Ferroelectricity-driven strain-mediated magnetoelectric coupling in two-dimensional multiferroic heterostructure

Domain: physics
Published: 2025-11-27
Editorial outcome: major_revision

Abstract
In the post-Moore era, CMOS technology faces challenges in storage and power consumption. Two-dimensional van der Waals ferromagnets, with their atomically sharp interfaces, enable heterostructure with ferroelectric materials. Through strong magnetoelectric coupling effects, they provide an ideal platform for developing highly efficient magnetoelectric interfaces. Leveraging this ideal platform, this study proposes a strain-modulation strategy based on vertically integrated two-dimensional van der Waals multiferroic heterojunctions Fe3GaTe2/P(VDF-TrFE) to address these challenges. This structure utilizes the inverse piezoelectric effect of ferroelectric polymers to induce strain. Through magnetoelectric coupling, the heterojunction achieves non-volatile reconfiguration of the magnetic anisotropy constant of Fe3GaTe2 at room temperature. This enables fully reversible electrical control of the anomalous Hall resistance and inverter functionality. Device integration validated reconfigurable logic gates and half-adder circuits, demonstrating ultra-low energy consumption (0.5 aJ), nanosecond-scale write speeds (5 ns), and high operational stability.

Introduction
In the development process of integrated circuits in the post-Moore era, the traditional silicon-based CMOS technology is facing the dual challenges of memory wall and power consumption limitation, which prompts researchers to turn their attention to the voltage-controlled magnetic technology with the characteristics of nonvolatility, reconfigurability, and high energy efficiency. As an important carrier in this field, spintronic devices realize information encoding through magnetic moment quantum states, and their natural non-volatile characteristics and operation energy consumption on the order of pico-joules provide a physical basis for breaking through the bottleneck of von Neumann architectures1,2. Conventional heterostructure devices suffer from lattice mismatch-induced interfacial defects, leading to inefficient magnetoelectric coupling and inadequate thermal stability, which severely hinder large-scale integration3,4. The emergence of 2D van der Waals (vdW) ferromagnets has addressed this challenge by offering atomically smooth interfaces, thus enabling the integration of diverse crystals with atomically sharp interfaces for intriguing functionalities and advanced strain regulation5,6. Precise regulation of magnetic exchange by strain can overcomethe lattice continuity limitation and Poisson effect of conventional ferromagnetic materials, and its high linearity and low hysteresis are superior to the nonlinear response and strain dissipation defects of conventional ferromagnetic materials2. The latest research demonstrates that the strong coupling effect between interface strain and magnetic order in these materials not only overcomes the energy efficiency bottleneck of traditional charge-based regulation but also elucidates the synergistic mechanism of magnetoelectric coupling of multi-physical fields7. This finding provides a theoretical foundation for constructing ultra-low-power spin-logic units.

2D vdW ferromagnetic materials provide a compelling platform for both logic device design and the investigation of magnetoelectric coupling, as their magnetoelectric properties can be effectively modulated via strain engineering and electrical gating8,9. The inherently weak interlayer magnetic interactions in these materials amplify interface effects, particularly in ferromagnetic/ferroelectric heterostructures. For example, ferroelectric polarization can significantly modulate the magnetic order and magnetic anisotropy of the ferromagnet through mechanisms such as charge transfer and spin-orbit coupling10,11. Additionally, a piezoelectric layer can couple to the magnetosphere via mechanical deformation, enabling dynamic modulation of magnetic properties12. As an illustrative case, ferroelectric gating of Fe3GeTe2 cannot only reorient its magnetization axis but also modulate the carrier type and spin polarization of Schottky barriers13. Furthermore, the engineered design of the vdW gap enhances the tunability of the magnetoelectric response14. Beyond Fe3GeTe2, novel materials like Fe3GaTe2, which exhibit room-temperature perpendicular magnetic anisotropy, a high spin-Hall angle, efficient charge-spin conversion, and excellent air stability, offer promising pathways for enabling low-power, nonvolatile operation in magnetooptical nano-devices and spin logic circuits15. These magnetoelectric coupling-based regulation strategies, which directly manipulate magnetic parameters such as Curie temperature and spin polarization through voltage or strain, represent a departure from traditional logic devices reliant on complex complementary MOSFET structures. Consequently, they are driving the advancement of highly integrated magnetoelectric heterostructure devices toward practical application.

In the ultra-low power consumption strategy based on strain control proposed here, the ferroelectric P(VDF-TrFE) bottom gate has been demonstrated to effectively regulate the magnetic anisotropy constant via strain-mediated magnetoelectric coupling. Specifically, the inverse piezoelectric effect in the P(VDF-TrFE) layer induces a non-uniform strain field, which, through mechanical conduction, acts upon the Fe3GaTe2 lattice. This interaction leads to a reorganization of the magnetic crystal’s anisotropic properties, resulting in a dynamic deflection of the magnetization axis. Consequently, the magnetic anisotropy constant, K, can be modulated by applying a polarization voltage. Reversing the polarization direction of the P(VDF-TrFE) layer induces contraction via the inverse piezoelectric effect, thereby altering the direction of the easy magnetization axis and enabling fully electrically reversible modulation of the anomalous Hall resistance. This strain-mediated coupling mechanism has been experimentally corroborated using Raman spectroscopy and X-ray diffraction (XRD). Furthermore, Fe3GaTe2 models incorporating various strain configurations were developed to elucidate the effects of strain on the exchange coupling energy and magnetic anisotropy of Fe3GaTe2. Finally, device integration was used to demonstrate reconfigurable logic gate arrays (AND/NAND/NOT) and half-adder circuits, providing a crucial theoretical foundation and a feasible technical pathway for the design of innovative magnetoelectric coupling devices.

Results
Electric field-dependent modulation of magnetic properties
To modulate the magnetic properties of two-dimensional ferromagnetic materials, we propose a method that introduces strain by stretching or compressing the crystal lattice through the inverse piezoelectric effect. To achieve this, we fabricated a vertically stacked, multi-layer magnetic device, schematically illustrated in Fig. 1a (optical images are shown in Supplementary Fig. 1a), with the fabrication process detailed in the Methods section. The ferroelectric layer comprises P(VDF-TrFE), which possesses a spiral ferroelectric β-phase crystalline structure, as depicted in the inset of Fig. 1a. X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR) characterization confirmed substantial ferroelectric β-phase crystallization within the P(VDF-TrFE) thin film. Moreover, piezoelectric force microscopy (PFM) and P-E loop measurements demonstrated its excellent ferroelectric properties (Supplementary Fig. 2). The two-dimensional ferromagnetic layer consists of Fe3GaTe2, wherein each layer features two non-equivalent Fe atomic sites among the five adjacent atoms (Fig. 1a inset)16. The Fe atoms, specifically their 3d electrons and magnetic moment arrangement, are the primary contributors to the ferromagnetism of Fe3GaTe2. The advantage of this organic-inorganic heterostructure lies in the strong polarization characteristics of the P(VDF-TrFE) spiral β phase at the interface. Coupling between the C-F dipoles and the lone pair electrons of Te atoms on the Fe3GaTe2 surface induces a local electric field, triggering the recombination of Fe atomic d-orbital electrons in spin states within Fe3GaTe2 and thereby significantly enhancing the magnetoelectric coupling efficiency of the device17. Furthermore, the synergistic effect of the Te atom passivation layer and the hydrophobic C-F chains of P(VDF-TrFE) effectively prevents the penetration of environmental oxygen or water molecules, inhibiting the oxidation of Fe3+ and preserving the intrinsic ferromagnetism of Fe3GaTe2 18,19. Concurrently, the lateral ferroelectric polarization of P(VDF-TrFE) can couple with the magnetic moments of Fe3GaTe2 through the interfacial polarization field, forming a magnetoelectric structure where the vertical magnetic anisotropy is orthogonal to the lateral electric polarization. The magnetoelectric coupling efficiency is further enhanced via the inverse Rashba-Edelstein effect (IREE)20–22. The high-quality, atomic-level steep P(VDF-TrFE)/Fe3GaTe2 interface effectively minimizes interface scattering effects during carrier migration23, leading to a more concentrated electric field distribution within the P(VDF-TrFE) layer. This, in turn, enhances the uniformity and stability of ferroelectric domain polarization reversal24. In addition, strong interface bonding, facilitated by hydrogen bonds or van der Waals interactions, ensures high consistency between the dipole alignment direction and the electric field direction, enabling a dynamic modulation range exceeding 104 in amplitude. Finally, the high-quality P(VDF-TrFE)/Fe3GaTe2 interface helps to mitigate lattice mismatch issues during organic film preparation, facilitating efficient strain transfer via the van der Waals interface through the inverse piezoelectric effect of P(VDF-TrFE), thereby enabling strain-modulated magnetism.

The anomalous Hall effect (AHE) curves for the device were measured at 300 K within a magnetic field range of −5 T to 5 T, as a function of magnetic field angle (θH) (Supplementary Fig. 3a), without the application of a polarization voltage. These magnetic field-dependent anomalous Hall resistance (Rxy-B) curves indicate strong perpendicular magnetization (PMA) in the device, primarily stemming from the unique crystal and electronic structure of Fe3GaTe2, which results in strong spin-orbit coupling (literature). Fitting the angular dependence of θH and θM (the tilt angle between the magnetization direction and the sample plane, as shown in Supplementary Fig. 3b) yields an estimated anisotropy constant Ku of approximately 4.82×105 J/m3. Applying a polarization voltage to the dual gate induces asymmetric modulation effects in the top and bottom layers of P(VDF-TrFE). Modulating Fe3GaTe2 via a polarization voltage applied to the bottom P(VDF-TrFE) layer involves both ferroelectric polarization modulation and strain regulation. Ferroelectric polarization is achieved through charge regulation mechanisms at the ferroelectric-ferromagnetic interface. Specifically, polarization reversal in the ferroelectric P(VDF-TrFE) generates a dynamic dipole field through interfacial charge transfer, indirectly and linearly regulating the carrier concentration of Fe3GaTe2. This change in carrier concentration within Fe3GaTe2, a self-doped semiconductor, alters the occupation state of the Fe atom 3d orbitals, thereby affecting the strength of electronic correlations. Consequently, this influences magnetic exchange interactions, leading to alterations in the magnetic moment and density of states of Fe3GaTe2, ultimately achieving magnetic modulation25. As shown in Supplementary Fig. 4, applying different polarization voltages to the bottom P(VDF-TrFE) layer, with a fixed magnetic field angle θH = 90°, results in variations in the device’s coercive field and anomalous Hall resistance. The coercive field (HC) and anomalous Hall resistance (Rxy) decrease under positive polarization voltages and increase under negative polarization voltages, consistent with prior reports26. Calculations indicate that the magnetoelectric coupling coefficient αCME is 8.6×10−6 S/m at a polarization voltage of −10 V and 6.4×10−6 S/m at a polarization voltage of 10 V27 (Supplementary Note 1).

P(VDF-TrFE)’s inherent ferroelectric and piezoelectric properties are crucial to the observed behavior. Application of a polarization voltage not only reorients the dipole distribution within the material but also induces deformation via the inverse piezoelectric effect. This phenomenon arises from the highly polarized nature of the C-F bonds in P(VDF-TrFE), causing the molecular dipole moment to respond to the electric field28, which in turn modifies intermolecular forces and results in macroscopic deformation. The P(VDF-TrFE) layer, forming a robust interfacial bond with the silicon substrate (Fig. 1b and Supplementary Fig. 5a), experiences significantly restricted out-of-plane displacement, effectively anchoring it to the substrate surface. Consequently, when the P(VDF-TrFE) layer undergoes inverse piezoelectric deformation, the rigid substrate prevents the release of strain in the downward direction. This constraint results in a substantial conversion of the deformation into in-plane stress, either tensile or compressive. This stress is then efficiently transferred to the adjacent Fe3GaTe2 layer via interfacial shear, facilitating effective utilization of the strain energy. Fundamentally, these constraint conditions promote the preferential transfer of piezoelectric strain energy as shear stress along the interface, rather than allowing for its dissipation through unconstrained deformation, thereby enhancing the overall efficiency of strain transfer. The resulting mechanical stress is transmitted to the ferromagnetic Fe3GaTe2 layer, inducing tensile strain and lattice expansion. Critically, the two-dimensional nature of the ferromagnetic material overcomes the limitations of traditional ferromagnetic systems imposed by rigid substrates, which often lead to lateral lattice relaxation and strain gradient dissipation. This is achieved through the synergistic effects of quantum confinement and interlayer slip barriers4,6. This unique structure enables efficient control of magnetic anisotropy under stress coupling, achieving lattice stress transmission efficiency far exceeding that of conventional ferromagnetic materials. Fe3GaTe2 exhibits strong perpendicular magnetic anisotropy (PMA), with its easy magnetization axis oriented perpendicular to the material plane. The applied strain distorts the lattice structure, leading to a redistribution of magnetic anisotropy by altering the orbital occupation state of iron atoms, thereby influencing the orientation of the easy magnetization axis29.

Furthermore, to better characterize the magnetic anisotropy of the dual-gate device, the magnetic anisotropy constant K1 was calculated under various polarization voltages16,30 (calculation details are provided in Supplementary Note 2). As shown in Fig. 1c, d, applying a polarization voltage to the bottom P(VDF-TrFE) ferroelectric layer, regardless of its polarity, induces a significant reduction in the magnetic crystalline anisotropy constant K1 of Fe3GaTe2, exhibiting a distinct hysteresis loop during the ±10V voltage sweep. This demonstrates that the polarization state of the underlying P(VDF-TrFE) layer effectively regulates the perpendicular magnetic anisotropy (PMA) of Fe3GaTe2. The underlying mechanism primarily stems from the electric field effect generated by the polarization charges of the ferroelectric layer at the interface. This electric field modulates the electronic structure of Fe3GaTe2 that determines the perpendicular anisotropy (particularly the orbital occupation states related to spin-orbit coupling) through interfacial charge transfer or orbital restructuring, thereby weakening its PMA strength, which is observed as a decrease in K1. In contrast, the K1 value for the top P(VDF-TrFE) layer exhibits no consistent changes upon application of a polarization voltage, remaining relatively stable. This indicates that the ferroelectric polarization of the top layer has a negligible effect on the vertical magnetic anisotropy of Fe3GaTe2. In summary, the charge transfer induced by the polarization of the top ferroelectric layer exhibits a negligible effect on the magnetic anisotropy of Fe3GaTe2. Conversely, the strain-mediated control exerted by the polarization of the bottom ferroelectric layer significantly modulates the vertical magnetic anisotropy of the Fe3GaTe2 film, as evidenced by a decrease in the K1 value.

Consequently, as shown in Fig. 2a, b, when the magnetic field angle θH = 0°, applying different polarization voltages causes the easy magnetization axis direction of the anomalous Hall curve in the device to deflect, reflecting changes in the in-plane magnetization direction. Specifically, applying a negative polarization voltage induces tensile strain in the P(VDF-TrFE), and subsequent strain transmission causes the Fe3GaTe2 lattice to stretch, thereby enhancing the out-of-plane component of the magnetization axis. This enhancement increases with the magnitude of the applied polarization voltage; at −10 V, the easy magnetization axis is deflected from its original 90° orientation to 95°. Conversely, reversing the polarization of the P(VDF-TrFE) layer induces contraction via the inverse piezoelectric effect, enhancing the in-plane component of the easy axis and causing the magnetization axis to deflect in the in-plane direction.

The distinct modulation mechanisms arising from the device’s asymmetry stem from the differential effects of voltage polarization on each P(VDF-TrFE) layer. Specifically, polarization of the bottom P(VDF-TrFE) layer induces both ferroelectric polarization modulation and strain modulation, whereas the top layer’s polarization primarily elicits ferroelectric polarization modulation. The former leverages charge control to effectively regulate HC, Rxy, and magnetic moment of the Fe3GaTe2 layer. Concurrently, strain modulation alters the Fe3GaTe2 lattice via strain transmission, thereby affecting the direction of the easy magnetization axis. The observed asymmetry between the top and bottom P(VDF-TrFE) layers is attributed to the presence of the rigid silicon substrate. The rigid substrate acts as a significant constraint, exerting considerable mechanical influence on both the top and bottom P(VDF-TrFE) layers. Analogous to a piezoelectric actuator configuration, the polymer layer functions as the driving element, generating strain through the inverse piezoelectric effect upon the application of an electric field. The robust adhesive interface between the polymer and the substrate mirrors the rigid substrate found in piezoelectric actuators31, effectively suppressing unproductive strain and facilitating the directional transfer of strain energy. However, disparities in interfacial constraints dictate that the stress transmission efficiency of the P(VDF-TrFE) layer is substantially bottom downward (towards the substrate) compared to its upward transmission (towards the functional material), thereby influencing the overall device performance.

Voltage polarization of the top P(VDF-TrFE) layer also induces carrier changes and deformation. Conversely, the mechanical environment of the top P(VDF-TrFE) layer differs significantly. Its bottom surface is bonded to the Fe3GaTe2/bottom P(VDF-TrFE)/substrate system, imposing constraints, while its top surface remains a free interface. Under voltage excitation, this disparity renders the top layer more susceptible to out-of-plane relaxation, such as warping or bending. Consequently, a greater proportion of mechanical energy dissipates through volumetric deformation within the layer itself, rather than being converted into in-plane strain directed toward the Fe3GaTe2 layer. This stems from insufficient constraints to effectively suppress unproductive deformation, leading to a shift in the strained transfer mechanism from efficient shear coupling to less efficient bending deformation. This transition ultimately contributes to a substantial decline in overall driving performance. Resulting in mechanical strain transmitted to the Fe3GaTe2 layer that remains below the critical threshold (Fig. 1b and Supplementary Fig. 5b). As shown in Supplementary Fig. 6, application of varying polarization voltages to the top P(VDF-TrFE) layer at a magnetic field angle (θH) of 90° leads to a reduction in HC and Rxy under positive polarization and an enhancement under negative polarization26. However, at θH = 90°, the easy magnetization axis of Fe3GaTe2 remains predominantly perpendicular, irrespective of the direction of the applied polarization voltage, and the anomalous Hall curve’s shape remains invariant, with only the magnitudes of HC and Rxy changing. This observation further suggests a negligible impact of strain on the magnetic properties of Fe3GaTe2 under these conditions.

