Two-dimensional magnetic tunnel p-n junctions for low-power electronics

Domain: physics
Published: 2025-12-30
Editorial outcome: major_revision

Abstract
For decades, semiconductors and their heterostructures have underpinned both fundamental and applied research across all areas of electronics. Two-dimensional, 2D (atomically thin) semiconductors have now the potential to push further the miniaturization of electronic components, enabling the development of more efficient electronics. Here, we report on a large tunneling magnetoresistance of 1100% at a bias current of 1 nA and a giant anomalous zero-bias spin voltage effect in magnetic tunnel junctions based on 2D materials. The generation, manipulation and detection of electron spin across a nanometer-thick magnetic tunnel junction do not require any applied bias. The large zero-bias spin voltage signal exceeds 30,000%, which is far greater than the highest magnetoresistance signals reported to date. This non-equilibrium spin-engine state arises from the asymmetric diffusion of spin-up/spin-down electrons across the junction. It is driven by the built-in electric field of the junction and occurs under continuous energy exchange of the junction with the environment. Our findings reveal unexplored opportunities to transform and amplify spin information for low-power electronics.

Introduction
The success of charge-based applications in semiconductor heterostructures suggests intriguing opportunities to combine spin and charge degrees of freedom in spintronics. To date, key progress in spintronics have focused on spin valves, including magnetic tunnel junctions (MTJs) with metallic ferromagnets. The resistance of these junctions varies with the relative magnetization orientation of the two ferromagnets. While metallic spin valves remain valuable for magnetically storing and sensing information, they are of limited use for transferring and processing information, where semiconductors excel.

Typically, there are two ways to integrate spin with the versatile charge control in semiconductors: chemical doping and spin injection. Adding magnetic impurities to common semiconductors comes at a high cost: the carrier mobility is drastically reduced and robust emission of light is lost. Alternatively, heterostructures combining common ferromagnets and semiconductors encounter different challenges: spin injection from a ferromagnet into a semiconductor can be strongly suppressed by the interface quality and the resistance mismatch between the materials. Although these problems can be alleviated by inserting a tunnel barrier, the current flow is impeded, requiring a larger applied bias and increased power consumption.

Building on advances in van der Waals (vdW) layered materials and vdW heterostructures, including a growing number of two-dimensional (2D) magnets, here we demonstrate a different platform to overcome these obstacles in spintronics. A hallmark of vdW layered materials is their strong covalent atomic bonding within the 2D planes and weak vdW bonding between the layers. This allows for the fabrication of stable thin films down to the monolayer level, avoiding interface and crystal defects that are detrimental for spin transport in covalently-bonded magnetic multilayers. As vdW bonding supports atomically-sharp interfaces between dissimilar materials, the same platform can also be suitable for atomically-thin electronic and photonic devices, relying on high-quality metal/semiconductor contacts. Here, we report on a large tunneling magnetoresistance (TMR) and a giant anomalous zero-bias spin voltage effect (SVE) in MTJs based on 2D magnet and semiconductor p-n junctions. Without applying an external bias, the generation, manipulation and detection of electron spin across a nanometer-thick MTJs are achieved by exploiting high quality ferromagnetic/semiconductor interfaces and semiconductor p-n junctions. To analyze the origin of the zero-bias SVE, we conducted a series of control studies: 1) The zero-bias SVE is not observed in MTJ devices with a single spacer layer, excluding noise from the measurement setup and 2) does not originate from the spin Seebeck effect, as confirmed by experiments with a temperature gradient along the junction; 3) a semiclassical model of the spin-dependent drift-diffusion combined with first-principles density functional theory (DFT) of the junction reveals a non-equilibrium spin-engine state. This features the injection of electron spins at the Fe3GeTe2/GaSe interface, their diffusion under the built-in electric field of the junction and their spin flipping at the InSe/Fe3GeTe2 interface.

Results
For our vdW heterostructures, as depicted in Fig. 1a, we select the layered ferromagnetic metal Fe3GeTe2 (FGT) owing to its desirable large coercivity, strong perpendicular magnetic anisotropy, and relatively high Curie temperature, Tc of up to 220 K. Unlike common spin valves, where two ferromagnets are separated by a single non-magnetic region, here we employ a vdW p-GaSe/n-InSe heterostructure composed of materials with different doping and composition. The vdW heterostructure is assembled by stacking 2D materials (FGT, γ-InSe, and ε-GaSe) exfoliated from bulk crystals (see Methods for details). The optical image of a typical device is shown in Fig. 1b, where the contours of different nanoflakes are outlined by dotted lines of different colors. Figure 1c shows the cross-sectional high-resolution transmission electron microscopy (HRTEM) image for a typical device structure. The HRTEM and energy-dispersive X-ray spectroscopy (Figure S1 in Supplementary Information) confirm atomically-sharp interfaces without contamination or amorphous oxide. We fabricated three MTJ devices with varying barrier layer thicknesses, where the barrier layers are 5-nm-GaSe/5-nm-InSe (device A), 10-nm-GaSe/5-nm-InSe (device B), and 15-nm-GaSe/5-nm-InSe (device C). The current-voltage (I-V) characteristic curves of these devices were measured, as shown in Fig. 1d. As the total thickness of the barrier layer increases, the I-V curves of the devices change from a nearly symmetrical, ohmic response to an increasingly asymmetrical, rectifying behavior.

Similar to conventional spin-valve devices, passing a charge current I through the FGT/p-GaSe/n-InSe/FGT vdW heterostructure under a magnetic field B perpendicular to the layers leads to a tunnel magnetoresistance, TMR = |(RAP − RP)/RP|, where RAP (RP) is the resistance for the antiparallel (parallel) configuration of the magnetization in the two FGTs. However, the inclusion of the vdW p-n junction leads to significant differences in the measured spin-voltage effect

