Temperature-dependence of the chirality-induced spin selectivity effect—Experiments and theory

As electrons pass through chiral molecules, the resulting current (either generated optically or electrically) can become spin-polarized,^1–4 implying that in effect spins of different species have different transport properties when interacting with a chiral moiety. This leads to the so-called chirality-induced spin selectivity (CISS) effects. The CISS effect has been observed in numerous experimental platforms and settings and can be used for various spintronic applications.^5–12 The observation of the CISS effect in molecular junctions is obtained by measuring the I–V curves through a chiral molecular moiety when the junction is comprised of one metallic (typically Au) electrode and one ferromagnetic (typically Ni) electrode. The hallmark of the CISS effect in molecular junctions is a different I–V response of the system when the magnetization of the Ni electrode is reversed, from being parallel to being antiparallel to the direction of the current (typically the molecular axis¹³).

Surprisingly, despite the fact that over a decade has passed since its discovery, the question of the physical origin of the CISS effect remains open.^4,14 Various theoretical studies proposed that the CISS effect originates from spin–orbit coupling (SOC) inside the chiral molecule.^15–19 However (as was recently pointed out explicitly^3,14,20), these explanations require a huge (several orders of magnitude) renormalization of the molecular SOC, and while electron correlations^21,22 or vibrations^{22–24,26,27} may reduce this normalization to some extent, realistic values for the SOC seem to predict a much smaller CISS effect than experimentally observed. While other theoretical ideas are beginning to emerge,^28–30 to date, none of the suggested theories have been able to quantitatively reproduce the experimental data.

Recently, an alternative theoretical explanation to the CISS effect was suggested,³¹ based on the so-called “spinterface” mechanism. As arises from this approach, the CISS effect is a result of interplay between the (spin–orbit induced) surface magnetization in the metal electrode and spin-imbalance in the molecule, which interact via a spin-torque. Due to spin-transfer torque, the surface magnetization obtains a preferred direction (parallel or antiparallel to the molecular axis), determined by the molecular chirality, thus forming a spin-dependent barrier for electrons entering the molecule. This theoretical approach can be used to reproduce the experimental data (the magnetization-dependent I–V currents) with remarkable accuracy.^32,33

The emergence of various theoretical suggestions, all plausible to the CISS effect, requires various experimental means to distinguish between them. One possible “experimental knob” that can help differentiate between different theories for the CISS effect is the temperature. Changing the temperature while observing the CISS effect seems only natural,^34,35 yet there are only a few precious experimental results in this direction. Perhaps the earliest example is in Ref. 36, where it was demonstrated that spin-polarization (obtained from a voltage difference between a magnetic layer and a metallic layer on which chiral molecules were placed) decreases with increasing temperatures.

More recently, several works reported a temperature-dependence of the CISS effect, yet they disagree. The authors of the work of Yang et al.³³ demonstrated a clear decrease of the CISS effect with increasing temperature, which was explained (and fitted quantitatively) with the so-called spinterface mechanism for the CISS effect. On the other hand, the authors of the work of Das et al.³⁷ showed an increase of the effect at high temperatures, explained via the so-called phonon mechanism²³ (yet not fitted quantitatively, see discussion in Ref. 32). The authors of the work of Kondou et al.³⁸ also show an increase in the signal when temperatures increase, via measurements of the current-in-plane magnetoresistance; however, in this experiment current does not pass through the molecular layer. Finally, the authors of the work of Qian et al.³⁹ claimed to show a decreasing CISS effect when temperature is increased, via measurements of the CISS effect in chiral molecular intercalation superlattices. However, as we show in detail in Sec. IV, the data presented in the work of Qian et al. actually point to the reverse—that in their system, the CISS effect is in fact largest at low temperatures and decreases as the temperature is increased, until the CISS signal vanishes at high enough temperature.

From the theoretical perspective, one can divide the proposed mechanisms for the CISS effect into two categories. The first consists of mechanisms that depend on interactions between vibrations (or phonons) and electrons in chiral molecules as a means to enhance the (typically weak) spin–orbit coupling.^{22,23,26,27,37} Since the excitation of vibrations increases with temperature, it follows that as temperature increases, more vibrational modes are excited, leading to an enhanced CISS effect. All the mechanisms that do not depend on vibrations belong to the second category. Naturally, if the vibrations are not involved in the mechanism leading to the CISS effect, one would expect that thermal fluctuations would destabilize it by competing with the interactions that give rise to it.