A systematic investigation was performed to control the polarization voltages of the top and bottom P(VDF-TrFE) layers in devices by sweeping the external voltage from −10 V to 10 V. The voltage-dependent coercive field and residual Hall resistance, as presented in Supplementary Fig. 7, both exhibit hysteresis loops. Supplementary Fig. 7 illustrates the regulatory effects of the top and bottom P(VDF-TrFE) ferroelectric gates on the residual Hall resistance and coercive field of the Fe3GaTe2 device, along with their corresponding hysteresis loops. The residual polarization intensity (Pr) of the device was measured under different polarization pulse voltages (Supplementary Fig. 8). The magnetically modulated hysteresis loop and the V-shaped hysteresis curve of the residual polarization intensity exhibited highly consistent trends, strongly confirming the effective modulation of ferromagnetic properties by ferroelectric polarization (Supplementary Note 3). Notably, the hysteresis loop associated with the bottom P(VDF-TrFE) structure is significantly wider than that of the top layer. This disparity arises from the distinct regulatory mechanisms in the device. The top layer structure is primarily governed by the direct influence of the ferroelectric polarization field (P), whereas the bottom layer structure is subject to the combined effects of the ferroelectric polarization field and the in-plane strain induced by the inverse piezoelectric effect of P(VDF-TrFE). The ferroelectric polarization field primarily regulates Fe3GaTe2 carriers through the ferroelectric-ferromagnetic interface. Conversely, the in-plane piezoelectric strain generated in the bottom layer structure can effectively modify the lattice parameters of Fe3GaTe2 or induce magnetoelastic coupling effects, directly influencing the easy axis orientation or altering the magnitude of its magnetic anisotropy constant. This dual orthogonal regulation mechanism, involving ferroelectric polarization and piezoelectric strain, synergistically enhances the energy barrier for magnetic domain switching in the bottom layer structure. Consequently, the magnetization reversal process requires overcoming a greater resistance, macroscopically manifesting as a larger coercive field and a broader hysteresis loop.

Voltage-induced strain in dual-gate devices
To further elucidate the strain regulation mechanism, transmission electron microscopy (TEM) samples were prepared using focused ion beam (FIB) milling for detailed interface microstructural characterization of the device (Fig. 2c, and Supplementary Fig. 9). These analyses revealed that Fe3GaTe2 forms molecular-scale, intimate heterointerfaces with both the top and bottom layers of the P(VDF-TrFE) ferroelectric polymer. Furthermore, TEM observations confirmed the characteristic spiral crystalline morphology of P(VDF-TrFE), indicative of molecular chains adopting a fully trans conformation and spontaneously twisting along the chain axis, a key structural signature of the dominant ferroelectric β phase. This close molecular-level interfacial contact is critical for efficient carrier control, as it minimizes interface defect state density, reduces carrier scattering barriers, and enhances the direct modulation of carrier concentration/type in the Fe3GaTe2 channel by the ferroelectric polarization field. Moreover, this interface provides an ideal platform for effective strain transmission. The robust physical contact between the two phases, coupled with low interfacial shear resistance, ensures that the strain generated within the polymer layer under applied gate voltage is efficiently transferred to the Fe3GaTe2 lattice via strong interfacial coupling. In summary, TEM characterization revealed the intimately coupled nature of the Fe3GaTe2/P(VDF-TrFE) interface at the molecular scale, providing key insights into the microscopic mechanisms underlying the simultaneous achievement of efficient carrier control and strain transmission. This analysis offers direct structural evidence crucial for understanding the multifunctional control mechanism operating within these dual-gate devices.

In order to deeply investigate the voltage-dependent strain modulation in the devices, the strains present in the devices were characterized by Raman spectroscopy and XRD. Raman spectra as a function of the top P(VDF-TrFE) polarization voltage V1 and the bottom P(VDF-TrFE) polarization voltage V2 are shown in the Supplementary Fig. 10 and 8. Raman spectroscopy is highly sensitive to lattice expansion or contraction, as reflected in the eigenwave number of phonons modes. Figure 2d illustrates the Raman shift associated with V2, measured at 300 K for the dual-gate device. The Raman spectrum, in the range of 120–150 cm−1, exhibit two prominent peaks. At zero bias (V2 = 0 V), these peaks are located at approximately ~125 cm−1 (A1g) and ~141 cm−1 (E12g), corresponding to Fe3GaTe232. For reference, the peaks associated with the β-phase and α-phase of P(VDF-TrFE) are located at 840 cm−1 and 1280 cm−1, respectively33. The positions of the Fe3GaTe2 and P(VDF-TrFE) peaks are indicated by dashed lines in Fig. 2d. A comprehensive summary of the Raman peak displacements and intensities as a function of V2 is presented in Fig. 2d and Supplementary Fig. 10. Notably, distinct trends were observed for all Fe3GaTe2 and P(VDF-TrFE) peaks. Under positive voltage polarization, the Fe3GaTe2 peaks at both 125 cm−1 and 141 cm−1 exhibit a blue shift (increase) relative to the zero-bias condition. Conversely, negative voltage polarization induces a red shift (decrease) in both peaks. This observation suggests a strong interfacial coupling between Fe3GaTe2 and P(VDF-TrFE), facilitating the transfer of the piezoelectric response from the P(VDF-TrFE) layer to the ferromagnetic Fe3GaTe2 layer. The red shift in Raman peak position is primarily attributed to lattice expansion of the material, consistent with prior research34. Based on the correlation between Raman shift and strain established by Eom et al., we estimate a tensile strain of 0.6-0.8% in Fe3GaTe2 at V2 = 10 V, and a compressive strain of 0.4-0.5% at V2 = −10 V35,36. It is important to note that the Raman spectra were acquired in the residual state at zero bias after applying the V2 polarization voltage. This approach effectively minimizes the influence of surface charge modulation induced by polarization at the device interface, and the polarization does not significantly affect the peak-to-peak intensity of the Fe3GaTe2 Raman peaks. The system characterization data show that the two-dimensional ferromagnetic system has the unique advantage of breaking through the strain modulation limit of conventional bulk materials. Its atomic-level thickness property fundamentally avoids the lateral lattice relaxation induced by mechanical confinement, while the out-of-plane flexible structure effectively suppresses the strain gradient dissipation induced by rigid substrate coupling2,4. This intrinsic advantage enables Fe3GaTe2 to achieve ultra-high stress transfer efficiency at the van der Waals heterointerface, which provides a pathway for realizing high-performance storage-computing-integrated magneto-electric coupling devices.

In situ Raman spectroscopy elucidates the lattice dynamics response mechanism of P(VDF-TrFE) to ferroelectric domain reorientation. Upon application of a polarization voltage (V2), the Raman displacement (Δν) of characteristic vibrational modes—specifically, the CF₂ antisymmetric telescopic vibration at 840 cm−1 and the CC backbone vibration at 1280 cm−1 exhibits only minor fluctuations (|Δν|<2 cm−1), irrespective of voltage polarity. This spectral stability suggests that the applied polarizing electric field primarily induces a collective reorientation of molecular chain dipole moments, rather than perturbing the ground-state vibrational potential energy surface of the β-phase unit cell17. Consequently, the characteristic peak positions remain largely unchanged. However, their regular jittering of peak positions observed with varying V2 (Supplementary Fig. 10) can be attributed to subtle stress redistribution within the molecular chains and fine-tuning of the crystal structure induced by positive and negative voltage polarization. These effects may result in minor peak shape narrowing or slight peak position shifts for certain modes. As illustrated in Fig. 2d, application of both positive and negative polarization voltages leads to an increase in the β-phase intensity and a corresponding decrease in the α-phase intensity of P(VDF-TrFE). These changes in P(VDF-TrFE) Raman spectra are predominantly reflected in peak intensities. Both positive and negative voltage polarization promote the alignment of molecular chains along the electric field direction, resulting in a significant enhancement of the β-phase characteristic peak at 840 cm−1 and a weakening of the α-phase characteristic peak at 1280 cm−1. The primary distinction lies in the opposing alignment directions of the dipole moments, which may account for variations in Raman peak intensities observed at specific polarization directions37. In order to explore the difference in strain transfer between the top and bottom layers, the Raman curves of the devices at different polarization voltages V1 were analyzed as in Supplementary Note 4. Analysis by time-resolved Raman spectroscopy revealed that the imposition of a polarized electric field in the device induced the formation of an all-trans conformation (TTT) of the P(VDF-TrFE) molecular chains38,39, and the strain-polarization synergistic introduced by the inverse piezoelectric effect further stabilized the nonvolatility40, in which the kinetic decoupling ratio between strain relaxation and electrical relaxation (1:1.68) was finally recovered after 288 h (Supplementary Note 5).

Raman spectra of the dual-gate device, with variations in V2, indicate that the bottom piezoelectric effect introduces strain into the Fe3GaTe2 layer, resulting in both tensile and compressive strains. X-ray diffraction (XRD) measurements were conducted to quantitatively determine the lattice changes in the ferromagnetic layer Fe3GaTe2 (Fig. 2e, a=3.972 Å, c=16.225 Å). The XRD curves of Fe3GaTe2 at different polarization voltages V2 are shown in the Supplementary Fig. 13, under positive polarization voltage, the mechanical strain conduction of P(VDF-TrFE) subjects the Fe3GaTe2 layer to in-plane compressive strain, leading to a decrease in the c axis and an increase in the a axis. Conversely, negative polarization voltage induces in-plane tensile strain in the Fe3GaTe2 layer, causing the c-axis to increase and the a-axis to decrease (As shown in the illustration in Fig. 2e). The in-plane strain εa of the Fe3GaTe2 layer is approximately 0.5% and 0.8% under 10 V and −10 V polarization, respectively, while the in-plane strain εc is approximately 0.45% and 0.48%41. The XRD change curves of the top-layer P(VDF-TrFE) polarized device are shown in Supplementary Fig. 14. The a axis/c-axis of Fe3GaTe2 exhibits disordered changes under different polarization voltages, indicating that the transferred strain has not caused changes in the Fe3GaTe2 lattice.

First principles calculations: strain-induced changes in magnetic anisotropy
To elucidate the physical mechanism underlying the strain-modulated magnetic anisotropy observed in the devices, we developed a multi-scale theoretical model for bulk Fe3GaTe2, detailed in Supplementary Fig. 15. Utilizing Green’s function perturbation theory, we calculated the exchange coupling constants for two strain-induced configurations of bulk Fe3GaTe2, considering magnetization aligned along the in-plane (mx) and out-of-plane (mz) directions, respectively. These analyses suggest that the Fe3GaTe2 layers within the structure exhibit distinct atomic arrangements under strain conditions of (a −0.5% c+0.45%) and (a+0.8% c-0.48%). As illustrated in Fig. 2f, our calculations demonstrate that under the a −0.5% c+0.45% strain, interlayer coupling is dominated by the in-plane direction, and the total coupling also favors in-plane alignment. Conversely, under the a+0.8% c-0.48% strain, while the interlayer coupling remains predominantly in-plane, the total coupling favors the out-of-plane direction. Furthermore, we systematically investigated the influence of the strain field on the magnetic anisotropy energy (MAE) of Fe3GaTe2, employing density functional theory (DFT) first-principles calculations. Here, MAE is defined as the energy difference: MAE = E[100] - E[001], where a positive MAE indicates a perpendicular, or out-of-plane, easy axis of magnetization, and a negative MAE signifies an in-plane easy axis. We subjected the Fe3GaTe2 layer to in-plane biaxial tensile strain ranging from 0.6% to 0.8%, mirroring the 0.8% strain implemented in our theoretical model. As shown in Supplementary Fig. 16, our calculations reveal that, at zero strain, the MAE of bulk Fe3GaTe2 is +2.158 meV/atom, and that of single-layer Fe3GaTe2 is +0.354 meV/atom42, both indicating a strong inherent preference for perpendicular magnetization. However, upon application of a +0.8% tensile strain, the MAE of the bulk and monolayer systems decreases to −0.233 meV/atom and −0.58 meV/atom, respectively, signifying a transition in magnetic anisotropy from perpendicular to in-plane.

Strain modulation of magnetic anisotropy in Fe3GaTe2 is a complex interaction between electronic states and magnetic order, involving atomic-scale orbital reconfiguration as well as synergistic responses to exchange interactions. The layered crystal structure of Fe3GaTe2 provides a unique ligand-field environment, where Fe atoms occupy the centers of Te atom octahedra. Consequently, the Fe d-orbitals split into energy levels due to the crystal field, with t2g orbitals (dxy, dxz, dyz) at bottom energies and eg orbitals (dx2-y2, dz2) at higher energies due to increased electron repulsion. As shown in Supplementary Fig. 17, the magnetic moment orientation of the Fe sites in Fe3GaTe2 exhibits anisotropy, with Fe atoms occupying specific lattice sites whose localized coordination environment leads to crystal field splitting, which causes the d-orbital energy level splitting to show anisotropy and affects the magnetic moment orientation. In the absence of strain, out-of-plane lattice contraction (c axis) results in a bottom energy level for dz2 orbitals compared to dx2-y2 orbitals, thermodynamically favoring out-of-plane magnetic anisotropy (MAE > 0). However, applying in-plane biaxial strain alters the energy competition that governs the orientation of the magnetic moment by modulating the d-orbit energy level difference (ΔE). When ΔE falls below 0.1 eV, the energy barrier for in-plane magnetization is significantly reduced, triggering a magnetic anisotropy reorientation (MAE < 0).

Strain significantly affects the magnetic anisotropy energy (MAE) of Fe3GaTe2 by modulating its magnetic exchange interaction. It is shown that under biaxial strain, the magnitude of MAE modulation in monolayer Fe3GaTe2 (−263.8%) is much higher than that of the bulk model (−110.7%), and this difference stems from the competing mechanisms of intra-layer exchange and inter-layer super-exchange. For the monolayer system, strain weakens the orbital hybridization between Fe atoms in the layer by changing the lattice constant (a axis elongation), leading to a decrease in d-orbital occupation, which reduces the perpendicular magnetic anisotropy and contributes to the MAE shift from out-of-plane to in-plane. In contrast, in the block model, the tensile strain induces c axis contraction while elongating the a axis, which significantly enhances the interlayer super-exchange effect, improves the hybridization strength of adjacent Fe atomic orbitals through the compression of the vdW gap, strengthens the perpendicular magnetic coupling and stabilizes the spin orientation. The competitive mechanism within the bulk Fe3GaTe2 results in the interlayer coupling partially counteracting the weakening effect of the intralayer exchange, causing the strain response of the bulk MAE to show a smaller amplitude modulation. Synchrotron X-ray magnetic circular dichroism measurements (XMCD) show that the contribution to the orbital magnetic moment of the Fe1 site increases under strain and is significantly higher than in the unstrained condition43, this enhanced orbital-spin coupling directly modulates the magnetic anisotropy axis orientation. Meanwhile, large biaxial strains (especially compressive strains close to −4% or tensile strains exceeding 1%) trigger significant changes in the MAE of Fe atoms, bringing the system close to the critical point of in-plane magnetization44. And interfacial strains along different in-plane directions trigger the switching of the susceptible magnetization axis. Atom- and orbital-resolved analyses attribute these anisotropic effects to the contributions of Fe-II and Te orbitals, especially the dyz-dz2 and dxz-dz2 orbitals of Fe atoms and the px-pz and py-pz orbitals of Te atoms45. First-principles calculations suggest that stress, including compressive strain, can modify magnetic exchange interactions by altering the spacing between Fe and Ga/Te atoms. In bulk Fe3GaTe2, Ga/Te atoms are antiferromagnetically coupled to Fe atoms, and its weak roving ferromagnetism suggests a significant spin upturn. Compressive strains may further inhibit the strength of the magnetic exchange couplings, leading to a reduction in the localization of the arrangement of the magnetic moments, thus weakening the dominant magnetic anisotropy in the perpendicular direction and promoting the deflection of the susceptibility axis of magnetization40.

In the layered ferromagnetic material Fe3GaTe2, which exhibits perpendicular magnetic anisotropy (PMA), the phenomenon of magnetic polarity reversal is influenced by the interplay between the external magnetic field and the magnetocrystalline anisotropy energy (MAE). The out-of-plane PMA is primarily governed by electron orbital rearrangement and crystal field cleavage effects, which are induced by strong spin-orbit coupling (SOC) at the Fe-Te interface46. When the magnetic field is tilted away from the out-of-plane direction (e.g., θ < 0°), this rotational symmetry breaking leads to a biostability characterized by axial (D) and equatorial (E) dipole configurations. In this scenario, the in-plane component of the external field facilitates a dynamic reorientation of the magnetic moments from the out-of-plane to the in-plane orientation, effectively bottoming the domain-wall pinning potentials47. This reorientation is accompanied by a symmetry reconfiguration of the effective magnetic anisotropy tensor, resulting in a notable enhancement of the in-plane monoclinic anisotropy term48. Concurrently, the SOC-mediated inversion of the Berry curvature in momentum space induces a significant alteration in the topological nature of the energy bands, as evidenced by the sign reversal of the anomalous Hall conductance40. The anomalous Hall conductance is directly dependent on the weight integral of the Berry curvature (σAxyHE = e2/h ∫ BZ Ω(k)f(k)dk, f(k) is the Fermi distribution function), and the reversal of the sign of the anomalous Hall resistivity indicates a change in the direction of the magnetization, corresponding to the inverse sign of the Berry curvature integral49,50. The underlying microscopic mechanism for this phenomenon can be elucidated using the orbital-selective hybridization model. Furthermore, studies on magnetic domain dynamics reveal that the collective motion of domain walls in response to the tilted magnetic field, along with the gradient distribution of local demagnetization field energy, synergistically drives the transition from multi-domain to single-domain states51. Magnetic moment reorientation builds a theoretical framework system for the development of spintronic devices based on critical angle modulation52.