SVE = |(VAP − VP)/VP| (1)

where VAP (VP) is the voltage for antiparallel (parallel) configuration. At a finite current I, the SVE coincides with the TMR for devices with symmetric linear I-V since VAP,P/I = RAP,P. Figure 1e and 1f, respectively, present the TMR of devices A, B, and C measured under a fixed bias current of 1 nA. As the barrier layer thickness increases, the TMR ratio decreases from a very large value of ~1100% in device A to 10% in device B, and eventually vanishes in device C. The TMR observed in device A is significantly higher than that in other similar 2D material-based MTJs. The origin of such a large TMR can be attributed to two factors: on the one hand, the two connected Brillouin zone filtering effect induced by the p-n tunnel junctions, where one spin conduction channel is selectively enhanced while the other is suppressed; on the other hand, the built-in electric field in the p-n junction induces a novel spin-dependent electric potential, which gives rise to the zero-bias SVE observed in our experiment. Remarkably, we observe a giant and reproducible zero-bias SVE across the p-n junction in the absence of any bias current. As shown in Fig. 1g, h, the SVE for device A reaches a value of ~1930% at 10 K and decreases to 30% in device B and disappears in device C. The V-B curves exhibit typical SVE with two states. Upon sweeping B from negative to positive values, a sharp jump to the high-voltage state occurs at B~0.15 T corresponding to the AP configuration ↓↑ or ↑↓, where the arrows denote the out-of-plane FGT magnetization. At B~0.21 T, a sharp jump to the low-voltage state corresponds to the P configuration ↓↓ or ↑↑. The voltage jumps are also observed for B < 0. The zero-bias SVE of several devices is summarized in Fig. 1i. As the resistance-area product increases, the zero-bias SVE decreases exponentially and disappears, indicating that it is dominated by the spin tunneling mechanism.

While a spin signal between two ferromagnets typically increases as their separation decreases, we observe the opposite behavior when we replace the p-n junction with individual thinner p- or n-type layers. Both TMR and SVE are significantly enhanced in the 10-nm-thick p-n junction compared to devices with a nonmagnetic region of either 5-nm-thick p-GaSe or n-InSe layers. For devices based on thin individual p- or n-doped vdW regions, there is no zero-bias SVE (SVE = 0 at I = 0). Even under I = 1 nA, the TMR for p-GaSe (~85%) and n-InSe (~41%) is significantly smaller than that for the p-GaSe/n-InSe junction (Supplementary Note 1 and Fig. S2). This dependence of the spin signal on the thickness of the spacer suggests that our observations do not arise from proximity effects, as proposed in other vdW spin valves. Thus, the data from different device structures suggest that the observation of the anomalous zero-bias SVE requires a thin p-n junction sandwiched between two FGT electrodes.

We now focus on the temperature- and current-dependent behavior of these devices. As shown in Fig. 2a for device A, clear V-B hysteresis loops without any applied bias current are observed up to the Curie temperature of FGT, Tc = 220 K. The measured widths of the voltage jumps for the antiparallel magnetic configurations of the FGT electrodes (↓↑ or ↑↓) change non-monotonically with increasing T. This is ascribed to the different T-dependence of the coercive field in the two FGT layers. Figure 2b shows the value of VAP and VP in the zero-bias state as a function of T extracted from the V-B curves: unlike the monotonic decrease of VAP with T, most likely related to the T-dependence of the spin-injection efficiency, the value of VP varies non-linearly with T and changes sign twice. This gives rise to a large SVE and singularities in the SVE versus T plot. The corresponding T-dependence of the magnitude of the zero-bias spin voltage is shown in Fig. 2c. It can be seen that the zero-bias SVE reaches a maximum value of 32,230% at T = 35 K. The SVE has excellent stability and the corresponding V-B loop at T = 35 K is presented in Supplementary Fig. S3.

The non-monotonic temperature dependence of the SVE suggests that, in addition to the properties of the FGT, other mechanisms need to be considered, such as the magnitude and direction of the spin polarization at the FGT/InSe and FGT/GaSe interfaces, and the spin transport along the p-n junction. We also extracted the temperature dependence of the spin accumulation voltage ΔV (ΔV = VAP - VP), as shown in Fig. 2c (red squares), and confirmed a clear trend: ΔV gradually decreases with increasing temperature and drops to zero when the temperature approaches 230 K. This trend directly confirms the intrinsic spin-dependent origin of the SVE: above FGT’s Curie temperature, FGT loses its ferromagnetic order, and electron spin polarization diminishes to zero. Consequently, the spin-dependent voltage difference between the parallel and antiparallel states vanishes (ΔV = 0), resulting in SVE = 0. This behavior stands in contrast to extrinsic effects (e.g., thermal noise), which would not exhibit such a sharp, temperature-dependent cutoff tied to FGT’s ferromagnetic phase transition.

At a given temperature, the magnitude of the SVE can be optimized by the bias current (Fig. 3a–d). For example, at T = 10 K, a large SVE of 15,720% is obtained for I = −1 nA (Fig. 3b). The SVE amplitude extracted from the V-B plots (Fig. 3d) agrees well with the values obtained from the I-V curves (Fig. 3c) measured in the parallel and antiparallel configurations. Figure 3e shows the color scale plot of the SVE amplitude versus the bias current and temperature. The maximum SVE at low T occurs under a negative current bias, switches to positive current bias at around 40 K, and then switches back under a negative current bias at 180 K, reflecting the T-dependence of VP. The conductance dI/dV of the device in the parallel state shows a similar T-dependence to that of the bias current for maximum SVE below 170 K (Fig. 3e). We attribute this non-monotonic T-dependence of the maximum SVE and dI/dV to the competition of two effects: with decreasing T the carrier densities in the p-GaSe and n-InSe layers decrease, which reduces the built-in electric field and consequently lowers the spin-dependent tunneling conductance; simultaneously the spin polarization at the interface increases and charge/spin scattering rate decreases, leading to longer spin lifetimes. The spin voltage effect in the FGT/p-GaSe/n-InSe/FGT vertical vdW devices with thin spacer layers is robust and reproducible. The temperature-dependent and bias-dependent SVE for the additional heterostructure device with 5 nm p-GaSe/5 nm n-InSe junction (device D) are shown in Supplementary Figs. S4-5.

