is created in silver. B) The model of panel A), reduced to its net spin-injection effect. The contribution from eachcomponent in the dashed box in A) cannot be clearly distinguished, therefore we treat them together as an ideal spin-currentsource Is with a parallel resistance R. Since the total impedance in PSI is much larger than that of silver, we consider R→ ∞.The net effect of this reduced model is to inject a spin current Is into the silver layer. Here we show the drawing for one PSIunit, but the spin currents (IPSI , Is) concern the values for the entire PSI ensemble on the device.

place upon the illumination of a 660-nm laser during theexperiments. It was described that the excited electrongot transferred to the Fe4S4 clusters at the other end ofPSI, and the hole left behind in P700 was refilled by anelectron from silver. This process causes a net upwardelectron transfer from silver to PSI, which, before relax-ation, results in a steady-state increase of the silver sur-face potential, as was observed using a Kelvin probe.26

In contrast, a device with PSI in the down orientationgave a decrease of silver surface potential upon light il-lumination, indicating a net downward electron transferfrom PSI into silver. Both devices were then placed un-der laser illumination in the presence of an out-of-planemagnetic field which was used to set the magnetizationof nickel in either the up or down direction. The chargevoltage between silver and the nickel layer was monitored.The absolute value of this voltage was found to be alwayslower when the electron transfer direction and the mag-netic field direction were parallel (both up or both down),and higher when they were anti-parallel (one up and onedown). This magnetic field dependence suggested thatthe electron transfer process in PSI was spin selective,and the preferred spin orientation was parallel to the elec-tron momentum. As PSI is one of Nature’s two majorlight-harvesting centers, this intriguing result indicatedthat electron spins may also play a role in photosynthe-sis.

However, an important question to address while con-sidering this conclusion is: How much of the observedmagnetic-field-dependent signal was from CISS? To an-

swer this question we need to understand the origin of themeasured steady-state magnetic-field-dependent voltage.Upon photo-excitation charge carriers were transferredfrom silver to PSI. These carriers must relax back to sil-ver via pathways inside PSI because there was no topelectrode providing alternative pathways. Both the ex-citation and relaxation pathways might exhibit spin se-lectivity. Qualitatively, as long as the CISS effects in thetwo pathways do not cancel each other, a net spin injec-tion into silver can be generated. This spin injection thencompetes with the spin relaxation process in silver, andresults in a steady-state spin accumulation which can in-deed be detected as a charge voltage between silver andthe nickel layer.38

To quantitatively evaluate this voltage signal, we adopta two-current circuit model where spin transport is de-scribed by two parallel channels (spin-up and spin-downchannels).39,40 The two channels are connected via a spin-flip resistance Rsf , which characterizes the spin relax-ation process in a nonmagnetic material. A derivation ofRsf and a more detailed introduction of the two-currentmodel concept can be found in Appendix A. For a thin-film nonmagnetic material, we find

Rsf = 2 ·λ2sf

d Arel σ(1)

(assuming d < λsf and Arel λ2sf ), where λsf is thespin-relaxation length of the material, σ is the conduc-tivity of the material, d is the thickness of the film, andArel is the relevant area of the film where spin injection

3

occurs. Notably, Rsf is entirely determined by the prop-erties of the material and the geometry of the device.

The role of PSI in the device can be characterized bytwo features. Firstly, due to the lack of a top electrode,there was (as a steady-state average) no net charge cur-rent flowing through PSI. Secondly, facilitated by CISS,PSI gave a net spin injection into silver. These two fea-tures resemble a pure spin-current source. Therefore,we model PSI as a pure spin-current source between thefully polarized spin-up (red) and spin-down (blue) chan-nels, as shown in Figure 2A). Upon photo-excitationPSI sources an internal spin current IPSI . The path-way with spin-flip resistance Rsf−PSI accounts for thespin relaxation inside PSI. At the PSI-silver interface thetwo channels encounter possibly spin-dependent contactresistances RcPSI↑ and RcPSI↓. The net spin current in-jected from PSI into silver is Is = η · IPSI , (−1 6 η 6 1),with η being the fraction of the photo-induced spin cur-rent that actually contributes to the spin accumulationin silver. Generically, we regard PSI as a black box: atwo-terminal unit that drives a spin current Is, as shownin Figure 2B). This will later be linked and comparedto known timescales for charge transfer processes insidePSI.