Through systematic experimental studies and theoretical analysis, this study reveals for the first time the dual regulation mechanism of Fe3GaTe2 magnetic materials by P(VDF-TrFE) ferroelectric polymers in heterostructures. The results show that the P(VDF-TrFE) located in the top layer regulates the carrier concentration distribution of Fe3GaTe2 through the ferroelectric polarization effect, while the bottom P(VDF-TrFE) achieves the dual regulation of carrier concentration and magnetic anisotropy axis orientation through the ferroelectric polarization effect and the inverse piezoelectric effect. In order to investigate the dual-gate synergistic modulation mechanism, a systematic voltage application scheme is designed: when −10 V polarization voltage is applied to both the top and bottom P(VDF-TrFE) layers, the synergistic enhancement of the isotropic ferroelectric polarization and the inverse piezoelectric stretching effect occurs (Supplementary Note 6), and the two effects show a significant voltage dependence (Supplementary Note 7); when both 10 V polarization voltages are applied, a synergistic enhancement of the ferroelectric polarization and inverse piezoelectric compression effect occurs (Supplementary Note 8). Notably, when the polarization voltages are applied to the top and bottom P(VDF-TrFE) layers with opposite polarity (V1/V2 = −10 V/10 V and 10 V/−10 V), the system exhibits a special coupling of ferroelectric competition with piezoelectric deformation competition (Supplementary Note 9). In addition, the properties of the ferromagnet Fe3GaTe2 and the organic P(VDF-TrFE) are closely related to the temperature, and the changes in the performance of the dual-gate device by applying different temperatures are shown in Supplementary Note 10. By optimizing the process parameters, a complete preparation scheme was ultimately obtained, controlling the differences in coercive field, Hall resistance, and switching voltage of the device within a fluctuation range of 5–10% (Supplementary Fig. 25). The dual-gate synergistic regulation system constructed in this work breaks through the functional limitation of the traditional single-gate device, and realizes a multidimensional parameter regulation space through the coupling of multi-physical fields. This breakthrough design not only provides a paradigm for the development of polymorphic non-volatile memory devices and reconfigurable spintronic devices.

Programmable logic operation of spin logic devices
Based on the above regulation principle, the device system can realize a multi-dimensional logic operation system through two modes: in-plane magnetization and out-plane magnetization. Compared to conventional single-axis magnetization devices, the dual-mode magnetization architecture greatly extends the coverage of logic operations with both in-plane and out-of-plane magnetization modes. It is noteworthy that the in-plane magnetization system using Fe3GaTe2/P(VDF-TrFE) heterostructure shows unique spin logic complementary characteristics, through the orthogonal coupling of spin orientation in the ferromagnetic layer and the synergistic regulation of the strain field in the piezoelectric layer, the complementary conversion of logic states can be realized in a single device, and this symmetric structure not only enhances the stability of the operation, but also significantly reduces the error code in the signal transmission by the spin polarization compensation effect. This symmetric structure not only enhances the arithmetic stability, but also significantly reduces the BER in signal transmission through the spin-polarization compensation effect. For the out-of-plane magnetization mode, the device exhibits excellent reconfigurable computing capability by constructing a dual-gate P(VDF-TrFE)/Fe3GaTe2/P(VDF-TrFE) heterostructure. The ferroelectric polarization generated by the dual-gate structure can independently modulate the strength of the out-of-plane magnetization vector, which, combined with the dynamic modulation of magnetic anisotropy by the anisotropic strain of the piezoelectric material, enables a single device to reconfigure complex and different logic functions, such as NAND, NOR, XOR, etc., in accordance with the combination of different gate pressures in real time. This hardware-level dynamic programmability breaks through the limitations of traditional logic devices in terms of function curing and provides a physical basis for adaptive computing architectures. In particular, it should be pointed out that both magnetization modes adopt an all-electric manipulation mechanism, which utilizes the piezoelectric and inverse piezoelectric effects of P(VDF-TrFE) to generate a non-volatile regulation of the magnetization state, resulting in a reduced energy consumption as compared to current-driven methods based on spin transfer moments or orbital moments. Specifically, as illustrated in the Supplementary Fig 28, the device maintains its properties for 120 hours following voltage polarization and subsequent removal of the electric field. Based on the concept of ultra-low power consumption, the single-operation power consumption of the bottom-gate device Fe3GaTe2/P(VDF-TrFE) is half that of the device. Therefore, the bottom-gate device was used in the demonstration, while the demonstration of the device was included in the supplementary information. This low power consumption feature combined with a scalable heterostructure preparation process provides an innovative solution for the development of energy-efficient storage-computing integrated systems.

The in-plane magnetization system based on Fe3GaTe2/P(VDF-TrFE) heterostructure is demonstrated first. Figure 3a shows a schematic of the logic devices in a Fe3GaTe2/P(VDF-TrFE)-based memory with two separate input terminals. Two input signals (denoted by V1 and V2) are fed into the P(VDF-TrFE) layer, and one control signal (denoted by IIN) is fed into the Fe3GaTe2 layer (spin logic devices A and B) for deterministic inversion of perpendicular magnetization in Fe3GaTe2 via strain-induced deflection control of the susceptibility axis of the magnetization in the P(VDF-TrFE). Therefore, it can be used to realize different logic functions (i.e., AND, NAND, NOT). The operation of the spin logic device is given in Fig. 3b, where we define the positive values of the inputs (V1 = 10 V, V2 = 10 V) as digital inputs “1” and their negative values (V1 = −10 V, V2 = −10 V) as digital inputs “0”. These inputs determine the outputs of the spin logic device, which are monitored by measuring the sum of the anomalous Hall resistor Hall resistors (Rout = Rxy,A + Rxy,B). To describe the logic operation, we define the reference value of the magnetization of the two devices Rref = (Rxy,A + Rxy,B)/2. The NOT gate can be implemented by flowing two voltages (V1 = V2) in the same direction (the implementation of the NOT gate is independent of the initial memory state), where UP magnetization (Rout > 0) corresponds to the digital output “1”, and DOWN magnetization (Rout < 0) is equivalent to the digital output “0”, and the truth table is shown in Fig. 3c.

Next demonstrated is an XOR gate fabricated based on two Fe3GaTe2/P(VDF-TrFE) heterostructure devices. The devices were fed with a current of IIN and magnetized using an in-plane magnetic field (θH = 0°). The connection diagrams of devices A and B are shown in Supplementary Fig. 29a. Before the demonstration, the device was processed using the V1/V2 input (00), at which time the overall magnetization state of the device was mz = 0, corresponding to the value of the anomalous Hall resistor: Rout = Rref, which corresponds to the digital output “0” (Supplementary Fig. 29b). Only when V1 ≠ V2, the overall magnetization state of the device is mz = 1, Rout ≠ Rref, corresponding to the digital output “1”; while V1 = V2, the overall magnetization state of the device is mz = 0, Rout = Rref, corresponding to the digital output “0”. The truth table is shown in Supplementary Fig. 29c, demonstrating a typical XOR operation. Demonstration of reconfigurable logic operations in out-of-plane magnetization mode (θH = 90°) is shown in Supplementary Notes 11 and 12.

The system-level implementation of higher-order logic operation functions can be realized through a multi-device co-integration strategy. In this study, a circuit implementation scheme of a half adder (SLHA) based on the Spin Logic Complementary Architecture (SLCA) is successfully verified. As the basic building block of digital multipliers, the standard half adder (HA) consists of an iso-or gate (XOR) and an and gate (AND) to form the core of Boolean algebra operations, and its topology strictly satisfies: HA(A, B) = (SUM, CARRY). The SLHA operation in in-plane mode (θH = 0°) is shown in Fig. 4a by implementing two heterostructures to form XOR gates (devices A and B) which have outputs of resistors RSUM = Rxy,A + Rxy,B. The other two heterostructures (devices C and D) are used for AND gates with outputs of RCARRY = Rxy,C + Rxy,D. The waveform of the SLHA operation is shown in Fig. 4b, demonstrating the operation of the XOR gate (SUM), which corresponds to the digital output “0” when defining the system mz = 0, and to the digital output “1” when defining the system mz = 1. Here, the positive input values of V1 and V2 (10 V) indicate the digital input “1”; the negative input value (−10 V) indicates “0”. When the two inputs have different signs, device A or device B is switched, resulting in RSUM ≠ Rref and thus digital output “1”. Otherwise, RSUM remains the same as the initial state, resulting in a digital output of “0”. In addition, the operation of the CARRY instruction is performed by device C and device D. The definition of RCARRY > Rref corresponds to the digital output “0”, and the definition of RCARRY < Rref corresponds to the digital output “1” (Rref = (Rxy,C + Rxy,D)/2). When both V1 and V2 inputs are “1”, RCARRY is switched, resulting in a digital output of “1”. The operation of the SLHA device is summarized in the truth table of Fig. 4c (Supplementary Table. 1). The SLHA operation in the out-of-plane magnetization mode (θH = 90°) is described in Supplementary Note 13.

As shown in Fig. 4b, multiferroic logic devices based on spin-transfer torque or piezoelectric strain co-regulation mechanisms exhibit breakthrough advantages in key performance parameters such as write time and energy consumption53–79. The multiferroic logic architecture generally exhibits better write speed and energy-efficiency characteristics compared with typical spin-transfer-torque (STT) and spin-orbit-torque (SOT) devices. Specifically, the novel devices proposed in this study achieve ultra-low operating energy consumption of 0.5 aJ and subthreshold write cycles of 5 ns (detailed parameters see Supplementary Table. 10 and 11). This remarkable performance advantage mainly stems from the enhanced effect of magnetic moment flip dynamics under multi-physics field coupling and the strain-mediated magnetic anisotropy modulation mechanism. The experimental data not only verify the technical superiority of multiferroic heterostructures in nonvolatile memory devices, but more importantly, the results of this study provide an important theoretical basis for the efficient design and performance optimization of spintronic devices.

This study addresses the intrinsic limitations of conventional complementary metal-oxide-semiconductor (CMOS) technology to develop innovative breakthroughs. The realization of traditional logic devices relies on the complementary stacking of N-type and P-type MOSFETs to realize the logic function by carrier types (electrons and holes), which, however, brings about problems such as doping process and material compatibility, and greatly increases the fabrication complexity80. The novel spintronic logic device proposed in this study fundamentally breaks the dependence on semiconductor doping type of conventional CMOS technology by innovatively adopting a ferroelectric/inverse piezoelectric coupling heterostructure architecture. The device does not need to distinguish between N-type and P-type materials, and is therefore universal. The core innovation lies in the construction of a vertical heterostructure with dual gates, which utilizes the synergistic regulation mechanism of the non-volatile polarization of ferroelectric materials and the inverse piezoelectric effect. The control of ferromagnetism by electric field enables complete Boolean logic operations such as AND to be realized in any carrier system. Meanwhile, in terms of process compatibility, spin-coating and van der Waals mechanical exfoliation techniques are used to construct the heterostructure system, which circumvents complex doping processes such as ion implantation and oxidization, and achieves seamless compatibility with the current CMOS process nodes, significantly reducing the integration and manufacturing costs81. Thanks to the intrinsic van der Waals interface properties of 2D ferromagnetic materials, the device interface forms a spontaneous chemical passivation layer, which effectively inhibits interfacial diffusion and oxidation reactions, resulting in improved wafer-level fabrication yields and more stable device performance.

Fe3GaTe2/P(VDF-TrFE) integration for binary classification
A multiferroic FeGaTe/P (VDF-TrFE) device based on reconfigurable functionality is used to demonstrate the proof of the binary classification principle. An analogue neural network system based on a transimpedance amplifier (TIA) with a hardware structure of “Transimpedance Amplifier (TIA) + Comparator” was simulated with the aim of verifying the feasibility of implementing machine learning algorithms using analog circuits (see Supplementary Note 14 for the core principles and other information). The input four-pixel × four-pixel patterns for the letter’s “W”, “H”, and “U” were labeled as class 1, and the input four-pixel × four-pixel patterns for the digits “1”, “3”, and “2” were labeled as class 0 (six randomly selected patterns are illustrated in Fig. 5a). The multiferroic device output resistance (Rxy) handles the nonlinear output with a reference resistance of Rref, which is similar to the S-shaped function (Fig. 5b). The computational schematic is shown in Fig. 5c, where the pixels are encoded as 16 input voltages to calculate the weighted average current in a transimpedance amplifier (TIA) that converts the weighted average current to a voltage output, with weighting achieved by adjusting the current magnitude, and a feedback resistor (R0) of 10 megohms to control the amplification gain. The voltage output from the TIA is compared to a reference voltage (Vref = 1.5 V), and the output is approximated by a Sigmoid function for nonlinear activation, with outputs greater than 0.5 determined to be class “1”, and those less than 0.5 determined to be class “0”. Figure 5 elucidates the pattern labels and predicted categories in the simulation and the experiment, and the similarity among the three plots indicates that the system is able to classify well and maintains its stability even in a noisy experimental environment and maintains stability. The average score (V) accuracy and cost of the training process for categories “0” and “1” in simulation and experiment are shown in Fig. 5e–g. The ROC curves and AUC values of the simulation and experimental models are analyzed in Fig. 5h, which shows that the models maintain stable performance under different decision thresholds, and the steep curve shapes indicate that the models and high AUC values prove that the system has a good ability to discriminate between the two categories of modes, demonstrating excellent generalization ability and robustness. In the model performance evaluation section, we systematically analyze the classification effect through visualization methods. The Simulated confusion matrix and Experimental confusion matrix presented in Fig. 5i show that the model exhibits excellent classification performance on both types of samples.

Methods
Preparation of samples
P(VDF-TrFE) powder for the ferroelectric layer in multiferroic heterostructures was purchased at Arkema with a molar ratio of 70/30. 0.5 g of P(VDF-TrFE) powder and 10 ml of N,N-dimethylformamide (DNF) or dimethyl sulfoxide (DMSO) were mixed under anhydrous conditions to obtain a homogeneous P(VDF-TrFE) solution and stirred using a magnetic stirrer at 300 rpm for 12 h. Excess air bubbles were removed using an evacuation machine. The sample of ferromagnet Fe3GaTe2 in multiferroic heterostructure was obtained by mechanical exfoliation of bulk Fe3GaTe2 crystals on SiO2/Si substrate, the thickness was initially determined by observing the optical comparison of the exfoliated sample with the substrate under an optical microscope, and the thickness was confirmed to be 12 nm by AFM (Dimension, ICON). The samples and the solutions were prepared and stored in an environment with oxygen and moisture content below 0.1 ppm in a glove box.

Dual-gate device construction
Electrodes were drawn on a 300 nm silicon oxide-coated silicon substrate using a photolithography machine (ATS-07-UV, Litho), and Cr (5 nm)/Au (50 nm) electrodes were evaporated using electron beam evaporation. The ferroelectric layer P(VDF-TrFE) was spin-coated using a spin coater (EZ4-S), and the coating was rotated at 5000 rpm for 30 s to obtain a 10 nm thick ferroelectric layer. After drying at 70 °C for 1 h, it was then annealed at 130 °C in a vacuum environment for 10 h for crystallinity. Selected FeGaTe samples were transferred onto spin-coated P(VDF-TrFE) gold-plated substrates by the PPMS thermal transfer method, and specific Hall device mask plates were mounted on the FeGaTe samples under a microscope, and the Cr (5 nm)/Au (50 nm) electrodes were prepared into Hall devices by evaporation using electron beam evaporation, and the electrodes were leaded out using a silver paste and a gold wire. The ferroelectric layer P(VDF-TrFE) was spin-coated using a spin coater (EZ4-S), and the coating was rotated at 3000 rpm for 30 s to obtain a 10 nm thick ferroelectric layer. After drying at 70 °C for 1 h, the layer was then annealed at 130 °C for 10 h in a vacuum environment for crystallinity treatment. After annealing, point electrodes were drawn on the ferroelectric layer, and Cr (5 nm)/Au (50 nm) electrodes were evaporated using electron beam evaporation, and the electrodes were led out using silver paste and gold wire.

Characterization of dual-gate devices
Optical microscopy and atomic force microscopy (AFM, Dimension ICON) were used to measure the thickness and surface morphology of FeGaTe nanosheets and P(VDF-TrFE), X-ray diffractometry (XRD, SmartLab-3kW) was used to characterize the crystal structure, and Raman spectroscopy (LabRAM Odyssey) was used to characterize the phonon modes of the devices. The multiferroic devices were sectioned using the focused ion beam (FIB, Thermo Fisher Scientific Nicolet iS20) slicing technique, and field emission transmission electron spectroscopy (TEM, JEOL F200) was used to study the cross-section microstructure.

Magnetic testing of dual-gate devices
In testing, a variable temperature environment and a constant magnetic field of ±5 T were applied to the devices using a Physical Properties Measurement System (PPMS, DynaCool, Quantum Design) system, which, by rotating the sample stage, allows the magnetic field to be applied in either an in-plane or out-of-plane direction along the device. In a logic demonstration, to characterize the magnetization state, the input current was first applied to the device using a Keithley 6221 current source meter, a Keithley 2182A nanovoltmeter was used to measure the transverse voltage between the devices, and two Keithley 2400 voltmeters were used to apply different states of the polarization voltage pulses to the top and bottom layers of the P(VDF-TrFE) to perform field scanning anomalous Hall effect measurements.

First-principles calculations
Density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP)82,83, employing the projector augmented-wave (PAW) method. The generalized gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof (PBE) was utilized for the exchange-correlation functional, and a plane-wave cutoff energy of 550 eV was set84. To accurately describe spin-orbit coupling, complete relativistic effects were included. Furthermore, to optimize the description of correlated interactions, a Hubbard U correction (Ueff = 4 eV) was applied to the Fe d-orbitals; this parameter was chosen to yield the best agreement between calculated magnetic states and experimental data85,86. The energy convergence criterion for the self-consistent solution of the Kohn-Sham equations was set to 10−7 eV. Brillouin zone sampling was performed using the Monkhorst-Pack scheme, ensuring a resolution better than 0.02 Å−187. All structures were fully relaxed until the Hellmann-Feynman forces on each atom converged to below 0.02 eV/Å. The atomic model of Fe3GaTe2 was constructed using VESTA88.