The zero-bias SVE is not caused by a temperature gradient due to the spin Seebeck effect. To exclude this phenomenon, we designed and fabricated a device structure comprising a magnetic tunnel junction and a heating element. As shown in Fig. 4a, the FGT/p-GaSe/n-InSe/FGT junction (device G) is capped with hBN/semi-metal Td-WTe2. WTe2 acts as the top heating resistor and is separated from the junction by a hBN layer. In this structure, we can create a thermal gradient along the vertical direction by applying an electrical current to the WTe2 layer. The temperature of the WTe2 layer was estimated from its resistance. Firstly, we tested the resistance curve of WTe2 as a function of the heating current. As the heating current increases, the resistance of WTe2 exhibits a quadratic increase, consistent with the Joule heating effect (details see Supplementary Note 2 and Fig. S6). We examined the relationship between the resistance and temperature of WTe2 under conditions (1 μA) of negligible Joule heating, as illustrated in Fig. 4b. Then, the temperature of the WTe2 layer was increased under different heating currents. As the heating current increases from 0 to 0.5, 0.75, and 1 mA, the corresponding temperature of the WTe2 layer increases from 10 to 15, 20, and 25 K, respectively. The hysteresis loops of zero-bias anomalous SVE under different heating currents are shown in Fig. 4c. We find that the zero-bias SVE is not sensitive to the thermal gradient. Thus, we conclude that the SVE cannot originate from the generation of a spin voltage due to the thermal injection of spin currents from the FGT into the junction.

We note that the zero-bias SVE was observed in several devices with a similar structure, but differing for the magnetic electrode or p-n junction, e.g. in MTJs based on FGT/p-GaSe/n-MoS2/FGT and on Fe3GeTe2/p-GaSe/n-InSe/Fe3GeTe2, supporting the universality of the measured phenomenon (Supplementary Note 3 and Figs. S7-8). To further test the SVE at zero-bias, we conducted additional experiments: a resistor was connected in series with a magnetic tunnel junction, which acts as a current source in the antiparallel configuration of the FGT (Supplementary Note 4 and Fig. S9).

To explain the zero-bias SVE, we examine the spin-polarization of electrons at the semiconductor/ferromagnet interface and the asymmetric diffusion of spin-up/spin-down electrons (Fig. 5). For a structure where a single spacer layer (GaSe or InSe) is embedded between two FGT layers (Fig. 5ai, ii), the bidirectional diffusion of spins between the FGT cannot generate any spin-voltage at zero-bias, regardless of whether the two FGT have the same or opposite spin polarization orientations. However, when a p-n junction is embedded between the FGT layers, the spin diffusion becomes asymmetric due to the built-in electric field of the p-n junction (Fig. 5aiii, iv). This asymmetry leads to a net spin diffusion in one direction, which we model by a combination of first-principles DFT and semiclassical transport equations.

From DFT, we derive the energy band diagram and electric field of the p-n junction, and the spin splitting of the energy bands due to the FGT (see details in the Supplementary Notes 5, 6 and Figs. S10−12). The spin-polarized transport across the p-n junction is simulated using drift-diffusion equations for electrons and holes. Due to the lighter mass and higher mobility of electrons, the spin signal is predominantly determined by electrons (see details in the Supplementary Note 7 and Fig. S13). Figure 5b shows the spin polarization P = (n↑ - n↓)/(n↑ + n↓), where n↑ and n↓ are the spin-resolved electron densities. At the FGT/GaSe interface, we assume P = 0.66 at zero-bias voltage, as informed by studies of FGT/hBN/FGT devices. In conventional spin valves, the spatial dependence of the spin polarization P and the spin density s = n↑ - n↓ are equivalent. However, while P decays monotonically away from the point of injection of electron spins at the FGT/GaSe interface, the dependence of s is non-monotonic (see inset of Fig. 5b). This non-monotonicity induces an asymmetric distribution of spin-polarized electrons at the FGT/GaSe and FGT/InSe interfaces.

Furthermore, the measured spin-voltage difference at zero bias between the parallel and antiparallel states is estimated by considering the energy cost of spin flipping at the FGT/InSe interface (see details in the Supplementary Note 8 and Fig. S14). Taking into account the spin polarization of the injected electrons at the interface between GaSe and FGT, the energy difference Δμ at the edge of the InSe is 1.17 meV for p-GaSe (5 nm)/n-InSe (5 nm) and 0.80 meV for p-GaSe (9 nm)/n-InSe (5 nm), respectively. For simplicity, the spin splitting of the top and bottom FGT is assumed to be the same, which is consistent with the DFT calculations. Then the energy level diagram for parallel and antiparallel states can be drawn as shown in Fig. 5c, d, respectively. The measurable voltage difference between antiparallel and parallel states generated by the spin flipping at the InSe/FGT interface is estimated to be 690.3 μV, which is the same order of magnitude as the experimental observation. The above theoretical analysis reveal the formation of a non-equilibrium spin-engine state, which is characterized by two key processes: 1) spin injection at the FGT/GaSe interface driven by the built-in electric field—this generates a spin current flowing across the junction, and the spin current induces spin accumulation, which gives rise to the detectable voltage signal; 2) spin flipping at the InSe/FGT interface—spin flipping reduces the spin energy state, prompting the device to absorb thermal fluctuations from the environment to maintain its own magnetic state. Since the SVE depends on the built-in electric field of the junction as well as on the spin polarization of the FGT/GaSe (InSe) interface, the non-monotonic SVE with both temperature and electric field can be explained.

Methods
Fabrication of the FGT/p-GaSe/n-InSe/FGT vertical heterostructure devices

Figure 1a in the main text shows a schematic illustration of our spin-valve devices. The few-layer Td-WTe2 (from HQ Graphene), FGT (from HQ Graphene), ε-GaSe (from 2D Semiconductors) and γ-InSe (was grown by the Bridgman method at the Frantsevich Institute for Problems of Materials Science, Ukraine) flakes were mechanically exfoliated using adhesive tape from bulk single crystals of Td-WTe2, FGT, ε-GaSe and γ-InSe, respectively. The few-layer FGT, serving as ferromagnetic electrode, was mechanically exfoliated onto a stamp. Then the stamp was adhered to a glass slide to facilitate handling and identification of thin layers by optical microscopy. Subsequently, the target FGT sheet was transferred onto a SiO2/p-Si substrate. Using the same method, the InSe sheet was transferred onto top of the FGT sheet. After that, the GaSe sheet was transferred onto the InSe sheet to fabricate a 2D heterojunction. Finally, another exfoliated few-layer FGT sheet was transferred onto the InSe sheet to form the top electrode. To prevent the FGT from oxidizing once the device was exposed to air, a 15 nm-thick hBN layer was used to cap the entire heterostructure stack.

The two FGT sheets were contacted with metallic electrodes, which were fabricated on the substrate prior to the transfer using standard photoetching, thermal evaporation and lift-off. After the transfer process, the MTJ devices were baked at 120 °C for 10 minutes to ensure intimate contact between the interfaces of the various vdW materials. The active overlap area of this vertical device is typically around 5 μm2. The thickness of the FGT, InSe and GaSe flakes was determined by atomic force microscopy (Bruker Multimode 8). The typical thickness of the 2D materials used for the vertical heterostructures in this work is between 5−15 nm. All the fabrication processes were carried out in a glove box with a concentration of less than one part per million of water and oxygen.