In the next sections, we describe in detail the temperature-dependence of the CISS effect, as arises from the spinterface mechanism.^31,32 We then discuss the work of Qian et al.³⁹ and show that, (i) the original interpretation of the data contains some possible flaws, which, when corrected, actually indicate that their data show a reduction in the CISS effect with increasing temperature, and (ii) the spinterface mechanism can quantitatively reproduce the experimental results presented in the work of Qian et al. remarkably well.

Within the spinterface model,^31,32 the CISS effect arises from the stabilization of surface magnetization at the interface between the metallic electrode and the chiral molecule. The stabilization of surface magnetization comes from spin-torque (or possibly spin-exchange) interactions between the metallic orbitals and the molecular states, and the symmetry is broken due to the (albeit small) current-induced solenoid magnetic field. Finally, the effect of surface magnetization on transport comes from the fact that in the metallic electrode there is substantial spin–orbit interaction, leading (in a mean-field description) to a spin-dependent effective chemical potential, or equivalently to a spin-dependent tunneling barrier.

This formulation shows two temperature dependencies. The first is a direct dependency coming from Eq. (3), where the temperature appears in the denominator of the expression. This can be easily understood by noting that this formulation comes from averaging over thermally fluctuating magnetic moments.³¹ Thus, it is natural that as the temperature increases, it becomes harder to “stabilize” the surface magnetization. Mathematically, as T increases the Bessel functions in Eq. (3) decrease, leading to a diminishing cos(θ_M) and a reduction in the CISS effect.

The second, more subtle dependence, comes from the dependence of I and, more importantly, Δs on temperature. These dependencies are less universal and may depend on the details of the specific system that show the CISS effect. However, one can largely assume that Δs decreases as temperature increases. This is indeed the case for the microscopic models examined in Ref. 31.

As a demonstration, in Fig. 1 we show how the CISS effect vanishes with increasing temperature, by plotting the current–voltage curves for different Ni electrode magnetizations (solid lines—magnetization parallel to the molecular axis, dashed lines—magnetization antiparallel to the molecular chiral axis) for different temperatures, ranging from 5 K up to 300 K. The system considered here is a single molecular orbital, and the currents are evaluated within the full temperature-dependent Landauer approach.⁴² 

We set the resonant energy at ɛ = −0.1 eV and level broadening at Γ = 0.01 eV, and the CISS parameters are α_A = 0.5 eV, α₀ = 10⁻⁷ eV/nA, and α₁ = 5 × 10⁻⁴ eV. Note that α₁ here is very small (in realistic systems it is probably closer to 10⁻² eV, see Ref. 32), which was chosen in order to demonstrate the temperature-dependence: The difference between the magnetization currents (which is color-filled for clarity), which is the hallmark of the CISS effect, vanishes as the temperature increases.

Such behavior has been demonstrated experimentally very recently³³ in molecular junctions with small molecules. The observation of the CISS effect at such small temperatures (where phonons are unimportant) corroborates the spinterface mechanisms for these systems. However, it is possible that for larger molecules (for example, biological molecules), vibrations play a dominant role in stabilizing the CISS effect.

Before discussing the relevant experimental results in Sec. IV, here we comment that while observing the temperature-dependence of the CISS effect from the magnetization-dependent currents is straightforward, quantifying it may be more complicated. The reason is that quantifying the CISS effect may actually depend on the theoretical modeling of the full system, including the properties of the ferromagnet electrodes, interfaces, and nonmagnetic electrodes. Hence, the quantification of the CISS temperature-dependence may depend on how the currents I_s(V) (and possibly other parameters) depend on temperature. Put simply, if the CISS effect depends (via some mechanism) on a magnitude X(V) (e.g., the currents), and X(V) is temperature-dependent, then the CISS effect will change with temperature even though the mechanism itself is temperature-independent, simply because X depends on temperature. A similar point was made in Ref. 32 regarding the length-dependence of the CISS effect.

We thus reiterate a key message—a theoretical description of the CISS effect in molecular junctions should be able to account for the basic raw data, the magnetization-dependent currents, and a qualitative (or even quantitative) agreement of any manipulated data must be rigorously justified. An example for such a case is described in Sec. IV.