Binary classification simulation
The system adopts the hardware structure of “Transimpedance Amplifier (TIA) + Comparator”, and uses 4 × 4-pixel miniature patterns as inputs, totaling 16 dimensional vectors. Class “0”: numeric patterns (“1”, “3”, “2”); Class “1”: alphabetic patterns (“W”, “H”, “U”). The input current (weighted sum of pixel values and weights) is converted to a voltage by a transimpedance amplifier (TIA), and a comparator compares the TIA output voltage to a reference voltage (Vref), which is used to output a binary result. The input pattern (16 dimensions) is multiplied with 16 trainable weights, and the sum of its product is used as the input current, which is converted to voltage by the TIA (Voltage = Current × Feedback Resistor R0), and then the voltage is compared with Vref through the Comparator or processed by the Sigmoid function, and the final output is greater than 0.5 to be judged as Class “1”, and less than 0.5 to be judged as Class “0”. The batch gradient descent method is used to update the 16 weights, the goal is to minimize the binary cross-entropy loss function, while the weights are updated in the simulation taking into account the effect of the feedback resistor R0.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors propose a scalable and energy-efficient logic technology strategy that surpasses conventional CMOS, leveraging vertically integrated 2D van der Waals multiferroic heterostructures composed of 2D Fe3GaTe2/P(VDF-TrFE) implementing logic gates-Since CMOS are producing billions of devices integrated in a single small chip, here there is no report about the number of devices and their reproductivity. The reproducibility is low because the vdW material is obtained by mechanical exfoliation. So, the surpassing of CMOS is simply untrue. -Moreover, the input voltage in the logic device puleses of amplitude of plusminus 10 V are used which are much higher than the amplitude of pulses used in CMOS digital circuits,soalso the idea of low-power devices is lost. -Since magnetic fields are used to tune electrical resistance ,this fact will be never used toimplement digital devices because the presence of a magnet in an electronic circuits will make it bulky will the aim is to reduce the dimensions of any electronic circuit. Due to these issues , the manuscript is rejected outright.", "reviewer_2": "The manuscript by Cai et al. reports that development of multiferroic vdW heterostructures by integrating two-dimensional ferromagnetic Fe3GaTe2 with ferroelectric P(VDF-TrFE). The coupling between ferroelectric polarization and strain enables tunable modification of magnetic properties. The scope of this work aligns well the aim of Nature Communications, and is expected to attract broad interest across materials science and logic in memory community. Therefore, I would recommend publication in Nature Communications, after the authors addressing some comments listed below. 1. The author claims that atomically sharp interface of P(VDF-TrFE) and Fe3GaTe2 interface reduces interfacial scattering. Can the authors provide experimental evidence to prove high-quality, atomically sharp nature of the interface? 2. The author attributes the modulation of Fe2GaTe2 magnetism to strain transferred via the inverse piezoelectric effect of P(VDF-TrFE). How do the authors distinguish charge-mediated mechanisms, such as electrostatic doping or interfacial electric field effects, as dominant factors? 3. P(VDF-TrFE) is a soft polymer. How did the author confirm efficient mechanical strain transfer to the Fe3GaTe2 layer through vdW interface? Can the author provide any experimental evidence of this? 4. In the multi-device logic array demonstrations (AND/NAND/NOT/half-adder), what is the device-to-device variability in coercivity, Hall resistance, or switching voltage? How reproducible are the operations across cycles or fabrication batches? 5. The author suggests, unlike conventional heterostructure devices suffering from lattice mismatch-induced interfacial defects, the van der Waals interface offers enhanced thermal stability. Have the authors quantitatively evaluated how device performance (e.g., AHE, coercivity, strain sensitivity) changes with temperature, particularly across the ferroelectric Curie temperature or near the upper limits of operational range?", "reviewer_3": "This manuscript reports a dual-gated Fe₃GaTe₂/P(VDF-TrFE) heterostructure with voltage-controlled modulation of magnetic properties and demonstration of spin-based logic functionality. While the subject falls within the general interest of multiferroic 2D devices, I have serious concerns regarding the novelty of the work, the clarity of the physical mechanisms involved, and the scientific rigor of the data interpretation. Based on the issues outlined below, I do not recommend publication of the manuscript. Below are my detailed comments: 1. This manuscript lacks novelty. The magnetic properties of Fe3GaTe2, such as perpendicular magnetic anisotropy and the anomalous Hall effect, have already been thoroughly investigated (for example doi.org/10.1038/s41467-022-32605-5). There is no need to revisit these aspects without offering new understanding. Moreover, the use of PVDF gating to modulate the magnetism of Fe3GaTe2 has already been explored in previous publications by the authors and their collaborators (doi.org/10.1038/s41467-025-62159-1). In this manuscript, the only potentially novel aspect is the use of a dual-gate configuration. However, this part is not clearly explained in the manuscript, and the physical mechanism behind it is not convincingly discussed. I find this unsatisfactory. The authors should reorganize the manuscript, remove results that are already known or unrelated, and focus on articulating the genuinely new contribution of this work. Only after establishing the novelty and underlying physics should the logic gate demonstrations be presented as outcomes of the new device structure. 2. The PVDF layers used in the device are spin-coated, which typically leads to lower crystallinity and weaker chain alignment compared to more controlled methods such as Langmuir-Blodgett techniques. However, the manuscript does not mention any post-deposition annealing or provide structural characterization data such as AFM or XRD. Given that the claimed device functionality relies heavily on the ferroelectric and piezoelectric properties of PVDF, the authors should include direct evidence supporting its crystallinity, beta-phase content, and ferroelectricity either in the main text discussion or in the supplementary materials. Measurements such as P–E loops, PFM, or other relevant characterizations are necessary to validate these properties. Without such evidence, the fundamental basis for the proposed mechanism remains unconfirmed. Further, according to the device setting, the electric field on the PVDF is as large as 10MV/cm, we suggest the author check the P-E loops to confirm the integrity of the material. 3. The anisotropy constant Ku and the modeling shown in Fig. 1c are not accompanied by any explanation of the fitting or calculation method. Since similar results have already been reported in the literature, this part does not represent a novel contribution. I suggest moving these data to the Supplementary Material. However, if the authors choose to keep them in the main text, they should include a clear and quantitative description of how Ku is extracted. Without such explanation, the figure lacks reproducibility and interpretive value. 4. I have serious concerns about the discussion of the topological Hall effect (THE) in lines 178–195. Based on the experimental data provided, I do not see convincing evidence of THE. The characteristic non-monotonic features, such as a peak or dip in the Hall resistance, are not clearly present. The monotonic decrease after magnetic flipping is more likely due to spin canting rather than the emergence of a topological contribution. Despite this, the authors devote substantial space to speculating about THE without providing any supporting evidence such as magnetic imaging, for example as shown in DOI: 10.1002/adma.202403154. This weakens the clarity of the manuscript and risks misleading readers. Moreover, the citation of Ref. 26 (doi.org/10.1038/s41467-022-32605-5) to support the presence of THE in Fe₃GaTe₂ is inappropriate, as this reference does not discuss THE in that system. I strongly recommend the authors revise this section thoroughly and reconsider the interpretation presented. 5. The authors propose that the bottom PVDF layer contributes both doping and strain, while the top PVDF layer contributes only doping. This asymmetry is used to explain the more pronounced effect of the bottom gate. However, the physical origin of this asymmetry is not clearly justified. It is unclear why the top PVDF layer would not also generate strain through the same inverse piezoelectric mechanism. The manuscript should provide a more detailed and mechanistic explanation for this asymmetry. 6. Moreover, I wonder whether the observed modulation is simply doping-driven rather than resulting from ferroelectric polarization. In the presented data, all responses to gate voltage, whether from the top or bottom PVDF layer, appear continuous and do not show any signature of abrupt switching or hysteresis that is typically associated with ferroelectric behavior. This could be because the applied gate voltages are much larger than the coercive voltage of PVDF, which may suppress the characteristic ferroelectric response. The authors should examine this carefully. Without such analysis, I have reason to suspect that similar modulation could be achieved using two non-ferroelectric dielectric layers, such as hBN and SiO2, through electrostatic doping alone. This possibility needs to be ruled out before drawing any conclusions about polarization-driven effects. 7. In lines 123–127, the authors cite Ref. 17 to support a mechanism involving C–F dipole coupling with Te lone pairs and spin-state reconfiguration of Fe atoms. However, Ref. 17 discusses PVDF/PAN/CNT composites and their bulk electrical conductivity, and is entirely unrelated to Fe3GaTe2 interfaces or d-orbital physics. This citation is inappropriate and misleading. The authors should replace or remove it and ensure that all references are directly relevant to the claims being made. 8. When building the spin logic devices, the author constructed the Fe3GaTe2/P(VDF-TrFE) bilayer rather than the discussed P(VDF-TrFE)/Fe3GaTe2/P(VDF-TrFE) trilayer system before, which causes inconsistency of the work. 9. How is Ref. 19 (DOI: 10.1038/s41467-021-26271-2), a paper related to breast cancer, cited in this 2D materials paper? 10. Figure 1b is never referenced in the main text. It is possible that there is a typo or omission around line 163 where it was intended to be mentioned. 11. In the script, the author call \\Theta_H=90 as perpendicular direction and \\Theta_H=0 as in plane direction. This is contradictory to the fig. 1c inset."}, "author_response": "We thank all the reviewers for positive recommendation and valuable comments regarding our research paper. Each of your insights have served to strengthen our manuscript. We have carefully revised the manuscript according to your constructive suggestions. Provided below is our detailed response to each comment raised. Reviewer #1: Main Comment. The authors propose a scalable and energy-efficient logic technology strategy that surpasses conventional CMOS, leveraging vertically integrated 2D van der Waals multiferroic heterostructures composed of 2D Fe3GaTe2/P(VDF-TrFE) implementing logic gates-Since CMOS are producing billions of devices integrated in a single small chip, here there is no report about the number of devices and their reproductivity. The reproducibility is low because the vdW material is obtained by mechanical exfoliation. So, the surpassing of CMOS is simply untrue. -Moreover, the input voltage in the logic device puleses of amplitude of plus minus 10 V are used which are much higher than the amplitude of pulses used in CMOS digital circuits, so also the idea of low-power devices is lost. -Since magnetic fields are used to tune electrical resistance, this fact will be never used to implement digital devices because the presence of a magnet in an electronic circuit will make it bulky will the aim is to reduce the dimensions of any electronic circuit. Due to these issues, the manuscript is rejected outright. Response. We have addressed the reviewers' comments. Below, we will respond in detail to the reviewers' feedback. Comment 1. The authors propose a scalable and energy-efficient logic technology strategy that surpasses conventional CMOS, leveraging vertically integrated 2D van der Waals multiferroic heterostructures composed of 2D Fe3GaTe2/P(VDF-TrFE) implementing logic gates-Since CMOS are producing billions of devices integrated in a single small chip, here there is no report about the number of devices and their reproductivity. The reproducibility is low because the vdW material is obtained by mechanical exfoliation. So, the surpassing of CMOS is simply untrue. Response 1: We appreciate the reviewers' insightful feedback and acknowledge their concerns regarding device quantity, reproducibility, and the current technological maturity of our approach. The paper focuses on innovative strategies and a novel prototype of an original device, rather than industrial manufacturing, aiming to address key scientific challenges such as high-power dissipation and the separation between storage and computation in the post-Moore era. It seeks to establish a foundation for groundbreaking advancements in compute-in-memory architectures that transcend the limitations of conventional von Neumann computing. Mechanical exfoliation was widely employed in two-dimensional material research for property exploration and proof-of-concept demonstrations of innovative strategies and novel device prototypes (Nature 2025, 641, 70-75; Nat. Electron. 2025, 8, 235-243; Nat. Mater. 2018, 17, 908-914; Nat. Synth. 2025, 4, 106-115). The central aim of this work is to introduce and validate a novel logic technology strategy predicated on the vertical stacking of two-dimensional van der Waals multiferroic heterostructures (e.g., Fe GaTe /P(VDF-TrFE)) to achieve ferroelectric-ferromagnetic coupling. Our primary objective is to explore, at a fundamental level, the potential for transcending the limitations inherent in CMOS technology. Previous research has proposed multiple low-power strategies based on mechanical exfoliation to address the limitations of CMOS technology, thereby laying the groundwork for the continued advancement of semiconductor devices. (Science 2019, 363, 6428; Nat. Electron. 2019, 2, 274-283; Nat. Commun. 2024, 15, 1902; Adv. Mater. 2025, 37, 2413916; Adv. Funct. Mater. 2023, 33, 2212722). While scalable preparation techniques such as chemical vapor deposition (CVD) and molecular beam epitaxy (MBE) have been developed in the industry, the focus of this work lies in validating the feasibility of the device prototype. While our current prototypes rely on mechanical exfoliation, we contend that the scalability of this strategy is not fundamentally restricted. Wafer-level two-dimensional material CVD growth, large-area fabrication of ferroelectric polymers, and advanced van der Waals integration technologies have demonstrated viable routes toward scalable implementation. Previous studies have explored the feasibility of using chemical vapour deposition (CVD) technology to achieve large-area preparation of iron gallium telluride (Fe GaTe ). (Mater. Sci. 2025, arXiv:2505.06128). Addressing key scientific challenges related to large-scale production, such as material preparation and the development of novel integration strategies, will be the next step following this foundational study(Nat. Commun. 2025, 16, 3691; Nat. Commun. 2025, 16, 3448; Nat. Commun. 2025, 16, 7305). The resulting reconfigurable spin-in-logic devices demonstrate outstanding performance characteristics, including ultra-low single-operation energy consumption (0.5 aJ), nanosecond-level write speeds (5 ns), and highly stable logic gate arrays (AND/NAND/NOT) and half-adder circuits. This work has demonstrated innovative strategies and a novel prototype of an original device within spin-in-logic architectures that transcend the limitations of conventional von Neumann computing. Comment 2. Moreover, the input voltage in the logic device puleses of amplitude of plus minus 10 V are used which are much higher than the amplitude of pulses used in CMOS digital circuits, so also the idea of low-power devices is lost. Response 2: We appreciate the insightful observation regarding the working voltage amplitude and acknowledge the potential impact on the perception of \"low-power\" operation. The current test voltage of ±10 V, exceeding standard CMOS levels, was primarily employed to ensure robust signals and reliable switching behavior during this initial phase of validating the Fe GaTe /P(VDF-TrFE) heterostructure's logic and coupling effects. Critically, this voltage level does not represent a fundamental material or physical limitation of the device; as demonstrated in Figure R1, reversal is achievable at substantially bottom voltages (±2 V). This achievement is attributed to the ultra-fast ferroelectric switching polarization reversal speed, inherent non-volatility, and the ultra-low current density characteristic of P(VDF-TrFE). The present higher voltage is thus a consequence of our experimental verification strategy. The core of our proposed \"low-power\" concept rests on two key attributes: non-volatility, utilizing ferroelectric/ferromagnetic states for data retention and eliminating static power consumption, thereby addressing a critical limitation of CMOS technology; and the potential for minimized dynamic power consumption, with demonstrated operating currents in the picoampere range and the requirement of only nanosecond-level pulses, resulting in low instantaneous power consumption and the absence of steady-state power dissipation. Figure R1 The bottom P(VDF-TrFE) layer is subjected to positive voltage polarization(a) and negative voltage polarization(b) driven magnetic modulation at an in-plane magnetic field (θ = 0°). H Static power consumption refers to the power consumed when a device is in a steady state (no operation). In traditional CMOS technology, static power consumption is mainly caused by leakage current, with the formula: Where: V is the operating voltage, an𝑃d𝑠𝑡 𝑎I 𝑡i𝑖s𝑐 t=he𝑉 le∗ak𝐼𝑙a𝑒g𝑎e𝑘 𝑎c𝑔u𝑒rrent. Due to the non-volatile nature of ferroelectric polarization, information is stored in the stable state of ferroelectric/ferromagnetic materials, and no power supply is required to maintain this state, resulting in zero leakage current (I = 0 A). Substituting into the formula: leakage Therefore, static power consumptio𝑃n𝑠 i𝑡s𝑎 𝑡z𝑖𝑐er=o. 