Measurements of SVE

A Keithley 2602 current source and a Keithley 2182A nanovoltmeter were used for the magnetoresistance effect measurements. An Agilent Technology B1500A parameter analyzer was used to study the output characteristics of the spin-valve devices. All measurements were conducted in a Cryogenic Probe Station with magnetic field out-of-plane and at temperatures below and above the Curie temperature (Tc = 220 K) of FGT.

Computational methods

The electronic structures of different layers γ-InSe, ε-GaSe, FGT and their heterostructures were investigated using the general potential linearized augmented plane-wave (LAPW) method as implemented in the WIEN2K code. The local density approximation (LDA) was used to describe the exchange and correlation functional, which can yield reasonable electronic structures for InSe, GaSe, and FGT. By fully relaxing both the lattice constants and atomic positions, the optimized lattice constants (a, c) of (3.7 Å, 15.7 Å), (4.0 Å, 24.4 Å), and (3.9 Å, 16.3 Å) were obtained for the bulk GaSe, InSe and FGT, respectively. The lattice constants of few-layer films were kept the same as those in the optimized bulk structures.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors report a magnetoresistance (MR) effect in van der Waals (vdW) magnetic tunnel junctions, where a semiconductor p-n junction serves as the tunnel barrier. A striking feature in their experimental data is the giant anomalous zero-bias spin voltage signals, accompanied by a magnetoresistance of up to 19,000%. This exceptionally large magnetoresistance at zero bias offers a promising platform for the conversion and amplification of spin information in low-power electronics. Furthermore, the authors have robustly supported their findings: they ruled out the influence of the spin Seebeck effect induced by thermal gradients and attributed the observed phenomenon to the asymmetric diffusion of spin-up and spin-down electrons across the semiconductor p-n junction. Overall, the paper presents highly convincing and intriguing results concerning the anomalous zero-bias spin voltage effect, and I strongly recommend its publication in Nature Communications. However, prior to the publication, the authors should clarify the following minor points:\n1. In Figure 1c, could the authors explain why the InSe layer and GaSe layer show the same color and thus cannot be distinguished?\n2. To verify the universality of the zero-bias spin voltage effect, it is recommended that the authors conduct additional experiments—for instance, using different p-n junctions with the same magnetic electrode, or employing different magnetic electrodes with the same p-n junction.\n3. Compared with the widely studied single semiconductor barrier layer, the Brillouin zone filtering effect of such a layer is key to enhancing tunnel magnetoresistance. Could the authors comment on whether the significant enhancement of magnetoresistance observed here is also related to the spin filter effect in the p-n junction?", "reviewer_2": "The authors claim that the spin-dependent electronic properties of two-dimensional (2D) van der Waals (vdW) heterostructures made of 2D ferromagnet Fe3GeTe2 (FGT) layers and asymmetric semiconducting tunnel junctions with p-type GaSe and n-type InSe layers can be epitomized by spin-voltage effect (SVE). Remarkably, they report that the SVE, even in the absence of a driving current across the junction, reaches magnitudes on the order of tens of thousands of percent. According to the manuscript, the SVE exhibits nonmonotonic temperature dependence and is highly sensitive to device parameters, such as the thickness of semiconducting layers: the largest effect is observed in devices with 5-nm-thick InSe and GaSe layers, while it diminishes with thicker barriers, becoming undetectable in the device with a 15-nm GaSe layer.\nIntroducing novel control parameters and material platforms is indeed important for advancing spintronic technologies. Moreover, the author’s effort to realize 2D spintronic devices with atomically controlled semiconducting p-n interfaces is highly commendable, showcasing the direction in which 2D vdW materials can outperform conventional magnetic thin films. However, I remain unconvinced that the observed SVE originates from intrinsic spin-dependent transport phenomena within the junctions.\nAs the authors claim, the SVE could be attributed to the magnitude and direction of spin polarization at the FGT/InSe and FGT/GaSe interfaces, and spin-dependent transport across the p-n junction. Nevertheless, I suspect that the observed SVE is predominantly influenced by extrinsic effects rather than intrinsic spintronic properties of the junctions. In the absence of internal power sources, such as solar cells or spin engines (Katcko et al. Communication Physics, 2, 116, 2019. Ref. 31 in the manuscript), the ‘equilibrium’ voltage across a junction should be zero without an external current source. This raises the question of whether SVE is the most appropriate figure of merit to describe the devices, especially considering that the reported SVE values (e.g. 15,720 % at I = -1 nA in Figure 3b) could alternatively be interpreted as exceptionally large tunneling magnetoresistance (TMR) ratios. If the measurements are valid, these values would represent the highest TMR ratios ever reported in magnetic tunnel junctions based on 2D materials. However, due to the lack of in-depth discussion while relying on speculative explanations (Figure 4), and the poorly constructed manuscript, I am unable to recommend it for publication in high-impact journals like Nature Communications at this stage.\nBelow are several questions and concerns the authors should address in future revisions:\n1. I find it extremely difficult to follow the manuscript, as the authors repeatedly direct readers to Supplementary Notes and Figures for essential information. Overuse of supplementary material in place of presenting key data and arguments in the main text severely detracts from the clarity and accessibility of the work.\n2. The authors should include full I-V characteristic curves in the main manuscript. Although these are referenced in Supplementary Note 1 (“Device structure and I-V characteristics”), the data are not provided, which reflects a significant oversight.\n3. On page 9, the authors state that similar zero-bias SVE was observed in several devices with similar structures. However, no supporting data or appropriate citations are provided. Without such evidence, I cannot find the credibility of the statement.\n4. I find the setup in Supplementary Note 7 and Figure 11 problematic. The resistor’s resistance is simply too low for driving current to the junction. The junction resistances, based on the I-V curves presented in Supplementary Figure 3, appear to be in the range of gigaohms. As a result, the junction current would be determined primarily by the junction itself, not the additional resistor, contradicting the author’s intent for the experiment.\n5. In Supplementary Figure 6, the SVE remains unexpectedly high (~ 200 %) even at T = 220 K. Although the SVE decreases by a factor of five compared to its value at T = 20 K, its persistence near the critical temperature of FGT films suggest that extrinsic factors, rather than intrinsic spin-dependent properties of the FGT-based heterostructure may play a significant role in the observed behavior.