In this section, we discuss in detail a recent report on the temperature-dependence of the CISS effect. Recently, the authors of the work of Qian et al.³⁹ (which we dub Q22 hereafter for brevity) demonstrated chiral molecular intercalation superlattices (CMIS) as a new class of solid-state chiral material platform for exploring the CISS effect. Specifically, Q22 showed that CMIS can be used to accurately characterize the CISS effect and explore its dependence on temperature and other material properties. They showed a very high degree of polarization of the spin-current P(T), which monotonically decreased with increasing temperature, and the average conductance G_SI(T) exhibited an Arrhenius behavior, viz., $GSI(T)=G0e−εAkBT$ corresponding to a thermally activated hopping. The spin-polarized conductance G_S(T), on the other hand, exhibited a non-monotonic dependence, increasing with temperature at low temperatures up to a certain temperature (⁠$∼100$ K) and then decreasing.

The authors of Q22 ascribed this non-monotonic behavior to two mechanisms (as stated in the description they provide below their Fig. 5): The increase up to 100 K is due to electron–phonon interaction assisted increase of the spin selectivity of the chiral molecule,^23,37 and subsequent decrease is due to decrease in the electron spin-polarization of the ferromagnetic Cr₃Te₄ lead. Put simply, they attribute the rise in polarization at low temperatures to the increasing CISS effect (because of the phonon-mechanism for the CISS effect). Thus, the interpretation of Q22 supports the phonon-mechanism for the CISS effect.

In this section, based on the data of Q22, we show that the non-monotonicity of the spin-polarized conductance G_S(T) may in fact arise from a different mechanism than that proposed by the authors. The low-temperature behavior comes from the Arrhenius envelope of the currents (and not the electron–phonon interaction assisted increase of the spin selectivity of the chiral molecule), and the reduction at high temperatures comes from the decrease in magnetism and polarization of the ferromagnetic electrode and from vanishing of the CISS effect at high temperatures. We show that this interpretation is consistent with the experimental findings reported. Based on this, we argue that in the CMIS system, the CISS effect actually grows with decreasing temperature.

We start by reiterating the definitions and central result pertaining to the temperature-dependence of the CISS effect of Q22. The authors measure their CMIS device with two different magnetization directions (parallel and antiparallel to the direction of current flow) and obtain two currents, marked I_high and I_Low, the difference between them representing the presence of a CISS effect.

The polarization is defined as $P=(Ihigh−Ilow)(Ihigh+Ilow)=IS/Itot$⁠, where I_tot is the average current (times 2), and I_S is the spin-polarized current. The spin-dependent (or CISS-) conductance is given by G_S = I_S/V. Their central result regarding the CISS effect is that although G_S → 0 as T → 0, P reaches a finite value (60%). This apparent opposite behaviors of P and G_S with temperature has been attributed to an increase in the CISS with temperature increase at low temperatures, followed by a global decrease due to tunneling effect in the material part.

Now, since P and G_S are proportional to one another (both having I_S in the numerator), the only way this can happen is if I_S and I_tot decay to zero as T → 0 with the same functional form. According to the work of Qian et al.,³⁹ the average conductance $GSI=Ihigh(T)+Ilow(T)2V$ exhibits an Arrhenius form with $GSI=G0e−εA/kBT$ with an activation energy ɛ_A = 12 meV, for a fixed (and of course temperature-independent) applied bias V (assuming V = 0.05 eV, corresponding to 5 V bias in Q22).

Therefore, the individual currents I_high(low) (T) must also exhibit an Arrhenius component when T → 0, i.e., $Ihigh(low)(T)=Ihigh(low)′(T)e−εA/kBT$⁠. This is evident from Fig. ext7(b-e) of Q22 and also supported by the fact that these currents are after all charge currents (see discussion in Ref. 25), and therefore they should also be affected by the same mechanism that determines the Arrhenius behavior. Denoting $Ihigh(low)′(T)$ as the Arrhenius normalized charge current, the spin conductance must be $GS(T)=Ihigh′(T)−Ilow′(T)e−εA/kBT=ΔI′(T)e−εA/kBT$⁠. This implies that the vanishing of G_S with decreasing temperature comes from the Arrhenius part, and the part coming from the CISS effect is actually ΔI′(T), the “Arrhenius normalized” spin-polarized current.

To show this from the data, we digitally extract the temperature-dependence of individual charge currents from Fig. 5(a) and ext7a of Q22. Figure 2(a) shows the “Arrhenius normalized” currents, $Ihigh(low)′(T)$⁠, as a function of temperature T. $Ihigh′(T)$ decreases monotonically with increasing temperature, while $Ilow′(T)$ first decreases and then increases, indicating non-monotonicity. However, Fig. 2(b) shows that their difference ΔI′(T) decreases monotonically with increasing temperature, indicating a monotonic decrease in the CISS effect.