𝑉∗0=0 𝑊 Dynamic power consumption occurs during dynamic operations (such as applying pulses for read/write operations) and is primarily caused by transient currents. Dynamic power is the product of voltage and operating current, and dynamic power consumption is determined by power and operating time(V= 10 V, I= 1*10-11 A). Since dynamic operations only requi𝑃r𝑑e𝑦 n𝑛𝑎a𝑚no𝑖𝑐se=co𝑉nd∗-l𝐼evel pulse drive (t = 5 ns), the energy consumed by each pulse is: As shown in Table R1, this is a param𝐸et=er 𝑃ch∗ar𝑡t =for0 t.h5e 𝑎 d𝐽evice. Table R1 Parameters of Fe GaTe /P(VDF-TrFE) heterostructure devices 3 2 Parameter Device 1 Device 2 Device 3 Device 4 Polarization voltage 90 V 60 V 30 V 10 V Electrical resistivity 1.07*1010Ω*m 1.03*1010Ω*m 1.05*1010Ω*m 1.01*1010Ω*m Thicknesses 40 nm 30 nm 20 nm 10 nm Electrode area 100 μm2 100 μm2 100 μm2 100 μm2 Magnitude of 2.25*10-11A 2*10-11A 1.5*10-11A 1*10-11A electric current Write time 5 ns 5 ns 5 ns 5 ns Power wastage 10.125 aJ 6 aJ 2.25 aJ 0.5 aJ In conclusion, while the current prototype utilizes a comparatively high-test voltage, grounded in clear physical principles governing ferroelectric thin films and coercive voltage, and supported by feasible technical pathways, we possess both the confidence and a concrete plan to optimize the operating voltage to levels consistent with low-power objectives. The inherent zero static power consumption afforded by non-volatility represents a fundamental advantage of this technological approach, unaffected by the current voltage level. Following voltage optimization, dynamic power consumption will be significantly curtailed, ultimately leading to a significant improvement in overall energy efficiency. Comment 3. Since magnetic fields are used to tune electrical resistance, this fact will be never used to implement digital devices because the presence of a magnet in an electronic circuit will make it bulky will the aim is to reduce the dimensions of any electronic circuit. Response 3: The operation mechanism of this device is based on electric field coupling, which is driven exclusively by an electric field rather than a magnetic field. Logical operations are entirely performed through electric pulses. By inducing polarization reversal in the P(VDF-TrFE) ferroelectric layer, the magnetic moment of Fe GaTe can be modulated via ferroelectric polarization and strain control, thereby tuning the device resistance (see Figures 3 and 4 in the main text). The external magnetic field is only required for initial setup—it serves solely to define the initial magnetization direction (analogous to the write field in MRAM) and is not applied during device operation. Modern magnetoelectronics and advancements in low-dimensional materials science have enabled significant progress in addressing the size limitations of traditional electromagnetic devices. In the proposed heterostructure, magnetism is inherent to the integrated two-dimensional ferromagnetic Fe GaTe layer, which is only a few to several dozen atomic layers (nanoscale) in thickness. This ultrathin magnetic layer functions as an integrated 'magnet,' vertically stacked within the nanoscale heterostructure alongside ferroelectric layers and electrodes, rather than existing as a discrete, macroscopic magnetic component. The magnetic field required for resistance control is generated by this integrated ultrathin ferromagnetic layer within the heterostructure, representing a highly localized phenomenon confined to the nanoscale region near the interface. Consequently, the entire device structure, including the magnetic components, can be fabricated at the micrometer scale or even smaller using advanced nanomanufacturing techniques. This van der Waals heterostructure strategy of vertically stacking two-dimensional materials effectively enhances functional density and integration per unit area, resulting in highly compact units containing magnetic layers. The successful commercialization of modern spin-electronic storage devices, such as STT-MRAM or SOT-MRAM based on magnetic tunnel junctions, integrated into CMOS processes at 22nm, 12nm, and more advanced nodes provides compelling evidence of this trend. The core of these storage units also incorporates nanoscale ferromagnetic layers (typically alloy films such as CoFeB, with thicknesses of only 1-2 nanometers), where the magnetic moment is switched using the torque generated by spin-polarized current, rather than an external magnetic field. This clearly demonstrates that magnetic functional components can be highly miniaturized and integrated akin to CMOS logic circuits, thereby meeting the stringent size requirements of modern digital chips. Therefore, the 'bulky' issue often associated with traditional magnetic components is not a primary concern in this context. Our strategy, based on two-dimensional multiferroic heterostructures, leverages magnetism as an intrinsic, nanoscale integrated functional layer with minimal thickness and spatial footprint, while efficiently utilizing space through a vertical stacking architecture. Combined with the ultimate goal of achieving electric field control via multiferroic coupling, this technological approach theoretically possesses the potential to realize high-density, miniaturized digital logic integration. This work is dedicated to exploring and validating the feasibility and unique advantages, such as non-volatility, of this novel integrated magnetoelectric device for logic functionalities. Reviewer #2: Main Comment. The manuscript by Cai et al. reports that development of multiferroic vdW heterostructures by integrating two-dimensional ferromagnetic Fe3GaTe2 with ferroelectric P(VDF-TrFE). The coupling between ferroelectric polarization and strain enables tunable modification of magnetic properties. The scope of this work aligns well the aim of Nature Communications, and is expected to attract broad interest across materials science and logic in memory community. Therefore, I would recommend publication in Nature Communications, after the authors addressing some comments listed below. Response: We greatly appreciate the reviewer for the positive recommendation and valuable comments. We thank the reviewer for the constructive suggestions that are important for the improvement of the manuscript. We have addressed the reviewer’s suggestion in the following and in the revised manuscript. Comment 1. The author claims that atomically sharp interface of P(VDF-TrFE) and Fe3GaTe2 interface reduces interfacial scattering. Can the authors provide experimental evidence to prove high-quality, atomically sharp nature of the interface? Response 1: We are grateful to the reviewers for their insightful feedback. In this study, the integration of a two-dimensional van der Waals material (Fe GaTe ) with an organic polymer (P(VDF-TrFE)) addresses challenges associated with lattice matching, as illustrated in Figure R2. The strong interfacial coupling observed in our device, encompassing both the upper P(VDF-TrFE)/ Fe GaTe and bottom Fe GaTe /P(VDF-TrFE) interfaces, is characteristic of organic-inorganic van der Waals heterostructures. Interface formation in such systems relies primarily on physical adsorption and intermolecular forces, circumventing the need for stringent chemical bonding or precise lattice alignment (Chem. Rev. 2025, 125, 445-520). Furthermore, the incorporation of organic molecules or polymers during the synthesis of two-dimensional materials allows for flexible control of interlayer spacing, effectively accommodating the size of the organic components and mitigating lattice mismatch (Chem. Mater. 2023, 35, 10295-10315; Chem. Soc. Rev. 2020, 49, 6866-6883). Our device fabrication process, involving spin-coating a P(VDF-TrFE) solution onto the Fe GaTe surface followed by annealing, leverages the ability to form large-area periodic structures through solvent control or twisted stacking. These periodicities, exceeding atomic lattice scales, further alleviate constraints imposed by atomic-level lattice matching (Nat. Chem. 2025). The non-crystalline nature of the organic-inorganic interface also facilitates the reduction of dislocation density through the formation of superlattices (Chem. Soc. Rev. 2020, 49, 6866-6883). Finally, the inherent flexibility of the ferroelectric polymer (PVDF-TrFE) chains allows for interfacial deformation, enabling adaptation to the rigid crystal lattice of the inorganic layer via localized bending or segmental reorganization (Chem. Rev. 2025 125, 445-520; Nat. Chem. 2025, 16, 201-209). Figure R2 a, TEM image of the interface between the upper layer P(VDF-TrFE) and Fe GaTe . b, TEM image of the interface between Fe GaTe and the bottom layer P(VDF-TrFE). Comment 2. The author attributes the modulation of Fe2GaTe2 magnetism to strain transferred via the inverse piezoelectric effect of P(VDF-TrFE). How do the authors distinguish charge-mediated mechanisms, such as electrostatic doping or interfacial electric field effects, as dominant factors? Response 2: We extend our sincere gratitude to the reviewers for their insightful suggestions. The primary innovation of this study lies in the manipulation of the Fe GaTe lattice structure via strain engineering, accomplished through the polarization of P(VDF-TrFE). Leveraging the significant piezoelectric and ferroelectric characteristics of P(VDF-TrFE) films, both the induced strain and ferroelectric polarization resulting from gate-voltage application have the potential to influence the electronic properties of Fe GaTe . To disentangle the contributions of these two mechanisms, we fabricated both top-gate and bottom-gate device architectures. In the bottom-gate configuration, P(VDF-TrFE) induces both pronounced strain modulation and ferroelectric polarization modulation under gate voltage. Conversely, in the top-gate configuration, the presence of interfacial shear hysteresis arising from the rigid substrate significantly diminishes device deformation, thereby substantially attenuating stress transfer to the Fe GaTe layer. Consequently, ferroelectric polarization modulation becomes the dominant effect in this configuration, rendering the strain effect negligible. Through a systematic comparison of the performance characteristics of Fe GaTe devices employing both top-gate and bottom-gate configurations, we have effectively achieved a separation of the strain modulation and ferroelectric modulation mechanisms. Figure R3 a, Schematic diagram of polarization strain control and ferroelectric control of the bottom layer P(VDF-TrFE) in a device. b, Schematic diagram of ferroelectric control of the polarization of the top layer P(VDF-TrFE) in a device. The primary mechanism by which the P(VDF-TrFE) layer influences Fe GaTe is through ferroelectric polarization control, with minimal contribution from strain effects. Application of an electric field to reverse the ferroelectric polarization generates bound charges within the P(VDF-TrFE) layer. These charges, through short-range Coulombic interactions, induce a redistribution of charge carriers at the Fe GaTe interface. This charge transfer directly modulates the Fermi level position within Fe GaTe , thereby affecting its electronic filling state. This interfacial charge transfer, a well-established mechanism in multiferroic heterostructures, facilitates magnetoelectric coupling whereby alterations in carrier concentration controlled by ferroelectric polarization reconfigure the magnetic properties, enabling non-volatile magnetic switching (ACS Nano 2018, 12, 9558-9567; Nano Lett. 2024, 24, 5929-5936; Adv. Mater. 2025, 2500534; Appl. Phys. Lett. 2025, 126, 122901). The strain imparted by the P(VDF-TrFE) layer is substantially constrained by the rigid substrate, leading to interfacial shear stress. Consequently, the strain gradient decays sharply with increasing distance from the interface, resulting in minimal mechanical strain being transmitted to the Fe GaTe layer. This strain is demonstrably below the threshold required to induce lattice changes (Figure R4, Raman and XRD measurements of the polarized P(VDF-TrFE) layer confirm the structural integrity of the Fe GaTe lattice). As depicted in Figure 1e, while the P(VDF-TrFE) layer modulates the anomalous Hall resistance and coercive field of the Fe GaTe device under varying voltage polarization conditions, the direction of the easy magnetization axis remains invariant. Figure R4 a, XRD change curve of the upper layer P(VDF-TrFE) polarized device. The inset shows the Fe GaTe a axis and c axis as a function of polarization voltage. b, Raman change curve of the upper layer P(VDF-TrFE) polarized device. In the bottom-gate configuration, the polarization of the P(VDF-TrFE) layer simultaneously induces ferroelectric modulation and piezoelectric strain effects within the Fe GaTe thin film. Raman spectroscopy and X-ray diffraction analyses performed under varying polarization voltages reveal discernible alterations in the Fe GaTe lattice structure, as evidenced by shifts in characteristic Raman peaks and systematic changes in the a/c lattice constant ratio (Fig. 2d-2e). These observations indicate effective strain transfer from the P(VDF-TrFE) layer to the Fe GaTe lattice, leading to lattice distortion and a subsequent redistribution of its magnetic anisotropy. First-principles calculations (Figure 2f) provide theoretical corroboration of the correlation between strain and changes in magnetic anisotropy, lending further support to the experimental findings. Figure 2 d, Raman spectra of the dual-gate device as a function of the bottom layer polarization voltage, V , and the Raman spectra were measured at 300 K. The Raman spectra of the dual-gate device are shown in the figure below. The insets show the variation of the A peak of Fe GaTe and the position of the β peak of P(VDF-TrFE) with the polarization voltage V , as well as the error bars for five devices measured under the same conditions. e, XRD image of a device obtained at zero bias, the inset shows the variation of the in-plane lattice constant a and the out-of-plane lattice constant c with the bottom polarization voltage V . f, Variation of Fe GaTe magnetic anisotropy with strain calculated from first principles, the inset shows a schematic diagram of the variation of the magnetic moment orientation of the Fe sites within Fe GaTe . Comment 3. P(VDF-TrFE) is a soft polymer. How did the author confirm efficient mechanical strain transfer to the Fe3GaTe2 layer through vdW interface? Can the author provide any experimental evidence of this? Response 3: We are deeply appreciative of the reviewers' insightful feedback. To ascertain the efficacy of strain transfer from the P(VDF-TrFE) ferroelectric polymer to the Fe GaTe lattice, we employed Raman spectroscopy and X-ray diffraction (XRD) to characterize the heterostructure device. As depicted in Figure 2d, application of varying polarization voltages to the underlying P(VDF-TrFE) layer resulted in a significant shift in the A Raman characteristic peak position of Fe GaTe . This peak position shift exhibited a linear relationship with the magnitude and direction of the polarization voltage, indicating controllable deformation of the Fe GaTe lattice structure. The systematic shift in Raman peak positions directly reflects alterations in interatomic bonding states or bond lengths, serving as a sensitive indicator of lattice strain or deformation. Complementary XRD results, presented in Figure 2e, demonstrate that the application of different polarization voltages systematically modulated the lattice constants a and c of Fe GaTe . Given that lattice constants (a, c) are fundamental parameters defining a crystal structure, their observed changes provide direct evidence of overall lattice deformation, encompassing in-plane compression/tension and out-of-plane expansion/contraction. These findings further substantiate the effective transfer of strain from P(VDF-TrFE), leading to a measurable alteration of the intrinsic lattice structure of Fe GaTe . Figure 2 d, Raman spectra of the dual-gate device as a function of the bottom layer polarization voltage, V , and the Raman spectra were measured at 300 K. The Raman spectra of the dual-gate device are shown in the figure below. The insets show the variation of the A peak of Fe GaTe and the position of the β peak of P(VDF-TrFE) with the polarization voltage V , as well as the error bars for five devices measured under the same conditions. Comment 4. In the multi-device logic array demonstrations (AND/NAND/NOT/half-adder), what is the device-to-device variability in coercivity, Hall resistance, or switching voltage? How reproducible are the operations across cycles or fabrication batches? Response 4: We gratefully acknowledge the reviewers' constructive feedback. In our multi-device logic array demonstrations, the variability observed in coercivity, Hall resistance, and switching voltage across devices is primarily attributable to inherent process-related factors. These include: (1) thickness variations (±10%) and domain structure inhomogeneities arising from the mechanical exfoliation of the Fe GaTe ferromagnetic layer; and (2) deviations in the spin-coated P(VDF-TrFE) ferroelectric polymer film thickness (<±5 nm), variations in the distribution of crystalline phases (with the β phase constituting 70-85%), and differences in domain size (50-200 nm), collectively leading to fluctuations in the electric field coupling efficiency. Through optimization of process parameters, we have successfully developed a comprehensive fabrication scheme, enabling us to constrain the variability in intrinsic device performance parameters, such as coercive field, Hall resistance, and switching voltage, to within a fluctuation range of 5-10%. As illustrated in the accompanying figure, the performance variability among 10 devices fabricated in different batches ranges from 3-6%. Figure R5 a-j, Anomalous Hall curves of 10 devices after upper polarization. k, Changes in R xy before and after polarization of 10 devices. i, Changes in H before and after polarization of 10 devices. Comment 5. The author suggests, unlike conventional heterostructure devices suffering from lattice mismatch-induced interfacial defects, the van der Waals interface offers enhanced thermal stability. Have the authors quantitatively evaluated how device performance (e.g., AHE, coercivity, strain sensitivity) changes with temperature, particularly across the ferroelectric Curie temperature or near the upper limits of operational range? Response 5: We appreciate the reviewers' insightful feedback. While all demonstrations in the main text were conducted at room temperature, we have included a temperature-dependent characterization of device performance in the supplementary information. Specifically, the polarization control characteristics were investigated within a temperature range of 280 K to 380 K. Figure R6a displays the device's resistance-temperature characteristics under an in-plane magnetic field (θ = 0°). As temperature increases from 280 K to 380 K, both the anomalous Hall resistance (R ) and coercive field (H ) exhibit a monotonic decrease, eventually vanishing above the Curie temperature (T ≈ 327 K) of Fe GaTe . This behavior stems from the ferromagnetic-to-paramagnetic phase transition in Fe GaTe at T , where the spontaneous magnetization strength and long-range ferromagnetic order are disrupted. Since the anomalous Hall effect is fundamentally a topological transport phenomenon induced by ferromagnetic order, its presence is contingent on a non-zero spontaneous magnetization and the associated band structure within the ferromagnetic material. Consequently, the anomalous Hall effect disappears in the paramagnetic phase. Upon applying a -10 V bottom gate voltage to control ferroelectric polarization, significant changes are observed in the anomalous Hall resistance, coercive field, and easy axis of magnetization. During the temperature ramp from 280 K to 380 K, both the anomalous Hall resistance and coercive field initially decrease. Notably, the anomalous Hall effect, which had previously vanished, reappears at approximately 340 K. This reappearance arises from ferroelectric-ferromagnetic coupling induced by the bottom-gate polarization. Polarized charges within the P(VDF-TrFE) ferroelectric layer modulate the carrier concentration in Fe GaTe , enhancing exchange interactions in the ferromagnetic layer through interfacial charge transfer, thus effectively increasing the Curie temperature of Fe GaTe above 340 K. Correspondingly, a marked jump in the coercive field is observed near 340 K. As the temperature further increases from 280 K to 380 K, the ferroelectricity of P(VDF-TrFE) (70:30) gradually diminishes due to enhanced thermal fluctuations. This decay is attributed to intensified thermal motion of molecular chains, leading to a reduction in the ordering of ferroelectric dipoles. As the temperature approaches its Curie temperature (T ≈ 380 K), the thermal fluctuation energy becomes comparable to the ferroelectric domain stability energy barrier, initiating the formation of polar nanodomains. Above 380 K, the dipole moments become disordered. This ferroelectric decay directly weakens the regulatory effect, manifesting in two ways: (1) the difference between the polarized and initial states for R and H gradually converges as temperature increases (as indicated by the decreasing area of the blue region in Figure R6c-6d); and (2) the orientation of the easy axis of magnetization gradually returns to 90°. These observations confirm the temperature sensitivity of the ferroelectric layer's ability to control magnetic parameters. Figure R6 a, Anomalous Hall curves of devices at different temperatures when θ = 0°. b, Anomalous Hall curves of devices with a -10 V bottom gate bias at different temperatures when θ H = 0°. c, Temperature-dependent R of devices before and after polarization. d, H versus temperature for the device before and after polarization. e, Voltage switching demonstration for the device at different temperatures, with the inset showing the switching time. Reviewer #3: Main Comment. This manuscript reports a dual-gated Fe₃GaTe₂/P(VDF-TrFE) heterostructure with voltage-controlled modulation of magnetic properties and demonstration of spin-based logic functionality. While the subject falls within the general interest of multiferroic 2D devices, I have serious concerns regarding the novelty of the work, the clarity of the physical mechanisms involved, and the scientific rigor of the data interpretation. Based on the issues outlined below, I do not recommend publication of the manuscript. Below are my detailed comments: Response: We sincerely thank the reviewers for their valuable comments and constructive suggestions. Their insightful observations and thoughtful feedback have greatly contributed to the improvement of our manuscript. We have carefully considered each point raised and provided detailed responses and revisions accordingly in the revised version. These efforts have substantially enhanced the clarity, rigor, and overall quality of the paper. Comment 1. This manuscript lacks novelty. The magnetic properties of Fe3GaTe2, such as perpendicular magnetic anisotropy and the anomalous Hall effect, have already been thoroughly investigated (for example doi.org/10.1038/s41467-022-32605-5). There is no need to revisit these aspects without offering new understanding. Moreover, the use of PVDF gating to modulate the magnetism of Fe3GaTe2 has already been explored in previous publications by the authors and their collaborators (doi.org/10.1038/s41467-025-62159-1). In this manuscript, the only potentially novel aspect is the use of a dual-gate configuration. However, this part is not clearly explained in the manuscript, and the physical mechanism behind it is not convincingly discussed. I find this unsatisfactory. The authors should reorganize the manuscript, remove results that are already known or unrelated, and focus on articulating the genuinely new contribution of this work. Only after establishing the novelty and underlying physics should the logic gate demonstrations be presented as outcomes of the new device structure. Response 1: We sincerely appreciate the reviewers' insightful and valuable comments, which have been crucial in refining the quality of our manuscript. We have reorganized the manuscript by removing previously reported results and focusing on the ferroelectricity-driven, strain-mediated magnetoelectric coupling mechanism. While the use of P(VDF-TrFE) gating to modulate room-temperature ferromagnetism in Fe GaTe heterostructures has been previously demonstrated (doi.org/10.1038/s41467-025-62159-1), this work introduces a top-gate configuration that enables control of carrier concentration, thereby influencing the ferromagnetic properties of Fe GaTe . However, the top gate suffers from the \"Shear Lag Effect\" (Nat. Commun. 