\n6. On page 11 and 12, the authors cite Refs. 27, 31 and 32 as prior examples of zero-bias SVE in other systems, such as CrO2/SnO2/Co structures and Co/C/MgO/C/Co MTJs. However, upon reviewing these references, I find no substantive evidence or discussion of zero-bias SVE, making these citations misleading.\nI recommend a substantial revision and reorganization of the manuscript, including clearer presentation of experimental methods, unambiguous definitions of figures of merit, and rigorous justification of claims. Without these improvements, the manuscript remains difficult to evaluate and is not suitable for publication in a high-impact venue, like Nature Communications."}, "author_response": "Response: Thank you for these positive remarks and requests for clarifications, which we address below.\n1. In Figure 1c, could the authors explain why the InSe layer and GaSe layer show the same color and thus cannot be distinguished?\nResponse: In the original STEM image of Fig. 1c, the indistinguishable contrast between the InSe and GaSe layers is partially attributed to the similar crystal structures of the layers. To reveal the interface between the two layers with better contrast, we have conducted further STEM studies. The new results are presented in Fig. R1 (see below). The image shows that the layered materials form high-quality van der Waals contacts, with distinct and sharp interfaces. Notably, the InSe and GaSe layers now exhibit clearly distinguishable contrast. Accordingly, Fig. R1 has replaced the original Fig. 1c in the revised manuscript to better illustrate the device's structural features.\nFig. R1 Cross-sectional high-resolution transmission electron microscopy (HRTEM) image of a Fe GeTe (FGT)/InSe/GaSe/FGT vertical heterostructure.\n3 2\n2. To verify the universality of the zero-bias spin voltage effect, it is recommended that the authors conduct additional experiments—for instance, using different p-n junctions with the same magnetic electrode, or employing different magnetic electrodes with the same p-n junction.\nResponse: Thank you for this insightful suggestion. To verify the universality of the zero-bias spin voltage effect (SVE), we designed and fabricated two additional magnetic tunnel junction (MTJ) devices with p-n junction spacer layers, featuring the following structures:\n1. Fe GeTe /n-MoS /p-GaSe/Fe GeTe /hBN (denoted as device H), which uses a different p-njunction from that in the main text;\n2. Fe GeTe /n-InSe/p-GaSe/Fe GeTe /hBN (denoted as device I), which adopts a new ferromagnetic electrode (Fe GeTe ) instead of the original one.\n5 2 5 2\nWe then characterized the SVE of these two devices as a function of bias current (see Figs. R2 and R3). Both devices exhibit distinct and robust SVE signals under zero-bias current conditions. This result confirms the universality of the zero-bias SVE in MTJs with a p-n junction spacer layer. In the revised Supplementary, Figs. R2 and R3 have been included as the new Figs. S7 and S8, respectively.\nFig. R2. SVE at different bias current intensities for device H with an FGT/5-nm-MoS /5-nm-GaSe/FGT junction at 10 K. a, V-B curves at different current biases. b, I-V curves in the parallel and antiparallel magnetization configurations. The inset presents the optical image of device H. c, The square symbols denote SVE values extracted from the V-B curves at different bias currents. All measurements were performed at a fixed temperature of 10 K.\nFig. R3 SVE at different bias current intensities for device I with a Fe GeTe /5-nm-InSe/5-nm-GaSe/Fe GeTe junction at 10 K. a, V-B curves at different current biases. b, I-V curves in the parallel and antiparallel magnetization alignments. The inset shows the optical image of the device I. c, The square symbols denote SVE values extracted from the V-B curves at different bias currents. The temperature is fixed at 10 K.\n3. Compared with the widely studied single semiconductor barrier layer, the Brillouin zone filtering effect of such a layer is key to enhancing tunnel magnetoresistance. Could the authors comment on whether the significant enhancement of magnetoresistance observed here is also related to the spin filter effect in the p-n junction?\nResponse: Thank you for your valuable suggestions. The Brillouin zone filtering effect refers to the phenomenon where electrons with different in-plane momenta (k ) exhibit distinct tunneling probabilities when tunneling through the spacer layer. By matching the k -resolved band structures of the ferromagnetic metal electrode and the spacer layer, one spin conduction channel can be selectively enhanced while the other is suppressed. This mechanism can significantly improve the spin polarization at the ferromagnetic/semiconductor interface and thereby enhance the tunneling magnetoresistance (TMR) effect. Compared with a single semiconductor barrier layer, when a p-n junction is employed as the tunneling barrier layer, electrons tunnel through two spacer layer materials sequentially. This configuration is equivalent to two connected Brillouin zone filters, which can further amplify the difference between different spin conduction channels, improve the spin injection efficiency at the ferromagnetic/semiconductor interface, and consequently enhance the TMR effect. In addition, the built-in electric field in the p-n junction induces a novel spin-dependent electric potential, which gives rise to the zero-bias SVE observed in our experiment. The zero-bias SVE not only injects new impetus into the development of low-power spintronic devices but also provides a new strategy for the structural design of spintronic devices, such as spin memory, spin engines, and spin light-emitting devices. To address this interesting prospect, we have revised the main text on page 5.\nResponse: Thank you for your positive comments on the innovation of our work, specifically regarding all-2D magnetic tunnel junctions with a p-n junction spacer layer. This feedback will greatly encourage our research in this field.\nResponse: Thank you for your valuable comment. To rule out the contribution of extrinsic effects to the observed zero-bias SVE, we designed and conducted a series of control experiments. These experiments focused on two key potential extrinsic factors: instrument measurement noise and the spin Seebeck effect induced by thermal gradients. For the first factor (instrument measurement noise), we fabricated three types of MTJ devices with distinct structures: FGT/p-GaSe/FGT, FGT/n-InSe/FGT, and FGT/p-GaSe/n-InSe/FGT (with varying GaSe thicknesses). Notably, no zero-bias SVE signal was detected in single-spacer-layer MTJs (either with GaSe or InSe alone). For p-n junction-based MTJs, the zero-bias SVE amplitude decreased sharply as the spacer layer thickness increased. This structural dependence of the zero-bias SVE directly excludes instrument noise as its origin, since noise would not exhibit such systematic variation with the device structure.