V

PSI Ag AlOx

𝑅𝑐𝐴𝑔 𝑅𝑐𝐴𝑔

Ni

𝑉𝑚𝑒𝑎𝑠

𝑅𝐴𝑔

𝑅𝐴𝑔

+

- 𝐼𝑆 𝑅 𝑅𝑠𝑓−𝐴𝑔

𝑅𝑡𝑢𝑛↑

𝑅𝑡𝑢𝑛↓

𝑅𝑐𝑁𝑖↑

𝑅𝑐𝑁𝑖↓

𝑅↑

𝑅↓

FIG. 3. Two-current circuit model for the spintronic deviceof Ref. 26 (symbols introduced in the main text). Differentparts of the device are separated by dashed lines. Spin-upand spin-down current channels are distinguished by color.PSI is represented by a pure spin-current source as introducedin Figure 2B). The spin relaxation in silver is modeled as apathway with spin-flip resistance Rsf−Ag connecting the twospin-current channels.

A circuit model for the entire device is shown in Fig-ure 3. RAg is the spin-independent resistance (in theout-of-plane direction) of the silver layer. Inside the sil-ver layer the spins can relax, as represented by a spin-flippathway with resistance Rsf−Ag. RcAg is the contact re-sistance between silver and the voltage meter. In prin-ciple these contacts could provide an extra pathway forelectron spins to relax, but in reality these contacts arelocated millimeters away from where spins are injected.This distance is much larger than the spin-relaxation

length in silver (about 150 nm at room temperature).41

Therefore, the spin relaxation through these contacts isnegligible and we can assume RcAg →∞.

Underneath the silver layer is the the AlOx tunnelbarrier and the ferromagnetic nickel layer. In theselayers electrons experience spin-dependent resistances:the tunnel resistance Rtun↑(↓) and the contact resistanceRcNi↑(↓) (which includes the out-of-plane resistance ofthe nickel layer). Note that here the subscript ↑(↓)refers to the corresponding spin-current channel, not tobe confused with the magnetization direction of nickelwhich determines the values of Rtun↑(↓) and RcNi↑(↓).These resistances can be combined using shorter nota-tions R↑ = Rtun↑ + RcNi↑ and R↓ = Rtun↓ + RcNi↓. Aninterchange of the R↑ and R↓ values thus accounts forthe reversal of the magnetization direction of nickel.

The magnetization direction of nickel can be describedas being parallel (p) or anti-parallel (ap) to the spin-upchannel. For each case the reading of the voltage meterVmeas is

V (p)meas =

1

2Is(R↑ −R↓)

Rsf−Ag

R↑ +R↓ +Rsf−Ag, (2a)

V (ap)meas =

1

2Is(R↓ −R↑)

Rsf−Ag

R↑ +R↓ +Rsf−Ag. (2b)

The change in the measured voltage upon the reversal ofthe nickel magnetization is therefore

Vdiff = V (ap)meas − V (p)

meas

= Is(R↓ −R↑)Rsf−Ag

R↑ +R↓ +Rsf−Ag

= IsReff ,

(3)

where Reff = Vdiff/Is is an effective spinvalve resis-tance.

For the envisioned spintronic behavior in Ref. 26, thismodel captures all relevant aspects for spintronic signalsin the linear transport regime, without making assump-tions that restrict its validity. It is thus suited for de-scribing the observed spin signals in a quantitative man-ner when the values of the circuit parameters are avail-able. For the device described in Ref. 26 we derive (seeAppendix B)

Reff ≈ 15 mΩ . (4)

Note that Reff is fully determined by the properties ofthe Ag-AlOx-Ni multilayer, and deriving its value doesnot use any estimates or assumptions concerning PSI.Furthermore, by carefully choosing material parameters,the estimate of Reff is of great accuracy. This is alsodiscussed in Appendix B.