2020, 11, 1151), which hinders effective strain coupling. In contrast, we demonstrate that the bottom ferroelectric P(VDF-TrFE) gate can effectively modulate the magnetic anisotropy constant through strain-mediated magnetoelectric coupling. This strain-mediated coupling has been confirmed by Raman spectroscopy and X-ray diffraction, as shown in Figure 2d-2e. Therefore, the underlying physics of this study is fundamentally different from the previously reported modulation of room-temperature ferromagnetism in Fe GaTe heterostructures (doi.org/10.1038/s41467-025-62159-1). In this work, the magnetic anisotropy constant K₁ is tunable via the bottom P(VDF-TrFE) layer under different polarization voltage scans, whereas it remains unaffected by the top P(VDF-TrFE) gate, as shown in Figure 1b. Figure 2 d, Raman spectra of the dual-gate device as a function of the bottom layer polarization voltage, V , and the Raman spectra were measured at 300 K. The Raman spectra of the dual-gate device are shown in the figure below. The insets show the variation of the A peak of Fe GaTe and the position of the β peak of P(VDF-TrFE) with the polarization voltage V , as well as the error bars for five devices measured under the same conditions. e, XRD image of a device obtained at zero bias, the inset shows the variation of the in-plane lattice constant a and the out-of-plane lattice constant c with the bottom polarization voltage V . 2 Figure 1 b, Schematic diagram of stress transfer during bottom gate P(VDF-TrFE) polarization and top gate P(VDF-TrFE) polarization processes. Figure 1 c, K variation curve of the bottom layer P(VDF-TrFE) under ±10 V polarization voltage scanning. d, K variation curve of the upper layer P(VDF-TrFE) under ±10 V polarization voltage scanning. The novelty and underlying physics of strain-mediated coupling have been established. The magnetic anisotropy constant K can be tuned by applying polarization voltage through this strain-mediated mechanism(Figure 1c-1d). Reversing the polarization of the P(VDF-TrFE) layer induces contraction via the inverse piezoelectric effect, thereby altering the direction of the easy magnetization axis. This enables fully electrical and reversible modulation of the anomalous Hall resistance(Figure 2a-2b). Applying polarization voltage achieves inverter functionality. Through device integration, we demonstrate reconfigurable logic gate arrays (AND/NAND/NOT) and half-adder circuits. Furthermore, these spin logic devices exhibit excellent performance, including ultra-low energy consumption (0.5 aJ per operation), fast write speeds (5 ns), and high stability during logic gate operations. Collaborative double-gate regulation is entirely implemented in Supplementary Information. Figure 2 Mechanism of polarization voltage modulation of magnetic properties of dual-gate devices. a-b, Anomalous Hall curves under different polarization voltages when the magnetic field angle θ =0°. a, Negative voltage polarization. b, Positive voltage polarization. H Comment 2. The PVDF layers used in the device are spin-coated, which typically leads to bottom crystallinity and weaker chain alignment compared to more controlled methods such as Langmuir-Blodgett techniques. However, the manuscript does not mention any post-deposition annealing or provide structural characterization data such as AFM or XRD. Given that the claimed device functionality relies heavily on the ferroelectric and piezoelectric properties of PVDF, the authors should include direct evidence supporting its crystallinity, beta-phase content, and ferroelectricity either in the main text discussion or in the supplementary materials. Measurements such as P–E loops, PFM, or other relevant characterizations are necessary to validate these properties. Without such evidence, the fundamental basis for the proposed mechanism remains unconfirmed. Further, according to the device setting, the electric field on the PVDF is as large as 10MV/cm, we suggest the author check the P-E loops to confirm the integrity of the material. Response 2: We sincerely thank the reviewers for their valuable comments. While the Langmuir-Blodgett (LB) technique offers a robust platform for fundamental research, enabling the fabrication of highly ordered model films, its inherent complexity, slow processing speed, elevated cost, and challenges in scalability limit its viability for the production of most practical devices. Conversely, although spin coating presents limitations regarding crystallinity and chain orientation control, these are counterbalanced by its considerable advantages in simplicity, speed, cost-effectiveness, scalability, adaptability to diverse substrates, and a practical range of achievable film thicknesses. Furthermore, extensive research has focused on spin-coated P(VDF-TrFE) ferroelectric thin films, yielding significant advancements in crystallinity and overall ferroelectric performance(Nature 2004, 428, 299-303 (2004); Science 2019, 364, 166-169; Small 2025, 21, 2502767; Adv. Funct. Mater. 2025, 35, 2412507; Polymers 2019, 11, 1096; Mat Sci Semicon Proc 2025, 196, 1109653; J Mater Sci 2020, 55:6696-6707). Following spin coating, the P(VDF-TrFE) film underwent a two-stage thermal treatment to enhance its ferroelectric properties. Initially, the film was dried at 70°C for 1 hour to facilitate solvent removal. Subsequently, it was annealed and crystallized at 130°C under vacuum(Nano Energy 2017, 32, 255-262; ACS Nano 2022, 16, 18355-18365; Polymer 2004, 45, 1679-1688; Polym Polym Compos 2016, 24, 167-172; Adv. Mater. Technol. 2025, e01513; J Mater Sci-mater El 2017, 28, 8391-8396). This process significantly improved the ferroelectricity of P(VDF-TrFE) through distinct mechanisms. The initial drying step at 70°C effectively removed residual solvents, mitigating defect formation during subsequent crystallization and preventing interference with the ordered alignment of molecular chains. Furthermore, vacuum annealing at 130°C, exceeding the material's Curie temperature, promoted enhanced molecular chain mobility, rearrangement, and growth. This resulted in the formation of larger, purer ferroelectric β-phase crystals characterized by a fully trans conformation. The vacuum environment also served to prevent high-temperature oxidative degradation. Collectively, these steps led to a significant enhancement in film crystallinity, β-phase content, and structural density, while simultaneously reducing grain boundaries and impurity defects. Consequently, spontaneous polarization strength was augmented, leakage current was diminished, and breakdown field strength was increased, culminating in optimized ferroelectric performance. The ferroelectric properties of the fabricated P(VDF-TrFE) film were characterized, and the corresponding data are presented in the Supplementary Information. Piezoelectric force microscopy (PFM) switching spectroscopy, as depicted in Figure R7a, reveals characteristic amplitude butterfly loops and a 180° phase reversal at the coercive voltage, indicative of robust ferroelectric polarization switching. The formation of a loop-shaped domain pattern after applying a ±10 V writing voltage (Figures R7b and R7c) further corroborates the reversible nature of electric domain switching. X-ray diffraction (XRD) analysis (Figure R7d) exhibits a prominent diffraction peak at 2θ ≈ 20.86°, signifying the high crystallinity and dominance of the ferroelectric β phase within the film. The presence of characteristic absorption peaks in the Fourier-transform infrared (FTIR) spectrum (Figure R7e) further confirms the prevalence of the β phase. Finally, the well-defined hysteresis loop (P-E loop) obtained under a ±10 V driving voltage (Figure R7f) unequivocally demonstrates the excellent ferroelectric performance of the P(VDF-TrFE) film. Figure R7 a, PFM amplitude and phase hysteresis loops of the ferroelectric thin film P(VDF-TrFE). b-c, Out-of-plane piezoelectric microscopy image of the ferroelectric thin film P(VDF-TrFE) displaying a zigzag domain structure under -10 V/+10 V bias. (b) Amplitude image. (c) Phase image. Backword domain fabrication was performed by sequentially applying +10 V, -10 V and +10 V bias to polarize, repolarize and repolarize the 50 μm × 50 μm, concentric 30 μm × 30 μm and innermost 10 μm × 10 μm regions of the surface of P(VDF-TrFE) ferroelectric films, respectively. d, XRD spectra of the ferroelectric thin film P(VDF-TrFE). e, FTIR spectra of the ferroelectric thin film P(VDF-TrFE). f, Ferroelectric hysteresis loops of multiferroic heterostructure P(VDF-TrFE)/Fe GaTe at different measurement voltages. Comment 3. The anisotropy constant Ku and the modeling shown in Fig. 1c are not accompanied by any explanation of the fitting or calculation method. Since similar results have already been reported in the literature, this part does not represent a novel contribution. I suggest moving these data to the Supplementary Material. However, if the authors choose to keep them in the main text, they should include a clear and quantitative description of how Ku is extracted. Without such explanation, the figure lacks reproducibility and interpretive value. Response 3: We are grateful to the reviewers for their insightful feedback, which has significantly improved the manuscript. In response to their comments, we have included a detailed description of the fitting method used to determine the anisotropy constant, Ku, within the supplementary information. In ferromagnetic materials exhibiting a rhombic crystal structure, the magnetic free energy, F is often effectively described using the Stoner-Wohlfarth model. This model incorporates a magnetic anisotropy term, crucial for characterizing the orientation of the material's easy axis of magnetization. (1) 2 Here, K₁ represents the uniaxi𝐹al =ma𝐾g1n𝑠e𝑖t𝑛ic 𝜃a𝑀nis−ot𝜇ro0𝐻py𝑀 coconsst(a𝜃n𝐻t, −th𝜃e 𝑀si)gn and magnitude of which dictate the orientation of the easy magnetization axis. μ H signifies the applied external magnetic 0 field strength. θ and θ denote the angles between the magnetization vector M and the external magnetic field μ H, respectively, relative to the sample plane normal (defined as θ = 0°). Under equilibrium conditions, where the free energy F is minimized, θ is defined by equation (1): M (2) 𝜕𝐹 𝜕𝜃𝑀 =𝑂 =2𝐾1sin𝜃𝑀cos𝜃𝑀−𝜇0𝐻𝑀sin(𝜃𝐻−𝜃𝑀) Equation (2) reveals that the system exhibits isotropic ferromagnetism when K = 0, with the 1 magnetization intensity M aligning parallel to the external magnetic field μ H. Conversely, when K 0 1 < 0, the system demonstrates uniaxial magnetic anisotropy ferromagnetism, characterized by an in-plane easy axis of magnetization. When K > 0, the system also exhibits uniaxial magnetic 1 anisotropy ferromagnetism, but with an out-of-plane easy axis, causing the magnetization intensity M to preferentially align along the sample plane's normal direction. The uniaxial magnetic anisotropy constant K can be experimentally determined through angle-dependent anomalous Hall 1 effect (AHE) measurements (Nature 2018, 563, 94-99; Nat. Commun. 2018, 9, 1554). Assuming the relationship R ∝ M ≈ M cosθ , where M represents the magnetization component AHE M ⟂ ⟂ perpendicular to the current direction, the equilibrium angle θ can be estimated from the external M field angle θ and the saturation anomalous Hall resistance Rs using the following expression: H AHE (3) 𝑠 ° 𝑅𝐴𝐻𝐸(𝜃𝑀) Where Rs = R |μ H = μ H (saturated c ) o . s W 𝜃 e 𝑀 u = se 𝑅 t 𝐴 𝑠 h 𝐻 e 𝐸 ( f 𝜃 o 𝐻 ll = o 0 w ) ing formula to calculate θ as a AHE AHE 0 0 M function of θ : H (4) 𝑠 𝑅𝐴𝐻𝐸(𝜃𝐻) 𝜃𝑀(𝜃𝐻)=arccos (𝑅𝐴 𝑠 𝐻𝐸(𝜃𝐻=0°)) The relationship between θ and θ provides insight into the orientation of the magnetic easy H M axis; specifically, θ > θ indicates a propensity for in-plane magnetization. The value of K , M H 1 representing the total magnetic anisotropy energy density, encompasses contributions from various sources. These include the intrinsic crystalline anisotropy energy (K ), the demagnetization energy c (K = -Dµ M /2, where D is the demagnetization factor), strain-induced anisotropy (K ), and demag 0 2 strain surface anisotropy (K). This can be expressed as: s (5) 𝐾𝑠 Among them, D and D are 𝐾 1 th = e 𝐾 de 𝑐 m + a 𝐾 gn 𝑑 e 𝑒𝑚 tiz 𝑎 a 𝑔 ti + on 𝐾 𝑠 f 𝑡 a 𝑟 c 𝑎 t 𝑖 o 𝑛 rs + fo𝑑r the in-plane and out-of-plane 0 1 magnetization directions, respectively, and d is the sample thickness. Comment 4. I have serious concerns about the discussion of the topological Hall effect (THE) in lines 178–195. Based on the experimental data provided, I do not see convincing evidence of THE. The characteristic non-monotonic features, such as a peak or dip in the Hall resistance, are not clearly present. The monotonic decrease after magnetic flipping is more likely due to spin canting rather than the emergence of a topological contribution. Despite this, the authors devote substantial space to speculating about THE without providing any supporting evidence such as magnetic imaging, for example as shown in DOI: 10.1002/adma.202403154. This weakens the clarity of the manuscript and risks misleading readers. Moreover, the citation of Ref. 26 (doi.org/10.1038/s41467-022-32605-5) to support the presence of THE in Fe₃GaTe₂ is inappropriate, as this reference does not discuss THE in that system. I strongly recommend the authors revise this section thoroughly and reconsider the interpretation presented. Response 4: Addressing the reviewers' central concerns, we have substantially revised lines 178-195 of the manuscript. This revision entails a complete reworking of the previous speculative analysis and discussion regarding the topological Hall effect. The revised manuscript now concentrates on the most plausible physical interpretation of the experimental data, ensuring closer alignment with the article’s central theme of the physical mechanisms governing dual-gate devices. This modification significantly enhances the rigor and clarity of the discussion within this section, precluding speculative interpretations that could potentially misdirect readers. We believe these considerable revisions have materially improved the quality and scientific robustness of the paper. We gratefully acknowledge the reviewers’ insightful observations and valuable suggestions, which have been instrumental in refining our work. Comment 5. The authors propose that the bottom PVDF layer contributes both doping and strain, while the top PVDF layer contributes only doping. This asymmetry is used to explain the more pronounced effect of the bottom gate. However, the physical origin of this asymmetry is not clearly justified. It is unclear why the top PVDF layer would not also generate strain through the same inverse piezoelectric mechanism. The manuscript should provide a more detailed and mechanistic explanation for this asymmetry. Response 5: We extend our sincere gratitude to the reviewers for their insightful comments on this manuscript. The magnetism of Fe GaTe can be manipulated through two distinct mechanisms when 3 2 coupled with polarized P(VDF-TrFE): ferroelectric polarization modulation and strain control. Ferroelectric polarization modulation enables non-volatile control of the interfacial charge configuration via the polarization of the P(VDF-TrFE) layer. Conversely, strain control, as detailed in previous work (Nat. Commun. 2025, 16, 6797), affects the magnetism, anomalous Hall resistance, and coercive field of Fe GaTe by altering its lattice structure through strain transmission. The 3 2 primary effect of strain modulation lies in the regulation of the easy axis of magnetization. However, when the P(VDF-TrFE) layer is situated above the Fe GaTe , control of the magnetism is primarily 3 2 achieved through ferroelectric polarization modulation. The distinction in strain transmission between the bottom and top layers is schematically illustrated in Figure R8. Figure R8 Schematic diagram of stress changes in a device under negative voltage polarization, a, upper layer P(VDF-TrFE). b, bottom layer P(VDF-TrFE). Schematic diagram of stress changes in a device under negative voltage polarization, c, upper layer P(VDF-TrFE). d, bottom layer P(VDF-TrFE). Despite the application of voltage polarization to P(VDF-TrFE) to induce the inverse piezoelectric effect, the rigid substrate imposes significant constraints on the resulting strain, leading to interfacial shear stress. Consequently, the strain gradient experiences a rapid decay along the thickness direction, diminishing the mechanical strain effectively transmitted to the Fe GaTe 3 2 intermediate layer to a level substantially below the required critical value. As evidenced by the Raman and XRD spectra presented in Figure R9, no discernible alteration in the crystal lattice of Fe GaTe was observed following polarization of the upper P(VDF-TrFE) layer. 3 2 Figure R9 a, XRD change curve of the upper layer P(VDF-TrFE) polarized device. The inset shows the Fe GaTe a axis and c axis as a function of polarization voltage. b, Raman change curve of the 3 2 upper layer P(VDF-TrFE) polarized device. Conversely, Raman spectroscopy and X-ray diffraction (XRD) analyses performed on the bottom-layer P(VDF-TrFE) following polarization reveal alterations within the Fe GaTe crystal lattice. 3 2 These changes are evidenced by shifts in Raman peak positions and modifications in the a-axis/c-axis ratio of the Fe GaTe structure (Fig. 2d-2e). We posit that strain propagation induces 3 2 deformation of the Fe₃GaTe₂ lattice, subsequently leading to a redistribution of magnetic anisotropy properties. This strain-induced structural modification may affect the spin-orbit coupling strength by altering the orbital occupancy of Fe atoms, thereby influencing the direction of the easy magnetization axis, a perspective further supported by first-principles calculations (Figure 2f). Figure 2 d, Raman spectra of the dual-gate device as a function of the bottom layer polarization voltage, V , and the Raman spectra were measured at 300 K. The Raman spectra of the dual-gate 2 device are shown in the figure below. The insets show the variation of the A peak of Fe GaTe and 1g 3 2 the position of the β peak of P(VDF-TrFE) with the polarization voltage V , as well as the error bars 2 for five devices measured under the same conditions. e, XRD image of a device obtained at zero bias, the inset shows the variation of the in-plane lattice constant a and the out-of-plane lattice constant c with the bottom polarization voltage V . f, Variation of Fe GaTe magnetic anisotropy 2 3 2 with strain calculated from first principles, the inset shows a schematic diagram of the variation of the magnetic moment orientation of the Fe sites within Fe GaTe . 