\nFor the second factor (spin Seebeck effect), we introduced a dedicated heating electrode to generate controllable thermal gradients across the device. Experimental results showed that the zero-bias SVE signal remained nearly unchanged with varying thermal gradient magnitudes. This confirms that the zero-bias SVE is not driven by the spin Seebeck effect induced by thermal gradients.\nWe agree with your insight regarding equilibrium voltage. In an adiabatic p-n junction (i.e., one with no energy exchange with the external environment), the junction voltage should indeed be zero in the absence of an external current source. However, our device operates in a non-adiabatic state, with continuous energy exchange with the environment occurs. This non-adiabatic condition enables the generation of a non-zero SVE signal without an external current source.\nThis non-equilibrium mechanism aligns with the principle reported in Ref. 31 (Katcko et al., Commun. Phys., 2, 116, 2019). In their work, Co/MgO/C/MgO/Co MTJs harvest thermal energy under non-equilibrium conditions, leveraging spin flips of paramagnetic carbon (C) centers in the barrier layer. Specifically, their results (Figure 3d of Ref. 31 is shown in the following figure) demonstrate non-zero parallel (I ) and antiparallel (I ) currents at a bias voltage of 0 V (V = 0). The magnitudes of these currents (-30 nA for I and -50 nA for I ) are nearly two orders of magnitude larger than any experimental offset, yielding a TMR of ~-70%. This clearly verifies the generation of non-equilibrium voltage.\nFigure 3. (Captured from Ref. 31) b Theoretical bias dependence of spin ↑ (solid) and spin ↓ (semitransparent) current in the magnetic tunnel junction’s parallel (P; black) and antiparallel (AP; red) magnetic states. c Theoretical and d averaged experimental bias dependencies of current in the MTJ’s P (black) and AP (red) magnetic states, and of the resulting tunneling magnetoresistance (TMR; green), using the same current/TMR scales. Within an apparent factor in the voltage scale, the analytical model including the out-of-equilibrium hypothesis strongly mimicks the room-temperature (RT) experiment, thereby linking it to the spin engine.\nTo further clarify the intrinsic mechanism of the observed zero-bias SVE, we employed a semiclassical model incorporating spin-dependent drift-diffusion theory to analyze the distribution of spin-polarized electrons and spin polarization in the p-n junction region. This analysis revealed a non-equilibrium state, which is characterized by two key processes: the spin injection at the FGT/GaSe interface driven by the built-in electric field, and spin flipping at the InSe/FGT interface. Figure R4 presents the spin electrochemical potential distribution diagrams of the device in the parallel and antiparallel states, respectively. At the FGT/GaSe interface, electrons are spin-polarized; with the assistance of the built-in electric field of the p-n junction, these spin-polarized electrons form a spin current. This spin current passes through the junction region, is detected by the ferromagnetic metal FGT, and generates a measurable spin accumulation voltage. To ensure the continuity of spin electrochemical potential at the InSe/FGT interface, different proportions of spin-polarized electrons undergo spin flipping at this interface in the parallel and antiparallel states: 3.5% in the parallel state and 62.5% in the antiparallel state. This spin flipping causes energy dissipation, leading to a reduction in spin energy states. Meanwhile, the device needs to absorb thermal fluctuations energy to maintain its magnetization state. These processes collectively establish a quasi-equilibrium state, which involves spin current injection, interfacial spin flipping, spin momentum transfer, spin energy dissipation, and recovery of spin energy states via absorption of thermal fluctuations energy. Our device was maintained at a constant temperature via a heating stage; thus, it continuously absorbed energy from the environment to sustain this non-equilibrium state. The dynamic balance between spin flipping and heat exchange constitutes the intrinsic physical origin of the observed zero-bias SVE. Our device operates in a non-adiabatic state, where continuous energy exchange with the environment occurs. This non-adiabatic condition enables the generation of a non-zero SVE signal without an external current source.\nIn the revised Supplementary Information, we have included Fig. R4 as Fig. S14 and added corresponding explanations to clarify the physical mechanism of the zero-bias SVE effect more explicitly.\nFig. R4. Schematic illustration of the zero-bias SVE mechanism. Diagrams showing the spin electrochemical potential distribution in the parallel state (a) and antiparallel state (b). In the figures: red arrows denote spin-up, blue arrows denote spin-down; thick arrows represent majority spins, thin arrows represent minority spins; the black dashed line indicates the Fermi level of FGT; the red and blue dashed lines represent the spin potential distribution before spin flipping.\nResponse: Thank you for your valuable comment regarding the distinction between spin voltage effect (SVE) and tunneling magnetoresistance (TMR), which we have considered and clarified in the revised version.\nWhen a finite bias current is applied to the junction, the TMR is calculated as: TMR = |(R - R )/R | = |(V /I- V /I)/(V /I)| = |(V - V )/V |. In this case, the expression for the TMR is mathematically identical to the SVE definition. However, our key observations focus on the zero-bias state, for which the most appropriate figure of merit is the SVE, as explained below.\nFor the parallel magnetic configuration (P-state), the measured voltage V is very small in the absence of an external bias current. In contrast, for the antiparallel magnetic configuration (AP-state), the measured voltage of V is significantly larger than V . This non-zero V is generated by spin-dependent transport in the p-n junction and gives rise to a large zero-bias SVE = |(V - V )/V |.\nThis zero-bias SVE is not a mere redefinition of TMR. Its physical origin lies in the intrinsic spin voltage generated by the p-n junction under non-equilibrium conditions, rather than the resistance difference driven by an external bias current (the core of TMR). This unique zero-bias response is a key highlight of our work, distinguishing it from conventional TMR effects.\nResponse: Thank you for your valuable feedback. We fully agree that over-reliance on supplementary materials for essential information undermines clarity, and we have taken targeted revisions to address this issue.\nFirst, we systematically reviewed all Supplementary Notes and Figures, identifying key data (e.g., core experimental results supporting the universality of SVE) and critical arguments that were previously included in the supplementary information. Following the reviewers’ suggestions, we have now integrated the I-V curves for different devices and the zero-bias SVE data for devices B and C into the main text, with the relevant figures renumbered as main text Figs. 1d and 1h. This ensures readers can access essential information without switching between sections.