Therefore, a consistent interpretation of the data (recalling that the polarization P and the CISS conductance G_S show distinctly different behaviors as T → 0) is that the CISS effect is finite at low temperatures and decreases with increasing temperature, while the total charge current increases with temperature, after being nearly zero at low temperatures. The competition between these two processes leads to non-monotonicity in G_S but to a monotonic polarization P.

The authors of Q22 interpreted their data using the Jullier model,⁴³ which implies G_S = G_TP₁P₂, where P₁ and P₂ are polarization of the Ferromagnetic lead and the equivalent polarization of the chiral molecular layers, respectively, and G_T is the overall conductance envelope. Following the convention in their paper, the spin conductance can be directly expressed as G_S = G_SIP, where P is related to the polarizations of the two layers and G_T to G_SI. The authors suggest, based on previous studies of different systems⁴⁴ (Ref. 50 in Q22) that G_T is temperature-independent. However, this is in contradiction to their own data: In their system, G_T is strongly temperature-dependent and has an Arrhenius form that vanishes at low temperatures based on our picture. Therefore, their basic form of the Jullier’s model, which assumes a temperature-independent conductance envelope, is inconsistent with their data. The direct conclusion from this analysis and Fig. 2 is that the CISS effect in Q22 cannot be interpreted using the phonon-mechanism for the CISS effect.

However, the data provided by Q22 can be interpreted by a mechanism for the CISS effect in which the CISS effect is enhanced when the temperature is reduced, such as the aformentioned spinterface mechanism.³¹ To further corroborate this claim, we performed a calculation based on the spinterface theory of Ref. 31, modified to account for the specific Arrhenius-type I–V characteristics observed in the experiments performed by Q22. As we demonstrate, there is an excellent qualitative agreement between this theory and the experimental results.

As described in Sec. III, for the spinterface theory one needs a model of currents and spin-densities. In the limit of weak coupling, compared to the temperature, between the molecular level and the electrodes, one can resort to the formulation of rate equations that simplifies the expressions for currents.³¹ For simplicity, we consider a single molecular level that mimics the complicated transport setup fabricated in Q22. We treat the transport setup corresponding to Q22 as a single level with an effective LUMO equal to the thermal activation energy. This way, we can separate the true thermal effects (i.e., the Arrhenius dependence found in Q22) from the spin-dependent effects.

The results of the calculation are presented in Fig. 3, showing the polarization P [Fig. 3(a)], the high and low currents [Fig. 3(c)] and the spin conductance G_s [Fig. 3(e)], all as a function of temperature. The right-hand panels [(b), (d), and (f)] show the experimental data. The qualitative resemblance between the theory and the data is clearly visible.

In summary, we discussed the temperature-dependence of the CISS effect as a means to differentiate between different theoretical suggestions for the physical origin of the CISS effect. Specifically, one can point to two main theoretical “branches.” The first, based on electron–phonon interactions (and represented by e.g., Ref. 23), suggests that the CISS effect increases with increasing temperatures and vanishes at low temperatures. The second, represented by, e.g., the spinterface model of Ref. 31, suggests that the CISS effect is finite at low temperatures and decreases with increasing temperatures.

Specifically, we showed how the CISS effect vanishes within the spinterface model, considering a single-level molecular junction within the full Landauer model and discussed how the temperature-dependent CISS effect should be quantified.

Finally, we discussed in some detail the temperature-dependence of the CISS effect as it arises from the recent experiments presented in the work of Qian et al.³⁹ These authors demonstrated that they are able to fabricate a remarkable, robust solid-state chiral material platform, based on chiral molecules intercalated between two-dimensional atomic crystals, which exhibits the CISS effect.

However, a consistent analysis of their data implies that, contrary to their suggestion, the CISS effect is finite at low temperatures and is reduced with increasing temperature. Thus, their data are more consistent with the “spinterface” model (which shows remarkable agreement to the experimental data) than with the phonon-mechanism for the CISS effect.

We encourage the experimental community of the CISS effect to further explore the temperature-dependence of the CISS effect, both in molecular transport setup and in photoemission experiments.⁴⁵ Observing the CISS effect at low temperatures and its temperature-dependence in different systems (e.g., different molecules and different electrodes) is necessary to help the community to fully understand the origin of the CISS effect.

Calculation details are available in the supplementary material.

The authors have no conflicts to disclose.

Seif Alwan: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Subhajit Sarkar: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Amos Sharoni: Writing – review & editing (equal). Yonatan Dubi: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the supplementary material.