This result for Reff directly yields values for the in-jected spin current that was flowing in the experimentof Ref. 26. For the up orientation of PSI, the mea-sured voltage difference Vdiff was about 50 nV. Thus,

4

the net spin current injected into silver must have beenIs = Vdiff/Reff ≈ 3 µA. For the opposite PSI orienta-tion, the measured Vdiff was about 10 nV, and accord-ingly, Is ≈ 0.6 µA.

Next, we turn these spin-current values into valuesfor the timescale τ that must then hold for the chargeexcitation-relaxation process for illuminated PSI. Here τcan be understood as the time interval between two con-secutive photo-excitation processes from the same PSIunit. By assuming that the intensity of the illumina-tion is strong enough to drive all the PSI units in con-tinuous excitation-relaxation cycles (saturated), we canwrite i = −e/τ , where e is the elementary charge and ithe photo-induced charge current in a PSI unit. The sumof all contributions i (sum over all PSI units) should thenbe high enough to provide the above Is values. In orderto check this, we will assume the highest number for PSIunits that can contribute, and that they all maximallycontribute. Therefore, we first assume that over the rel-evant area of the device the PSI units form a denselypacked, fully oriented monolayer, and that all PSI unitsfunction identically. Secondly, we assume that photo-induced spin current from each PSI unit is fully injectedinto the silver layer, i.e. η = 1. Further, we assumethat the polarization of the CISS effect in PSI is 50%,on par with the reported CISS polarization in other chi-ral systems.3,8,26 For these assumptions we find (detailsin Appendix C) that for the up orientation of PSI, τshould not be larger than 100 ps. For the down orienta-tion this limit is τ 6 500 ps. Note that the boundarieshere correspond to the most ideal scenario, and in prac-tice the required τ values could be much smaller thanthese boundaries.

P700

A0

A1 FX

FA FB

ℎ𝜐

30 ps

20 ns 1 µs

Ag

2.2 nm 3.0 nm

EF

FIG. 4. Electron transfer process and corresponding timescales in PSI, here depicted in a manner where the verticalplacements of states reflect their energy levels. Here the PSIunit is in the up orientation. The excitation process is labeledby the black arrows with corresponding time scales marked.However, the relaxation process is unknown (dashed arrow).The blue scale shows the spatial distance between differentparts of the electron transfer chain.

We now compare these requirements for τ with thewell-studied timescales of the electron transfer processin PSI. During photosynthesis, the photo-induced chargeseparation in PSI takes place at the primary donor P700.Electrons are then transferred through a series of ac-cepters along the electron transfer chain: A0, A1, andthe Fe4S4 clusters FX, FA and FB (see Figure 4).37,42,43

The initial electron transfer from P700 to A1 is ultra-fast (∼30 ps), and further transfer to FX happens in 20-200 ns. Then, the electron transfer from FX through FA

to FB typically takes 500 ns to 1 µs.43

The requirements for τ values that we found are–regardless the PSI orientation–only compatible with theinitial ultrafast electron transfer from P700 to A1. Thesubsequent steps are at least two orders of magnitude tooslow. Thus, concluding that the observed signals fullyresult from the CISS effect requires the existence of anultrafast relaxation process where electrons immediatelyreturn to P700 after their initial transfer from P700 toA1. This process does not exist in Nature, because itwould stop the trans-membrane electron transfer in pho-tosynthesis. We should, nevertheless, consider whetherit can occur in the device, since PSI is there located in avery different environment.

In the solid-state environment, faster relaxation thanin Nature could be due to, for instance, the use of linkermolecules, the mutations of PSI, or the presence of sil-ver (thanks to its high density of states). The linkermolecules are unlikely to be the reason, because theirsize is significantly smaller than PSI, and the electrontransfer chain is positioned deeply in the center of PSI(Figure 4). Moreover, it was stated in Ref. 26 that theobserved signals do not depend on the linker molecules.