\nSecond, we organized the figures in the supplementary materials by combining multiple related separate figures into single ones, thereby simplifying the total number of figures in the supplementary information. For instance, the Figs. 6, 7, 8, and 9 were merged into new Figs. 4 and 5; the Figs. 16, 17, 18, and 19 were combined into new Fig. 13. This organization has made the figures and their corresponding descriptions more coherent and fluent. These revisions aim to centralize key content in the main text, making the work’s logic and evidence more straightforward to follow.\nResponse: Thank you for your valuable suggestion. In the revised main text, we have added the I-V curve to the main text as Fig. 1d.\nResponse: Thank you for pointing out this mistake. To verify the universality of the zero-bias SVE, we designed and fabricated two additional magnetic tunnel junction (MTJ) devices with p-n junction spacer layers, featuring the following structures:\n1. Fe GeTe /n-MoS /p-GaSe/Fe GeTe /hBN (denoted as device H), which uses a different p-njunction from that in the main text;\n2. Fe GeTe /n-InSe/p-GaSe/Fe GeTe /hBN (denoted as device I), which adopts a new ferromagnetic electrode instead of the original one.\nWe then characterized the SVE of these two devices as a function of bias current (see Figs. R2 and R3). Both devices exhibited distinct and robust SVE signals under zero-bias current conditions. This result confirms the universality of the zero-bias SVE in MTJs with a p-n junction spacer layer. In the revised Supplementary, Figs. R2 and R3 have been included as the new Figs. S7 and S8, respectively.\nFig. R2. SVE at different bias current intensities for device H with an FGT/5-nm-MoS /5-nm-GaSe/FGT junction at 10 K. a, V-B curves at different current biases. b, I-V curves in the parallel and antiparallel magnetization configurations. The inset presents the optical image of device H. c, The square symbols denote SVE values extracted from the V-B curves at different bias currents. All measurements were performed at a fixed temperature of 10 K.\nFig. R3 SVE at different bias current intensities for device I with a Fe GeTe /5-nm-InSe/5-nm-GaSe/Fe GeTe junction at 10 K. a, V-B curves at different current biases. b, I-V curves in the parallel and antiparallel magnetization alignments. The inset shows the optical image of the device I. c, The square symbols denote SVE values extracted from the V-B curves at different bias currents. The temperature is fixed at 10 K.\nResponse: Thank you for pointing out this critical detail. Your observation has helped us clarify a key experimental parameter. We appreciate the opportunity to address the inconsistency regarding device resistance and the role of the external resistor.\nFirst, we would like to correct the device resistance value: Based on actual measurement data of device A (with FGT/5-nm-GaSe/5-nm-InSe/FGT junction), when the applied bias current (I) is 1 nA, the corresponding device voltage (V) is 25 μV, as shown in the revised Fig. 1e of the main manuscript. Using Ohm’s law (R = V/I), the device resistance is calculated to be 25 kΩ, which is not in the gigaohm range as inferred from Supplementary Figure 3 (now Fig. 1d in the revised version). This lower resistance value is consistent with the design of our external resistor and ensures the resistor can effectively regulate the junction current.\nTo further verify this, we conducted an additional control experiment: a 1 MΩ external resistor was added to the circuit, and the junction current was measured. As shown in Fig. R5, the current was only 0.1 nA in the antiparallel magnetization state, confirming that the external resistor dominates the current. Specifically, the current is limited by the 1 MΩ external resistor rather than the 25 kΩ device itself.\nIn the revised Supplementary Information, we have supplemented this verification data in a new Fig. S9, which includes the current data obtained with both the 100 kΩ and 1 MΩ external resistors. We have also updated the description in Supplementary Note 4 to explicitly outline the device resistance calculation process, thereby avoiding any potential misunderstanding.\nFig. R5. Current generated by a FGT/5-nm-GaSe/5-nm-InSe/FGT junction device under an applied magnetic field. a, Schematic of the measurement setup, where R denotes the resistor connected in series with the device. The current was measured using an Agilent B1500A with the voltage output set to zero and the device at a temperature of T = 10 K. b-c, A magnetic field B perpendicular to the plane of the device was applied to switch the magnetic orientation of the two FGT electrodes and thereby modulating the current I. Quasi-steady currents were measured when the two FGTs in the parallel (-0.4 T) and antiparallel (0.2 T) magnetization states. The series resistors used were 100 kΩ (b) and 1 MΩ (c), respectively.\nResponse: Thank you for your valuable comment. This question helps us further clarify the temperature dependence of the SVE and its intrinsic origin. We agree that analyzing the SVE behavior near the critical temperature of FGT is key to distinguishing intrinsic from extrinsic effects, and we address this with both experimental data and physical reasoning below.\nFirst, we examined the variation of the zero-bias SVE near the Curie temperature. For device D presented in Supplementary Figure 6, the SVE decreases from ~300% at 210 K to ~170% at 220 K and vanishes completely at 230 K. For device A exhibited in Fig. 2 of the main text, the SVE decreases from ~100% at 210 K to ~40% at 220 K, and vanishes completely at 230 K. The SVE of both devices drops to zero at 230 K, which is slightly above the Curie temperature of Fe GeTe . We have added the V-B hysteresis loops of these two devices measured at 230 K, as shown in Fig. R6a and Fig. R7a. Then, we extracted the temperature dependence of the spin accumulation voltage ΔV (ΔV = V - V ), as shown in Fig. R6b and Fig. R7c, and confirmed a clear trend: ΔV gradually decreases with increasing temperature and drops to zero when the temperature approaches 230 K. This trend directly confirms the intrinsic spin-dependent origin of the SVE: above FGT’s Curie temperature, FGT loses its ferromagnetic order, and electron spin polarization diminishes to zero. Consequently, the spin-dependent voltage difference between the parallel and antiparallel states vanishes (ΔV = 0), resulting in SVE = 0. This behavior stands in contrast to extrinsic effects (e.g., thermal noise), which would not exhibit such a sharp, temperature-dependent cutoff tied to FGT’s ferromagnetic phase transition.\nIn the revised main text and supplementary information, we have replaced the original content with Fig. R6 (now redesignated as the new Supplementary Fig. S5) and Fig. R7 (now redesignated as the new Fig. 2) to explicitly illustrate the ΔV-temperature relationship. We have also added a detailed discussion on the zero-bias SVE near FGT’s Curie temperature in the main text, making the underlying physical mechanism more transparent.\nFig. R6. Temperature dependence of the zero-bias SVE for device D with 5 nm p-GaSe/5 nm n-InSe junction. a, SVE-B curves without external bias applied at different temperatures. b, The magnitude of the zero-bias SVE and spin accumulation voltage ΔV (ΔV= V - V ) as a function of the temperature. c, Color scale plot of SVE ratios versus temperature and bias current. The hollow squares represent the conductance as a function of temperature in the parallel magnetization alignment.