3 2 Comment 6. Moreover, I wonder whether the observed modulation is simply doping-driven rather than resulting from ferroelectric polarization. In the presented data, all responses to gate voltage, whether from the top or bottom PVDF layer, appear continuous and do not show any signature of abrupt switching or hysteresis that is typically associated with ferroelectric behavior. This could be because the applied gate voltages are much larger than the coercive voltage of PVDF, which may suppress the characteristic ferroelectric response. The authors should examine this carefully. Without such analysis, I have reason to suspect that similar modulation could be achieved using two non-ferroelectric dielectric layers, such as hBN and SiO , through electrostatic doping alone. This 2 possibility needs to be ruled out before drawing any conclusions about polarization-driven effects. Response 6: We would like to thank the reviewers for their constructive comments on our paper. In double-gate devices, ferroelectric polarization modulation and strain modulation exist, but no other modulation such as doping is present. We supplemented the hysteresis curves showing the variation of device magnetization with ferroelectric polarization, demonstrating that the modulation phenomenon described in the manuscript originates from P(VDF-TrFE) ferroelectric polarization(Figure R10). Figure R10 Magnetization of the device as a function of the P(VDF-TrFE) polarization voltage. In both poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] copolymers and polycrystalline PVDF thin films, a reduction in film thickness induces a significant size effect, primarily evidenced by grain refinement and a concomitant increase in domain wall density. This elevated domain wall density promotes a randomized distribution of local polarization orientations, thereby diminishing the cooperative polarization reversal between adjacent domains. Furthermore, decreasing the film thickness substantially amplifies the influence of interfacial effects on bulk polarization, macroscopically suppressing the characteristic discontinuous, non-linear polarization reversal process typically observed in ferroelectrics (Phys. Rev. Lett. 2018, 120, 26760). Analogous mechanisms are prevalent in other ferroelectric systems. For example, in PbTiO /SmScO 3 3 superlattices, the built-in electric field modulates polarization symmetry, and the interplay between elastic and electrostatic energies engenders macroscopically continuous piezoelectric responses despite the presence of microscopically discontinuous domains (Adv. Funct. Mater. 2025, e10402). Similarly, in BaTiO films with thicknesses ranging from 2 to 10 nm, nanoscale domains with 3 thicknesses as small as 0.4-0.8 nm (1-2 unit cells) have been observed. High tensile stress in these films inhibits domain wall motion, resulting in a continuous polarization reversal response (Mater Lett 2005, 59, 1598-1602). In Hf Zr O films stabilized in the orthogonal phase through the use 0.5 0.5 2 of an oxide buffer layer, uniaxial in-plane ferroelectric polarization (1.0 nm) was achieved, with in-plane ferroelectric switching exhibiting an ultra-low coercivity of 0.5 MV/cm (Nat. Commun. 2025, 16, 7385). Finally, in epitaxially grown PbTiO films thinner than or equal to 20 nm, lattice coherent 3 strain maintains a single-domain state, leading to a continuous phase transition during polarization reversal (Phys. Rev. B 2008, 78, 104112). Figure R11 Ferroelectric hysteresis loops of multiferroic heterostructure P(VDF-TrFE)/Fe GaTe at 3 2 different measurement voltages. Unlike conventional electrostatic gating, this work leverages the ferroelectric polarization of P(VDF-TrFE) to modulate the magnetic properties of Fe GaTe . This approach achieves non- 3 2 volatile control of the interfacial charge distribution via P(VDF-TrFE) polarization, enabling regulation of Fe GaTe 's magnetic characteristics, including magnetic susceptibility, anomalous 3 2 Hall resistance, and coercive field (Nat. Commun. 2025, 16, 6797). In contrast, electrostatic gating relies on the accumulation of charge carriers (electrons or holes) at the magnetic layer's surface through an external electric field. This directly alters the charge carrier concentration to modulate magnetic exchange interactions or magnetic anisotropy. However, electrostatic gating necessitates a sustained bias to maintain charge carrier accumulation and is inherently inefficient for metallic materials like Fe₃GaTe₂, which possess high charge carrier concentrations (Nat. Commun. 2024, 15, 2408; ACS Nano 2023, 17, 25348-25356; Acta Phys. Sin. 2019, 68, 108501). Comment 7. In lines 123–127, the authors cite Ref. 17 to support a mechanism involving C–F dipole coupling with Te lone pairs and spin-state reconfiguration of Fe atoms. However, Ref. 17 discusses PVDF/PAN/CNT composites and their bulk electrical conductivity, and is entirely unrelated to Fe3GaTe2 interfaces or d-orbital physics. This citation is inappropriate and misleading. The authors should replace or remove it and ensure that all references are directly relevant to the claims being made. Response 7: We express our gratitude to the reviewers for their insightful comments. In response, we have updated the citations to better reflect our perspective. Specifically, the helical β phase of P(VDF-TrFE) is characterized by a high-density, ordered arrangement of C-F dipole moments. This characteristic arises from the polymer chains within the β phase adopting a fully trans (TTTT) conformation, where fluorine (F) and hydrogen (H) atoms are positioned on opposing sides of the carbon chain, thereby generating strong dipole moments perpendicular to the chain direction (Science 2021, 371, 1050-1056). The tellurium (Te) atoms on the Fe GaTe surface contribute 5p 3 2 orbital lone pair electrons, which interact with the C-F dipoles of P(VDF-TrFE) through electrostatic coupling. A comparable mechanism has been observed in BiFeO /P(VDF-TrFE) composite films, 3 where the lone pair electrons on the BiFeO surface couple with the C-F dipoles, creating a localized 3 electric field. This interfacial electric field, in turn, modulates the d electrons of Fe atoms in Fe GaTe through the orbital-spin correlation effect (Smart Mater. Struct. 2023, 32 045017). 3 2 Comment 8. When building the spin logic devices, the author constructed the Fe3GaTe2/P(VDF-TrFE) bilayer rather than the discussed P(VDF-TrFE)/Fe3GaTe2/P(VDF-TrFE) trilayer system before, which causes inconsistency of the work. Response 8: The authors gratefully acknowledge the reviewers' insightful feedback. This study explored two device configurations for spin-electronic logic devices: an asymmetric Fe GaTe /P(VDF-TrFE) bilayer heterostructure and a symmetric P(VDF-TrFE)/ Fe GaTe /P(VDF-TrFE) 3 2 3 2 double gate heterostructure. While both configurations successfully implemented fundamental logic gate functions, the bilayer configuration exhibited a crucial advantage: a two-fold reduction in energy consumption per logic operation compared to the double gate configuration. Given this significant reduction in energy dissipation, the manuscript's primary focus is on demonstrating the logic functionality of the Fe GaTe /P(VDF-TrFE) bilayer heterostructure. 3 2 Consequently, the experimental data and logic functionality demonstration for the P(VDF-TrFE)/ Fe GaTe /P(VDF-TrFE) double gate heterostructure are comprehensively detailed in the 3 2 supplementary materials for further investigation. Comment 9. How is Ref. 19 (DOI: 10.1038/s41467-021-26271-2), a paper related to breast cancer, cited in this 2D materials paper? Response 9: We sincerely appreciate the reviewers' insightful comments and suggestions. We acknowledge and apologize for the inaccurate application of reference 19 in the original manuscript. We have rectified this oversight by correcting the citation to: Lv, L., Zhuge, F., Xie, F. et al. Reconfigurable two-dimensional optoelectronic devices enabled by local ferroelectric polarisation. Nat Commun 10, 3331 (2019). The manuscript has been thoroughly revised to reflect this correction. Comment 10. Figure 1b is never referenced in the main text. It is possible that there is a typo or omission around line 163 where it was intended to be mentioned. Response 10: We thank the reviewers for bringing this oversight to our attention. We sincerely apologize for the missing citation for Figure 1b, an omission which has now been rectified. We have explicitly added the relevant citation to ensure clarity and accuracy in the correspondence between the text and the figure. We appreciate the reviewers' assistance in improving the rigor and readability of this manuscript. Comment 11. In the script, the author call \\Theta_H=90 as perpendicular direction and \\Theta_H=0 as in plane direction. This is contradictory to the fig. 1c inset. Response 11: We are deeply grateful to the reviewers for identifying a critical error in the directional labels within Figure 1c, specifically the misidentification of the vertical direction as θ =90° and the H horizontal direction as θ =0°. We sincerely apologize for this oversight and any potential confusion H it may have caused. To ensure the scientific accuracy of the manuscript, we have corrected Figure 1c and revised the corresponding description accordingly. REVIEWER COMMENTS Reviewer #1 (Remarks to the Author): The authors have responded in detail to my comments improving their manuscripts and making it more clear. Reviewer #2 (Remarks to the Author): The authors have addressed nicely the comments, and now the paper is ready to be published. Reviewer #3 (Remarks to the Author): The authors have made targeted revisions in response to my earlier comments, including correcting inappropriate citations and substantially reorganizing the main text and figures. However, I still find the explanation for the asymmetry between the top and bottom PVDF layers unsatisfactory, and the experimental results remain inconclusive. Overall, I consider the conclusions of this work unconvincing, and the quality does not meet the standard of Nature Communications. I therefore maintain my recommendation not to publish. 1. Asymmetry between top and bottom PVDF layers is not explained properly. The author’s explanation in Response 5 says that the bottom PVDF can strain control Fe3GaTe2 while the top layer cannot due to the constraint of the rigid substrate. However, in the actual device structure discussed in the main text (P(VDF-TrFE)/Fe3GaTe2/P(VDF-TrFE)), Fe3GaTe2 is sandwiched between two PVDF layers, the presence of a rigid substrate does not apply here! The XRD and Raman data shown only characterize the observed phenomena but do not provide a mechanistic explanation for the origin of the asymmetry. This asymmetry is counterintuitive, yet the authors have not provided a satisfactory physical justification, which undermines the publish-ability of the work. 2. Ferroelectric control of magnetic properties is still not convincing. In my original Comment 6, I questioned whether the observed magnetic modulation arises directly from ferroelectric polarization, or instead from the large applied voltages directly affecting Fe3GaTe2. Response 6 does not fully resolve my concern. I do not dispute the intrinsic ferroelectricity of PVDF in this work. And authors have Figure R11 demonstrate the hysteresis loop of this. However, whether the modulation of Fe3GaTe2 magnetism originates from ferroelectric polarization remains unproven. In Figures R8 and supplementary material Figure S7, the hysteresis loops associated with magnetic modulation are weak, continuous, and lack clear abrupt switching. Why don’t they follow the hysteresis loop of PVDF (R11)? This raises the possibility that the results may be indistinguishable from leakage induced “pseudoloops”. The examples authors give on continuous hysteresis loop in BTO, PTO, HZO are about ferroelectricity itself and don’t explain my concern. Such inconclusive evidence does not establish the causal link between ferroelectric switching and magnetic modulation, which is important. ."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have responded in detail to my comments improving their manuscripts and making it more clear.", "reviewer_2": "The authors have addressed nicely the comments, and now the paper is ready to be published.", "reviewer_3": "The authors have made targeted revisions in response to my earlier comments, including correcting inappropriate citations and substantially reorganizing the main text and figures. However, I still find the explanation for the asymmetry between the top and bottom PVDF layers unsatisfactory, and the experimental results remain inconclusive. Overall, I consider the conclusions of this work unconvincing, and the quality does not meet the standard of Nature Communications. I therefore maintain my recommendation not to publish. 1. Asymmetry between top and bottom PVDF layers is not explained properly. The author’s explanation in Response 5 says that the bottom PVDF can strain control Fe3GaTe2 while the top layer cannot due to the constraint of the rigid substrate. However, in the actual device structure discussed in the main text (P(VDF-TrFE)/Fe3GaTe2/P(VDF-TrFE)), Fe3GaTe2 is sandwiched between two PVDF layers, the presence of a rigid substrate does not apply here! The XRD and Raman data shown only characterize the observed phenomena but do not provide a mechanistic explanation for the origin of the asymmetry. This asymmetry is counterintuitive, yet the authors have not provided a satisfactory physical justification, which undermines the publish-ability of the work. 2. Ferroelectric control of magnetic properties is still not convincing. In my original Comment 6, I questioned whether the observed magnetic modulation arises directly from ferroelectric polarization, or instead from the large applied voltages directly affecting Fe3GaTe2. Response 6 does not fully resolve my concern. I do not dispute the intrinsic ferroelectricity of PVDF in this work. And authors have Figure R11 demonstrate the hysteresis loop of this. However, whether the modulation of Fe3GaTe2 magnetism originates from ferroelectric polarization remains unproven. In Figures R8 and supplementary material Figure S7, the hysteresis loops associated with magnetic modulation are weak, continuous, and lack clear abrupt switching. Why don’t they follow the hysteresis loop of PVDF (R11)? This raises the possibility that the results may be indistinguishable from leakage induced “pseudoloops”. The examples authors give on continuous hysteresis loop in BTO, PTO, HZO are about ferroelectricity itself and don’t explain my concern. Such inconclusive evidence does not establish the causal link between ferroelectric switching and magnetic modulation, which is important."}, "author_response": "We thank all the reviewers for positive recommendation and valuable comments regarding our research paper. Each of your insights have served to strengthen our manuscript. We have carefully revised the manuscript according to your constructive suggestions. Provided below is our detailed response to each comment raised. Reviewer #1: Main Comment. The authors have responded in detail to my comments improving their manuscripts and making it more clear. Our reply: We are deeply grateful to the reviewers for their insightful and constructive feedback, which has been invaluable in strengthening this manuscript. Reviewer #2: Main Comment. The authors have addressed nicely the comments, and now the paper is ready to be published. Our reply: Once again, we extend our heartfelt thanks to the reviewer for their positive, thoughtful, and constructive suggestions on our manuscript. Reviewer #3: Main Comment. The authors have made targeted revisions in response to my earlier comments, including correcting inappropriate citations and substantially reorganizing the main text and figures. However, I still find the explanation for the asymmetry between the top and bottom PVDF layers unsatisfactory, and the experimental results remain inconclusive. Overall, I consider the conclusions of this work unconvincing, and the quality does not meet the standard of Nature Communications. I therefore maintain my recommendation not to publish. Our reply: We sincerely appreciate the reviewer’s constructive suggestions. Below, we provide a detailed response to the reviewer’s feedback. Comment 1. Asymmetry between top and bottom PVDF layers is not explained properly. The author’s explanation in Response 5 says that the bottom PVDF can strain control Fe3GaTe2 while the top layer cannot due to the constraint of the rigid substrate. However, in the actual device structure discussed in the main text (P(VDF-TrFE)/Fe3GaTe2/P(VDF-TrFE)), Fe3GaTe2 is sandwiched between two PVDF layers, the presence of a rigid substrate does not apply here! The XRD and Raman data shown only characterize the observed phenomena but do not provide a mechanistic explanation for the origin of the asymmetry. This asymmetry is counterintuitive, yet the authors have not provided a satisfactory physical justification, which undermines the publish-ability of the work. Response 1: We sincerely appreciate the reviewer's insightful comments and valuable suggestions. These crucial points have prompted us to conduct a more in-depth mechanical analysis of the device's operating mechanism. While we acknowledge that symmetrical shear constraints on the upper and lower polymer layers are ideal in a perfectly symmetrical suspended structure, the practical fabrication of devices introduces a critical asymmetry in mechanical boundary conditions. Specifically, the presence of the silicon substrate creates a fundamental disparity in strain transfer efficiency between the upper and lower polymer layers. Analogous to piezoelectric actuators, when P(VDF-TrFE) is situated on a silicon substrate, the strain generated through the inverse piezoelectric effect experiences significantly greater mechanical constraints during downward transmission due to the substrate's rigidity. These constraints are substantially more pronounced than those encountered during upward transmission. As a consequence, the strain transmission efficiency in the downward direction is demonstrably lower than that in the upward direction. Piezoelectric actuators have garnered significant attention as promising microactuators owing to their ease of fabrication, rapid response times, and compact form factors, leading to their widespread application in areas such as soft robotics, artificial muscles, and electronic devices. Among piezoelectric polymers, polyvinylidene fluoride (PVDF) and its copolymers are particularly prevalent in the development of piezoelectric actuators. This is attributable to their lightweight nature, facile processing, high flexibility, and, crucially, the presence of the polar β-phase, which endows them with piezoelectric properties by facilitating dipole alignment in a unified direction(Chem. Rev. 2009, 109, 6632-6686; J. Intell. Mater. Syst. Struct. 2018, 29 2096−2104; Phys. Rev. Lett. 2007, 99, 047801). The extensive research focused on PVDF and its copolymer-based piezoelectric actuators is illustrated in Figure R1(Chem. Rev. 2023, 123, 11392-11487; Composites Part B 2021, 222, 109060; Sens. Actuators, A 2008, 144, 231-241; J. Phys. Chem. C 2019, 123, 12744-12752; Sci. Rep. 2019, 9, 9877; Adv. Sci. 2016, 3, 1500438; Nano Energy 2025, 139, 110994). Figure Redacted Figure R1 a, The Figure extracted from Composites Part B 2021, 222, 109060. Piezoelectric actuation of PVDF nanofibers under 4 V·μm-1. Schematic of the downward and upward bending of the actuators. b, The Figure extracted from Sens. Actuators, A 2008, 144, 231-241. Design of the IPMC/PVDF composite structure for sensing of bending output (force sensor not shown). c, The Figure extracted from J. Phys. Chem. C 2019, 123, 12744-12752. Schematic representation of the ion migration and bending response and bending motion as a function of time for the [PVDF]/[Pmim][TFSI] composite at a 100 mHz frequency and 5 V. d, The Figure extracted from Sci. Rep. 2019, 9, 9877. Successive deflection behaviour of PVDF/SGO/Pt and PVDF/SGO/PPy/ ionic polymer metal composite membrane actuators. e, The Figure extracted from Adv. Sci. 2016, 3, 1500438. The experimental setup: when the power is on, the bimorph actuator will bend down; when the power is off, the actuator will bend back to its initial position. Diagram to demonstrate the fish-like robot swimming, when the power is on or off, the “tail” bends down or up, then the fish-like robot will swim forward. The optical images of an artificial fish-like robot. The dimensions of the fish tail (the graphene-PVDF bimorph robot and the fish body (Expandable polystyrene) are 14 × 3 mm2 and 30 × 8 mm2, respectively. The fish-like robot moves from left to right at a speed of 5.02 mm s-1 applied the voltage of 0-13.0 V and the frequency of 0.4 Hz. f, The Figure extracted from Nano Energy 2025, 139, 110994. Schematic diagram of PVDF/MXene soft actuator mechanism. The display of soft actuators application. As illustrated in Figure R2, the actuator comprises a central carbon fiber layer serving as a rigid substrate, with polyvinylidene fluoride (PVDF) piezoelectric layers fabricated on either end. Deformation is achieved through the inverse piezoelectric effect of the PVDF material; the application of voltage to the PVDF layers induces axial strain (expansion or contraction). Given the actuator's multilayer composite structure (e.g., a symmetrical PVDF-carbon fiber-PVDF laminate), the central carbon fiber layer functions as a rigid substrate, thereby constraining deformation in proximity to the neutral axis. Consequently, stress propagation is impeded near the substrate interface, necessitating its transfer to the opposing end. This generates an asymmetric strain distribution across the upper and lower surfaces of the PVDF layers. Under voltage excitation, one surface of the PVDF layer elongates while the other contracts. Due to the stress boundary conditions imposed by the substrate, deformation is restricted near the rigid substrate surface. Stress is coupled through the layers and transmitted to the opposing surface of the PVDF layer, thereby inducing a greater bending motion (oscillatory deflection) across the entire actuator. Figure Redacted Figure R2 The Figure extracted from Smart Mater. Struct. 