The mutations and the metal substrate, on the otherhand, could indeed affect the electron transfer. To as-sess the effects, we can draw direct comparisons be-tween Ref. 26 and Ref. 44. In both works the samemutations of PSI were performed in order to covalentlybind PSI to metal substrates (Ag and Au respectively).Ref. 44 found, for the bound PSI, the fastest excitation-relaxation cycle of around 15 ns. For Ref. 26 the valueshould be on the same order of magnitude due to the largesimilarities between the two experiments. However, thisvalue is still two orders of magnitude slower than themost ideal scenario that we have assumed. Therefore,the CISS-related spin signals in Ref. 26 was at least twoorders of magnitude lower than the measured value. Infact, if we consider a realistic situation where PSI unitsdo not form a fully-oriented and densely-packed layer onsilver and |η| < 1, the actual CISS signals should be evensmaller.

Although other mechanisms may still be at play,45,46

they are not able to make up for the orders of magnitudeof deviation. We thus conclude that the observed signalsin Ref. 26 cannot be fully due to the light-induced spininjection from PSI, unless the very similar PSI conditionsin Ref. 26 and Ref. 44 could lead to orders of magnitudeof difference in PSI charge transfer time scales. This sug-

5

gests that the magnetic-field dependence of the signals inRef. 26 may predominantly originate from other effects.Some possible sources are discussed in Appendix D.

Nevertheless, our analysis shows that an experimentalapproach as in Ref. 26 is in principle suited for confirmingspin signals with CISS origin. It also provides insight inhow one can optimize this type of experiments towards asystem that would yield CISS spin signals with a highermagnitude. The most direct improvement can be ob-tained via a system that has higher values for Rsf andReff in Eqs. (1)-(4). A good example to consider is to usegraphene as replacement for the silver layer. This shouldboost the spin signals by four orders of magnitude, sinceit would increase the value of Reff from ∼15 mΩ to avalue of ∼0.5 kΩ (see Appendix B for details).

In summary, we introduced a two-current circuit-modelapproach to quantitatively assessing spintronic signalsin hybrid devices which combine conventional electronicmaterials with (bio)organic molecules that are spin-activedue to the CISS effect. As an example, we applied it toa case where the active layer has electrical contact onlyon one side, and we showed how the quantitative anal-ysis can link the observed spin signals to charge excita-tion and relaxation times in the molecules. Our analysisshowed that such devices can readily give spintronic sig-nals that are strong enough for detection with currenttechnologies. However, it also revealed that in the ex-periment of our case study (Ref. 26), the observed sig-nals must have had strong contributions from other ef-fects. Future experimental work should aim at separatingother signals from signals given by CISS, and our circuit-model approach assists in designing these experiments.We also recommend using devices with nonlocal geome-tries in order to separate charge and spin signals.36,38 Inthese geometries, the spin signals can also be quantita-tively assessed using our circuit-model approach.

ACKNOWLEDGMENTS

The authors acknowledge the financial support fromthe Zernike Institute for Advanced Materials (ZIAM),and the Spinoza prize awarded to Prof. B. J. van Wees bythe Nederlandse Organisatie voor Wetenschappelijk On-derzoek (NWO). We thank A. Herrmann and P. Gordi-ichuk for stimulating discussions.

Appendix A: Two-current model and derivation ofRsf

In this section we use a simple example to introducethe concept of two-current circuit models39,40 and to il-lustrate what can be experimentally detected. Along theway we derive Rsf (Equation 1).

For describing spintronic signals, we use modelingwhere spin transport in conductors is described as twoparallel channels each allowing only one type of spin

(spin-up and spin-down channels, colored in red and bluerespectively in Figure 5).39,40 This allows us to separatethe total electrical current I into spin-up and spin-downcomponents: I = I↑ + I↓. The difference between thetwo components is referred to as a spin current I↑↓, withI↑↓ = I↑−I↓. A spin current injected into a non-magneticmaterial will result in a spin accumulation (chemicalpotential difference between the spin-up and spin-downchannels) µ↑↓ = µ↑ − µ↓. Within the material spin ac-cumulation decays exponentially over time due to spinrelaxation mechanisms.47 As an introduction to this typeof modeling, we first show a simple case with a pure spincurrent in a nonmagnetic material, as shown in Figure 5.A pure spin current means that the net charge currentI = I↑ + I↓ = 0. The spin relaxation is modeled as apathway connecting the two channels, with a spin-flipresistance Rsf . The voltage difference between the twochannels, as measured with fully spin-selective contacts,is therefore V↑↓ = I↑↓ ·Rsf .