\nFig. R7. Temperature-dependent zero-bias SVE. a, Zero-bias SVE for different temperatures T for Device A. b, The value of V and V at zero-bias versus T, as extracted from the V-B curves in part (a). c, The zero-bias SVE and spin accumulation voltage ΔV (ΔV= V - V ) versus T, as derived from the V-B curves in part (a).\nResponse: Thank you for your valuable comments. We further explain the zero-bias spin voltage phenomenon reported in Refs. 27, 31. As shown in Fig. R8a (reproduced from Fig. 5 of Ref. 27), the voltage across the junction was measured with sweeping an external magnetic field, but with no net flow of current (achieved by directly connecting the junction to a high-impedance nanovoltmeter). Two clearly distinguishable voltage states are observed, corresponding to the P and AP spin configurations. Thus, the CrO /SnO /Co MTJ device exhibits spin-dependent voltage signals without an applied bias current (I = 0). At 5 K, the measured voltage in the parallel state is close to 0 V, while that in the antiparallel state is close to 60 μV, resulting in a significant zero-bias SVE.As shown in Fig. R8b (reproduced from Fig. 3 of Ref. 31), when the applied bias voltage is zero (V = 0), the measured currents ofCo/C/MgO/C/Co MTJs in the parallel and antiparallel states are non-zero (I ≠ I ≠ 0). This also gives rise to a significant zero-bias SVE. In summary, the above literature reports observe current or voltage signals that depend on the relative orientation of magnetic moments in ferromagnetic metal electrodes in the absence of external electrical power excitation. This is consistent with our findings: in our ferromagnetic/p-n junction/ferromagnetic MTJs, non-zero voltage signals are measured in the parallel and antiparallel states under zero-bias current (V ≠ V ≠ 0 at I = 0),which directly gives rise to the observed zero-bias SVE.\nFig. R8. a, (Captured from Ref. 27) Spin-dependent voltage shift with the application of an external field, for a MTJ with SnO barrier thickness of 4 nm. Inset shows the variations of RA and ∆V as a function of barrier thickness at 10 K. The solid lines are provided only as a visual guide. b, (Captured from Ref. 31) Averaged experimental bias dependencies of current in the MTJ’s P (black) and AP (red) magnetic states, and of the resulting tunneling magnetoresistance (TMR; green), using the same current/TMR scales.\nThank you for your valuable suggestion. After taking the suggestion from the reviewer, we carefully discussed and tried our best effort to modify the revised manuscript. We believe the revised version is now much clearer and easier to understand."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have responded to my comments. I am satisfied with the answer. The quality of the manuscript has been improved. It can be accepted now.", "reviewer_2": "I thank the authors for their extensive revision of the manuscript and for the detailed explanations in the rebuttal letter. The revised version addresses the major concerns raised in my initial report. The main results—including zero-bias spin-voltage signals—are now presented more clearly, with full I–V characteristics and key device data included in the main text. The readability of the manuscript has significantly improved, and the Supplementary Information now plays an appropriate supporting role rather than carrying essential arguments.\nThe newly added control experiments, including the temperature dependence approaching the Curie temperature and the use of differing material combinations with MoS2 and Fe5GeTe2, considerably strengthen the case that the observed signal originates from intrinsic spin-dependent transport across the vdW p–n junction, rather than extrinsic effects such as instrumental artifacts or trivial thermoelectric contributions.\nWith respect to the physical mechanism, the authors now provide a more coherent description in terms of a non-equilibrium “spin-engine” scenario, supported by semiclassical modelling based on DFT-derived band alignment and spin-dependent drift-diffusion. While the model remains partly phenomenological—including the lack of explanation for the critical temperatures (e.g., ~ 35 K) and the optimal insulating-layer thickness (~ 5 nm)—it reasonably captures the observed magnitude and temperature/thickness trends of the zero-bias spin voltage. To ensure clarity for readers, I might suggest that the authors describe the key conceptual statement about the “non-equilibrium spin engine” (as emphasized in the rebuttal letter) in an earlier part of the main manuscript and clearly separate experimentally established observations from model-based interpretations.\nOverall, the authors have satisfactorily resolved my major concerns. The manuscript now contains strong experimental evidence and an improved mechanistic discussion that, in my opinion, meet the publication standards of Nature Communications. I therefore support publication of the current article in Nature Communications."}, "author_response": "Response: We sincerely appreciate the reviewers’ recommendation for the acceptance and publication of our manuscript.\nResponse: We appreciate the reviewers’ positive comments and would like to thank the reviewer for the valuable suggestion. In the revised manuscript, we have clearly distinguished between experimental results and theoretical analyses, and further elaborated on the key conceptual of our theoretical model in both the abstract and the Introduction section,the revised parts in the manuscript are marked in blue. The revised abstract is presented as follows:\n“The large zero-bias spin voltage signal exceeds 30,000%, which is far greater than the highest magnetoresistance signals reported to date. This non-equilibrium spin-engine state arises from the asymmetric diffusion of spin-up/spin-down electrons across the junction. It is driven by the built-in electric field of the junction and occurs under continuous energy exchange of the junction with the environment.”\nThe revised Introduction section is presented as follows:\nTo analyze the origin of the zero-bias SVE, we conducted a series of control studies: 1) The zero-bias SVE is not observed in MTJ devices with a single spacer layer, excluding noise from the measurement setup and 2) does not originate from the spin Seebeck effect, as confirmed by experiments with a temperature gradient along the junction; 3) a semiclassical model of the spin-dependent drift-diffusion combined with first-principles density functional theory (DFT) of the junction reveals a non-equilibrium spin-engine state. This features the injection of electron spins at the FGT/GaSe interface, their diffusion under the built-in electric field of the junction and their spin flipping at the InSe/FGT interface.\nOverall, the authors have satisfactorily resolved my major concerns. The manuscript now contains strong experimental evidence and an improved mechanistic discussion that, in my opinion, meet the publication standards of Nature Communications. I therefore support publication of the current article in Nature Communications.\nResponse: We sincerely appreciate the reviewers’ recommendation for the publication of our manuscript in Nature Communications."}]

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