2025, 34, 035004. Electrical layout of the PVDF sensing actuator. Overview of electrical connections with the high voltage signals (Bias and Signal) located on the one side and the sensing layer connected to the ground side of the actuator. Electrical driving setup for the bimorph actuator showing the sensing electrodes isolated at the ground layer with adhesive. The device fabrication on a rigid SiO /Si substrate, as depicted in Figure R3, imposes inherent 2 limitations on the system's mechanical behavior. The rigid substrate acts as a significant constraint, exerting considerable mechanical influence on both the top and bottom P(VDF-TrFE) layers. Analogous to a piezoelectric actuator configuration, the polymer layer functions as the driving element, generating strain through the inverse piezoelectric effect upon the application of an electric field. The robust adhesive interface between the polymer and the substrate mirrors the rigid substrate found in piezoelectric actuators, effectively suppressing unproductive strain and facilitating the directional transfer of strain energy. However, disparities in interfacial constraints dictate that the stress transmission efficiency of the P(VDF-TrFE) layer is substantially lower downward (towards the substrate) compared to its upward transmission (towards the functional material), thereby influencing the overall device performance. Figure R3 Schematic Diagram of the P(VDF-TrFE)/Fe GaTe /P(VDF-TrFE) Device Structure 3 2 The P(VDF-TrFE) layer, forming a robust interfacial bond with the silicon substrate (Figure R4), experiences significantly restricted out-of-plane displacement, effectively anchoring it to the substrate surface. Consequently, when the P(VDF-TrFE) layer undergoes inverse piezoelectric deformation, the rigid substrate prevents the release of strain in the downward direction. This constraint results in a substantial conversion of the deformation into in-plane stress, either tensile or compressive. This stress is then efficiently transferred to the adjacent Fe GaTe layer via interfacial shear, facilitating 3 2 effective utilization of the strain energy (the Fe GaTe layer demonstrates close 3 2 bonding with the underlying P(VDF-TrFE) interface, as depicted in Figure R4). Fundamentally, these constraint conditions promote the preferential transfer of piezoelectric strain energy as shear stress along the interface, rather than allowing for its dissipation through unconstrained deformation, thereby enhancing the overall efficiency of strain transfer. Figure R4 a, Transmission electron microscopy image of the device's bottom surface. b, Interface image between Fe GaTe and bottom P(VDF-TrFE) on the device's bottom surface. 3 2 Analysis of lattice structure modifications in Fe GaTe , achieved through X-ray diffraction (XRD) 3 2 and Raman spectroscopy, corroborates the efficacy of stress transfer. As illustrated in Figure R5, the application of a bias polarization to the underlying ferroelectric polymer P(VDF-TrFE) induces deformation predicated on the inverse piezoelectric effect. Constrained by the rigid substrate, deformation at the P(VDF-TrFE)-substrate interface is suppressed, converting the strain energy within this region into substantial in-plane stress, which can be either tensile or compressive. This stress is then effectively transferred to the adjacent Fe GaTe thin film via interfacial shear. Raman 3 2 spectroscopy reveals systematic shifts in the characteristic Fe GaTe peaks; specifically, in-plane 3 2 tensile stress induces chemical bond elongation and a concomitant reduction in vibrational frequencies, manifesting as a redshift in Raman peaks. Conversely, in-plane compressive stress results in chemical bond contraction and increased vibrational frequencies, leading to a blueshift in Raman peaks. Complementary X-ray diffraction (XRD) analyses reveal systematic shifts in the diffraction peak positions of Fe GaTe , indicative of corresponding adjustments in the a-axis and c- 3 2 axis lattice parameters induced by the in-plane stress. These collective observations reflect the anisotropic strain response of the Fe GaTe lattice under the influence of the external electric field. 3 2 In summary, the consistent shifts observed in Raman peak positions and the systematic displacement of XRD diffraction angles demonstrate that in-plane stresses induced by the inverse piezoelectric effect of P(VDF-TrFE) effectively modulate the lattice parameters and interlayer coupling strength of Fe GaTe . This provides compelling evidence for the viability of stress transfer mechanisms 3 2 within two-dimensional material/ferroelectric polymer heterostructures. Figure R5 a, Raman spectra of the dual-gate device as a function of the bottom layer polarization voltage, and the Raman spectra were measured at 300 K. The Raman spectra of the dual-gate device are shown in the figure below. The insets show the variation of the A peak of Fe GaTe and the 1g 3 2 position of the β peak of P(VDF-TrFE) with the polarization voltage V , as well as the error bars for 2 five devices measured under the same conditions. b, XRD image of a device obtained at zero bias, the inset shows the variation of the in-plane lattice constant a and the out-of-plane lattice constant c with the bottom polarization voltage V . 2 Conversely, the mechanical environment of the top P(VDF-TrFE) layer differs significantly. Its bottom surface is bonded to the Fe GaTe /bottom P(VDF-TrFE)/substrate system, imposing 3 2 constraints, while its top surface remains a free interface. Under voltage excitation, this disparity renders the top layer more susceptible to out-of-plane relaxation, such as warping or bending. Consequently, a greater proportion of mechanical energy dissipates through volumetric deformation within the layer itself, rather than being converted into in-plane strain directed toward the Fe GaTe layer. This stems from insufficient constraints to effectively 3 2 suppress unproductive deformation, leading to a shift in the strained transfer mechanism from efficient shear coupling to less efficient bending deformation. This transition ultimately contributes to a substantial decline in overall driving performance. The distinct stress transfer mechanisms for the bottom and top P(VDF-TrFE) layers are schematically depicted in Figure R6. Figure R6 Schematic diagram of stress transfer during bottom gate P(VDF-TrFE) polarization(a) and top gate P(VDF-TrFE) polarization processes(b). Following the application of an electric field to polarize the P(VDF-TrFE) layer atop the heterojunction, X-ray diffraction (XRD) and Raman spectroscopy were employed to characterize the Fe GaTe layer, with the corresponding data presented in Figure R7. These analyses revealed no 3 2 discernible shift in either the Raman characteristic peak positions or the XRD diffraction peaks of Fe GaTe , irrespective of the applied polarization voltage magnitude. This absence of change 3 2 suggests that the strain generated by the top P(VDF-TrFE) layer was not effectively transmitted to the underlying Fe GaTe layer. This limitation likely stems from the constraint imposed on the 3 2 deformation of the top P(VDF-TrFE) layer by the rigid structure beneath it, encompassing the Fe₃GaTe₂ layer, the bottom P(VDF-TrFE) layer, and the substrate. Consequently, the stress induced by the inverse piezoelectric effect appears to be primarily dissipated through macroscopic deformation at the free surface (upper surface) of the top P(VDF-TrFE) layer, rather than propagating downwards to influence the Fe GaTe lattice parameters. This behavior, in contrast to 3 2 the observed polarization in the bottom layer, further supports the conclusion regarding the directionality and effectiveness of stress transmission pathways within the described heterojunction structure. Figure R7 a, XRD change curve of the upper layer P(VDF-TrFE) polarized device. The inset shows the Fe GaTe a axis and c axis as a function of polarization voltage. b, Raman change curve of the 3 2 upper layer P(VDF-TrFE) polarized device. The bottom layer of P(VDF-TrFE) functions as the primary active layer, effectively modulating the strain state within the Fe GaTe . Conversely, the mechanical contribution of the top P(VDF-TrFE) 3 2 layer is considered negligible. We acknowledge and appreciate the reviewers' diligent feedback, which has been instrumental in clarifying the mechanical mechanisms presented in this paper. In response, we have incorporated a more detailed discussion of these mechanisms, including the aforementioned mechanical analysis and supporting references, within the revised manuscript. We have added descriptions to the manuscript: “The P(VDF-TrFE) layer, forming a robust interfacial bond with the silicon substrate (Figure 1b and Supplementary Fig. 5a), experiences significantly restricted out-of-plane displacement, effectively anchoring it to the substrate surface. Consequently, when the P(VDF-TrFE) layer undergoes inverse piezoelectric deformation, the rigid substrate prevents the release of strain in the downward direction. This constraint results in a substantial conversion of the deformation into in-plane stress, either tensile or compressive. This stress is then efficiently transferred to the adjacent Fe GaTe layer via interfacial shear, facilitating 3 2 effective utilization of the strain energy. Fundamentally, these constraint conditions promote the preferential transfer of piezoelectric strain energy as shear stress along the interface, rather than allowing for its dissipation through unconstrained deformation, thereby enhancing the overall efficiency of strain transfer.)” (page 7, lines 187); “The observed asymmetry between the upper and lower P(VDF-TrFE) layers is attributed to the presence of the rigid silicon substrate. The rigid substrate acts as a significant constraint, exerting considerable mechanical influence on both the top and bottom P(VDF-TrFE) layers. Analogous to a piezoelectric actuator configuration, the polymer layer functions as the driving element, generating strain through the inverse piezoelectric effect upon the application of an electric field. The robust adhesive interface between the polymer and the substrate mirrors the rigid substrate found in piezoelectric actuators32, effectively suppressing unproductive strain and facilitating the directional transfer of strain energy. However, disparities in interfacial constraints dictate that the stress transmission efficiency of the P(VDF-TrFE) layer is substantially lower downward (towards the substrate) compared to its upward transmission (towards the functional material), thereby influencing the overall device performance.”(page 9, lines 252) and “Conversely, the mechanical environment of the top P(VDF-TrFE) layer differs significantly. Its bottom surface is bonded to the Fe GaTe /bottom P(VDF- 3 2 TrFE)/substrate system, imposing constraints, while its top surface remains a free interface. Under voltage excitation, this disparity renders the top layer more susceptible to out-of-plane relaxation, such as warping or bending. Consequently, a greater proportion of mechanical energy dissipates through volumetric deformation within the layer itself, rather than being converted into in-plane strain directed toward the Fe GaTe layer. This stems from insufficient constraints to effectively 3 2 suppress unproductive deformation, leading to a shift in the strained transfer mechanism from efficient shear coupling to less efficient bending deformation. This transition ultimately contributes to a substantial decline in overall driving performance.”(page 10, lines 266) Comment 2. Ferroelectric control of magnetic properties is still not convincing. In my original Comment 6, I questioned whether the observed magnetic modulation arises directly from ferroelectric polarization, or instead from the large applied voltages directly affecting Fe3GaTe2. Response 6 does not fully resolve my concern. I do not dispute the intrinsic ferroelectricity of PVDF in this work. And authors have Figure R11 demonstrate the hysteresis loop of this. However, whether the modulation of Fe3GaTe2 magnetism originates from ferroelectric polarization remains unproven. In Figures R8 and supplementary material Figure S7, the hysteresis loops associated with magnetic modulation are weak, continuous, and lack clear abrupt switching. Why don’t they follow the hysteresis loop of PVDF (R11)? This raises the possibility that the results may be indistinguishable from leakage induced “pseudoloops”. The examples authors give on continuous hysteresis loop in BTO, PTO, HZO are about ferroelectricity itself and don’t explain my concern. Such inconclusive evidence does not establish the causal link between ferroelectric switching and magnetic modulation, which is important. Response 2: We acknowledge the insightful suggestions from the reviewers. The magnetic modulation effect reported in this manuscript is attributed to ferroelectric polarization, rather than the direct influence of applied voltage on the Fe GaTe layer. This conclusion is primarily 3 2 substantiated by the following experimental observations: the persistence of the magnetic state modulation after the removal of the electric field indicates non-volatile behavior, suggesting its origin in the residual polarization of the ferroelectric material. Specifically, the residual polarization (Pr) of the P(VDF-TrFE) film remains after the electric field is removed, thus enabling a sustained modulation of the magnetic layer. Furthermore, the observed evolution of the magnetic hysteresis loops is consistent with this mechanism, providing further support for the dominant role of ferroelectric polarization in the observed effects. Within the device, P(VDF-TrFE) undergoes ferroelectric polarization when subjected to an electric field. The resulting remanent polarization induces a non-uniform stress field that, through interfacial coupling, generates elastic lattice distortions within the Fe GaTe layer. This lattice 3 2 deformation, in turn, modulates the magnetic anisotropy of Fe GaTe via magnetoelastic coupling, 3 2 leading to reconfigurable shifts in its easy magnetization axis. Crucially, the ferroelectric polarization of P(VDF-TrFE) is nonvolatile, meaning it retains its polarization state and corresponding stress field even after the removal of the external electric field. Consequently, the modulation of Fe GaTe 's magnetic properties also exhibits nonvolatile behavior, as illustrated in 3 2 Figure R8. This mechanism enables nonvolatile magnetic state writing and retention predicated on ferroelectric remanent polarization. Figure R8 Following voltage polarization, the device exhibited a time-varying curve of R . xy The observed morphological differences between the polarization-electric field (P-E) loops of P(VDF-TrFE) measured at varying voltages and the magnetically modulated hysteresis loops arise from their fundamentally disparate physical origins and measurement methodologies(Figure R9). Specifically, the P-E loop reflects the dynamic response of the ferroelectric material, continuously monitoring polarization strength under a time-varying electric field. The characteristic steep reversal observed in P-E loops is indicative of the cooperative switching dynamics of ferroelectric domains under an applied electric field. In contrast, the magnetic modulation hysteresis loop, under the experimental conditions described, is not derived from a dynamic P-E measurement. Instead, it is constructed by applying a series of discrete, pulsed polarization voltages to the P(VDF-TrFE) film, each maintained for a defined duration before removal. The non-volatile ferroelectric polarization of P(VDF-TrFE) ensures that the residual polarization (Pr) persists after each pulse, enabling sustained control over the magnetism of Fe GaTe . Therefore, given that these hysteresis loops arise 3 2 from distinct physical processes and disparate measurement protocols, a direct comparison or combined discussion is not appropriate. Figure R9 a, Ferroelectric hysteresis loops of multiferroic heterostructure P(VDF-TrFE)/Fe GaTe 3 2 at different measurement voltages. Figure R10a illustrates the measured residual polarization (Pr) of the device as a function of varying polarization pulse voltages. The observed behavior reveals a characteristic V-shaped hysteresis. Beginning from an initial 0 V state, the residual polarization increases progressively with increasing positive pulse amplitude, reflecting the gradual reversal of ferroelectric domains aligned with the applied electric field. This saturation occurs at +10 V. As the voltage decreases from +10 V, the residual polarization does not retrace its initial path due to energy barriers and pinning effects, such as interfacial charge trapping, which impede the complete recovery of partial polarization states. Application of a negative voltage pulse initiates the nucleation and growth of oppositely oriented ferroelectric domains, counteracting the initial positive polarization and leading to a gradual decrease in the net residual polarization. Reverse saturation is achieved at -10 V. Subsequently, during the decrease of the negative voltage, domain wall pinning and internal depolarization fields cause the recovery path of the residual polarization to be higher than its trajectory during the previous voltage decrease, resulting in an asymmetric V-shaped hysteresis loop. Figure R10 a, The trend of residual polarization intensity as a function of pulse voltage, with each pulse voltage value tested 10 times. b, R of the dual-gate device as a function of the bottom-layer xy P(VDF-TrFE) polarization voltage. The residual polarization intensity (Pr) curve independently measured for P(VDF-TrFE) consistently exhibits positive values. This is attributable to the definition of Pr as the vertical coordinate of the electric hysteresis loop at zero electric field, where the sign is contingent upon the initial polarization direction. Consequently, regardless of the applied polarization voltage's polarity, Pr is invariably measured with a single sign, while its absolute value demonstrates a V-shaped variation as a function of voltage polarity. In contrast, within the P(VDF-TrFE)/Fe GaTe 3 2 heterojunction device, the mechanism underlying magnetic control stems from interface charge effects induced by ferroelectric polymer polarization. The application of a positive polarization voltage orients the P(VDF-TrFE) polarization to drive interfacial charge accumulation, modulating the carrier concentration in Fe GaTe via charge effects and consequently suppressing its magnetism. 3 2 Conversely, a negative polarization voltage reverses the P(VDF-TrFE) polarization, inducing interfacial charges of opposite sign and enhancing the magnetism of Fe GaTe . Therefore, while the 3 2 residual polarization strength of P(VDF-TrFE) consistently manifests a positive value, its polarization direction - corresponding to the absolute magnitude and trend of Pr – directly dictates the sign and concentration of interfacial charges(Figure R10b). This enables non-volatile, bidirectional regulation of magnetism. Consequently, the hysteresis loop observed in magnetic regulation exhibits a strong correlation with the V-shaped hysteresis curve of residual polarization strength, providing compelling evidence for the effective modulation of ferromagnetic properties by ferroelectric polarization. We have added a description of the device's non-volatility in the article. “Specifically, as illustrated in the Supplementary Fig 27, the device maintains its properties for 120 hours following voltage polarization and subsequent removal of the electric field.”(page 22, lines 605) and “The residual polarization intensity (Pr) of the device was measured under different polarization pulse voltages (Supplementary Fig. 8). The magnetically modulated hysteresis loop and the V-shaped hysteresis curve of the residual polarization intensity exhibited highly consistent trends, strongly confirming the effective modulation of ferromagnetic properties by ferroelectric polarization (Supplementary Note 3).”(page 11, lines 293) Reviewers’ Comments: Reviewer #3 (Remarks to the Author): The authors have addressed my questions, revised the figures, and added new content. I believe the manuscript is now suitable for publication. 1 Response to Reviewer #3: The authors have addressed my questions, revised the figures, and added new content. I believe the manuscript is now suitable for publication. Our reply: We are deeply grateful to the reviewers for their insightful and constructive feedback, which has been invaluable in strengthening this manuscript. 2"}, {"round": 3, "reviewer_comments": {"reviewer_3": "The authors have addressed my questions, revised the figures, and added new content. I believe the manuscript is now suitable for publication."}, "author_response": ""}]

Decision letter