Within the nonmagnetic material the steady-state spinaccumulation is a balance between the spin injection dueto I↑↓ and the spin relaxation in the material. This isdescribed as

0 =dµ↑↓dt

= −µ↑↓τsf

+ 2 · I↑↓e· 1

ν3D · Vrel, (A1)

where τsf is the spin-relaxation time in the material, ν3Dis the three-dimensional (3D) density of states (units ofeV−1m−3), and Vrel is the relevant volume for the spininjection-relaxation balance in the material. The factor 2arises from the fact that when one electron is transferredfrom the spin-down channel to the spin-up channel, thedifference between the spin-up and spin-down populationincreases by two. The steady state solution for the mea-sured voltage is

V↑↓ =µ↑↓e

= I↑↓ ·1

Vrel· 1

ν3D· 2τsfe2

. (A2)

+

- 𝐼↑↓ 𝑉↑↓ V 𝑅𝑠𝑓

FIG. 5. A circuit model considering the spin injection ina nonmagnetic conducting material. Spin-up and spin-downcomponents are separated into red and blue channels. A purespin current I↑↓ is sourced between the two channels. Spinrelaxation is modeled as a spin-flip resistance Rsf . The spinaccumulation is measured as the signal V↑↓ from a voltagemeter that has fully spin-selective contacts.

6

For further analysis we also consider the role of the spinrelaxation length of the material, λsf =

√D τsf , where

D is the diffusion coefficient for electrons in the mate-rial. The Einstein relation gives σ = e2ν3DD, where σ isthe conductivity of the material.38 Consequently, Equa-tion (A2) becomes

V↑↓ = 2 I↑↓λ2sfVrel σ

, (A3)

and therefore:

Rsf =V↑↓I↑↓

= 2λ2sfVrel σ

. (A4)

We can see that the spin-flip resistance is completely de-termined by the properties of the material and the rele-vant volume concerned for each specific device.

Now we determine the relevant volume Vrel for a par-ticular device geometry: a thin layer of a nonmagneticconducting material. The spin accumulation spreads outin a volume that is limited by either the spin relaxationlength λsf , or the boundaries of the device, whicheveris smaller. For the thin layer, we assume that the spincurrent is homogeneously injected from its top surfaceover a limited area, which is referred to as the relevantarea Arel. Spin accumulation then occurs in the thinlayer within the area Arel, as well as directly outside theboundaries of Arel, up to a distance of ∼λsf . However,we consider here the situation where Arel λ2sf , andwe can therefore neglect the spin accumulation outsideArel. In the perpendicular direction we consider the casethat the thickness of the layer d < λsf , which meansthat the spin-transport length is limited by the thick-ness of the layer rather than the spin relaxation length ofthe material. As a consequence, we have Vrel = d Arel.Substituting this into Equation (A4) gives

Rsf = 2λ2sf

d Arel σ. (A5)

When the thin layer (three-dimensional) is replacedby a truly two-dimensional material, such as graphene,the thickness of the material can no longer be defined.The material then has a two-dimensional density of statesν2D (units of eV−1m−2), and one should use the Einsteinrelation for the 2D conductivity σ2D = e2ν2DD. Whenassuming again Arel λ2sf , the spin-flip resistance for a2D system is given as

Rsf−2D = 2λ2sf

Arel σ2D. (A6)

Appendix B: Estimate for the value of Reff

In this section we estimate a value for the effectivespinvalve resistance Reff . We first focus on a value forthe experimental work of Ref. 26, and then on a similarsystem that has the silver layer replaced by graphene.

The tunneling resistance between silver and nickel wasmeasured to be about 1 kΩ in Ref. 23, which used a de-vice identical to that in Ref. 26. The change of this resis-tance under magnetization reversal, as characterized byits tunneling magnetoresistance (TMR = (R↓−R↑)/R↑),depends on the spin polarization of nickel PNi, anddoes not depend on the magnetization axis.48–50 It fol-lows TMR = 2PNi/(1 − PNi), and takes a value ofTMR ≈ 100% for the PNi ≈ 33% value used in Ref. 26.The actual TMR value may be lower than 100% becauseof temperature and bias voltage, but should be on thesame order of magnitude.50,51 Moreover, taking the up-per limit of TMR is consistent with us deriving the lowerlimit of Is and the upper limit of τ . Therefore, we mayassume R↓ = 1 kΩ and R↑ = 0.5 kΩ. While this is anestimate, the value must be of the correct order of magni-tude. Furthermore, later analysis will show that it is thespin-flip resistance of silver that governs the magnitudeof the effective resistance Reff .

To determine the spin-flip resistance of silver, we usethe previously derived Equation (A5). For the devicewe discuss, the thickness of the silver layer d = 50 nm,the area of the junction Arel = 1 µm × 1 µm. For spinrelaxation parameters we take reported values for a meso-scopic silver strip at room temperature λsf−Ag ≈ 150 nm,and ρAg = 1/σAg ≈ 50 nΩ · m.41 We point out thatthese parameters are not only affected by the materialchoice, but also by factors such as device geometry, fab-rication techniques, and temperature.52 The values wechose were reported for a device that had geometries veryclose to that used in Ref. 26, was fabricated with the sametechnique, and was measured at the same temperature.With these, we get the spin-flip resistance in our modelRsf−Ag = 45 mΩ.

Substituting Rsf−Ag, together with the assumed R↑,R↓ values in Equation 3 gives an effective resistance

Reff ≈ 15 mΩ. (B1)

Note that Reff is fully determined by the propertiesof the Ag-AlOx-Ni multilayer device, and estimating itsvalue did not use any estimates or assumptions concern-ing PSI.

For the scenario where the silver layer is replaced by agraphene layer, we apply a similar analysis, while usingEquation (A6) instead of Equation (A5). For graphene,typical material parameters are a square resistance of theorder of 1 kΩ,53,54 and a spin relaxation length of λsf ≈10 µm.54,55 This gives Rsf−2D ≈ 1 MΩ, and Reff ≈0.5 kΩ for a device that is for other aspects identical tothe device of Ref. 26

Appendix C: Analysis of compatible PSI excitationand relaxation times

In the main text we derived the Is values without us-ing any information about PSI. Here we analyze what thevalues mean in terms of photo-excitation and relaxation

7

times of individual PSI units. We first assume that Is isfully induced by the spin-selective electron transfer dur-ing photo-excitation and relaxation cycles in PSI. Thenwe examine the validity of this assumption by deriving(from Is) the values of photo-excitation and relaxationtimes of individual PSI units. In the following discussiona few more assumptions are made. We carefully assumescenarios which consistently lead to the upper bound-ary of the photo-excitation-relaxation times. In the maintext we showed that even this upper boundary is still toolow to be realistic.

We write Is as a sum of the contributions from indi-vidual PSI units,

Is =

N∑n=1

is,n (C1)

where is is the spin current injected from each PSI unitinto silver, the index n runs over all individual PSI units,and N is the number of PSI units within the relevant area(area of the junction) Arel. We assume that all PSI unitsare oriented in the same direction, so that each of themcontribute equally to the total current Is. Therefore, wehave is,n ≡ is, hence

Is = is ·N = is · ρ ·Arel (C2)

where ρ is the number density, or coverage, of PSI. Toestimate the coverage we need to take into considerationthe size of PSI units. Isolated cyanobacterial PSI sys-tems usually appear in trimers with typical diameters ofaround 30 nm. This means three PSI units reside in anarea of about 700 nm2, or for convenience, approximatelya coverage of ρ = 0.004 nm−2. Note that this is thehighest possible coverage for a monolayer of PSI, sinceit corresponds to the entire silver surface being coveredwith a uniform, densely-packed PSI layer. We assumethis maximum coverage for the entire junction area. Wefurther assume that the total injected spin current Is isequally contributed by all the PSI units. This gives usan estimate of the lower boundary of is, the spin-currentinjection per PSI unit. For the up orientation of PSI, wehave is > 750 pA. For the down orientation this lowerlimit is 150 pA.

Next, we analyze the magnitude of the charge currentneeded to produce this spin current via CISS effect. Inour model, each PSI unit injects a spin current is intosilver, which is a fraction of the total spin current iPSI

inside PSI. We have is = η · iPSI , with −1 6 η 6 1being the fraction parameter. The value of η dependson the spin-relaxation process inside PSI. In order to ob-tain a lower estimate of iPSI , we assume η = 1 (all thephoto-induced spin current in PSI can be injected to thesilver layer), hence iPSI = is. This spin current, iPSI , isagain a fraction of the charge current i induced by thecontinuous electron transfer during photo-excitation andrelaxation cycles in a PSI unit. The conversion from acharge current into a spin current is due to the CISS ef-fect and its efficiency is characterized by its polarization

PPSI = iPSI/i. The CISS polarization of other chiralsystems is reported to be about 50%,3,8,26 so here weadopt the same value. Taking the above into account,we can derive the lower boundary of the charge currentdriven by photo-excitation and relaxation processes in aPSI unit: i > 1.5 nA for the up orientation, and 300 pAfor the down orientation.

Finally, we translate this current into a value for theexcitation-relaxation time τ . Here, τ can be under-stood as the turn-over time, or the time interval betweentwo consecutive photo-excitation processes from the samePSI unit. By assuming the intensity of the illuminationis strong enough to drive all the PSI units in continu-ous excitation-relaxation cycles (saturated), we can writei = −e/τ . A lower boundary of i corresponds to an upperboundary of τ . For the up orientation of PSI, i > 1.5 nAcorresponds to τ 6 100 ps. For the down orientation thelimit is τ 6 500 ps.

Appendix D: Possible origins of magnetic-fielddependent signals in hybrid CISS devices

There are other effects that can give rise to themagnetic-field-dependent signals in devices as used inRef. 26. One of these effects is the photo-response ofsilver. Any modification of the silver surface can changeits work function. A work function as low as 1.8 eVwas reported for modified silver surfaces.56,57 It is there-fore possible that the adsorbed PSI units and bindermolecules modified the silver surface in a way that pho-toemission was allowed at the photon energies used inthe experiment. This photoemission can be spin polar-ized due to the spin-orbit effect in silver and possiblespin-dependent scattering at the surface.58 Alternatively,the signals could also arise from a pure charge effect.Even without photoemission, the change of silver workfunction can lead to a voltage signal in the Ni-AlOx-Agcapacitor. This voltage signal may depend on illumina-tion and magnetic field, because the adsorbed PSI (whichmodifies the silver surface and thus the voltage signal)is highly photo-sensitive and contains large iron clustersthat may respond to magnetic field. In such a scenario(where spin transport does not play a role), the orien-tation of PSI can only affect the magnitude but not thesign of the magnetic-field dependence. In fact, this isindeed the case if one considers the full signals reportedin Figure 2A(ii) and Figure 2B(ii) of Ref. 26 instead ofonly their absolute values. In both figures, the measuredsignals can be separated into two parts: a nonzero back-ground and a magnetic-field-dependent component thatshows a step upon magnetic-field reversal. Figure 2B(ii)differs from Figure 2A(ii) by having an opposite sign forthe background and a smaller step size upon magnetic-field reversal. The directions of the steps (i.e. the signsof the magnetic-field dependence) in both figures are thesame: Both signals shift tens of nanovolts to less posi-tive (more negative) values when reversing the magnetic

8

field from down to up direction. The opposite signs forthe background can be explained by the opposite orienta-tions of PSI (just as how the PSI orientation affected thesilver surface potential measured with a Kelvin probe),

whereas the change of step size may be given by thechange of position of the iron clusters with respect tothe silver surface.

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