Multilevel resistance states in van der Waals multiferroic tunnel junctions based on In₂Se₃/CuInP₂S₆ ferroelectric heterostructures

Abstract

Multiferroic tunnel junction (MFTJ) integrating magnetic electrodes with semiconducting ferroelectrics (FEs) as central tunneling barrier holds great promise for next-generation nonvolatile memory. The emergence of room-temperature van der Waals ferromagnets (e.g., Fe₃GaTe₂) and FEs (e.g., α-In₂Se₃, CuInP₂S₆) renders the possibility of all-vdW MFTJ under ambient conditions. Here, we employ first-principles calculations combined with nonequilibrium Green’s function methods to explore spin-dependent transport in Fe₃GaTe₂/α-In₂Se₃/CuInP₂S₆/Fe₃GaTe₂ junctions. The α-In₂Se₃/CuInP₂S₆ dual FE heterojunction introduces an additional degree of freedom for band alignment and interfacial charge modulation under external electric field, dramatically enhancing tunneling electroresistance. We find that polarization reversal leads to a giant tunneling electroresistance exceeding 6.2 × 10⁴ %, far surpassing conventional tunnel junction with a single barrier. Furthermore, adjusting the relative magnetization of Fe₃GaTe₂ electrodes yields a colossal tunneling magnetoresistance up to 5.8 × 10⁶ % upon polarization reversal. These results demonstrate the feasibility of multiple resistance states in MFTJ through coupled electric and magnetic field control, establishing ferroelectric heterojunctions as a powerful route toward high-density, multifunctional memory technologies.

Graphical abstract

Keywords

multiferroic tunnel junctions / ferroelectric heterojunctions / tunneling electroresistance / tunneling magnetoresistance / transport property

1 Introduction

The relentless demand for faster, denser, and more energy-efficient data storage has spurred intensive research into emerging non-volatile memory technologies. Among these, multiferroic tunnel junctions (MFTJs), which integrate a ferroelectric (FE) tunnel barrier with magnetic electrodes, are particularly appealing because they directly couple electric and magnetic order parameters [1−3]. This dual functionality induces both tunneling electroresistance (TER) and tunneling magnetoresistance (TMR) within a single device [4−6], thereby enabling multilevel resistance states and offering a pathway toward ultrahigh storage density. The TER effect arises from polarization-controlled modulation of the tunneling barrier [7−10], typically due to the incomplete screening of polarization charges at the electrode/barrier interface. Traditional strategies to enhance TER, such as employing strongly asymmetric electrodes [11−13] or tailoring interfacial properties [14−17], have achieved only moderate improvements and are constrained by intrinsic trade-offs. For instance, increasing electrode asymmetry can boost TER but often degrades polarization switchability, whereas interface engineering demands atomically precise epitaxial control, posing significant challenges for large-scale integration.

A promising strategy to overcome these trade-offs is to actively modulate the FE barrier [18]. FE heterojunctions can intrinsically alter their band structure upon polarization reversal, enabling large TER without relying on electrode asymmetry [19, 20]. However, in conventional three-dimensional (3D) FEs, strong bonding across the adjacent layers constrains stable, non-volatile switching between distinct polarization states [21]. The emergence of two-dimensional (2D) van der Waals (vdW) FEs, such as CuInP₂S₆ [22] and α-In₂Se₃ [23], provides a compelling solution. Their weak interlayer coupling supports multiple stable dipole configurations with comparable energies, allowing robust polarization switching and pronounced band-structure modulation [24−27]. In particular, the middle heterojunction barriers in MFTJs formed from dissimilar vdW FEs [28] introduce an intrinsic structural asymmetry, which amplifies the polarization-dependent potential profile and yields giant TER effects that surpass those attainable in conventional homojunctions [13, 21]. However, the modulation of spin-injection efficiency across the FEs by polarization reversal remains elusive and has yet to be systematically investigated.

Here, we construct MFTJs that integrate dual-type vdW FE heterojunctions (α-In₂Se₃/CuInP₂S₆) with two vdW ferromagnetic Fe₃GaTe₂ electrodes. First-principles and nonequilibrium Green’s function (NEGF) calculations reveal that the reversal of the FE polarization in the central FEs layers strongly modulates the band alignment of the heterojunction barrier of the junction, thereby exerting a profound influence on electron transport. As a result, control of the polarization in α-In₂Se₃/CuInP₂S₆ heterojunction yields an ultrahigh TER exceeding 6.2 × 10⁴ %, while control of the relative alignment of magnetic ordering in the Fe₃GaTe₂ electrodes delivers a colossal TMR approaching 5.8 × 10⁶ %. This synergistic interplay between FE heterojunctions and vdW ferromagnets enables multiple, well-separated resistance states, offering a robust platform for next-generation, multifunctional, and high-density non-volatile memory technologies.

2 Calculation methods

The atomic structures were optimized using density functional theory (DFT), as implemented in the DS-PAW package [29]. The exchange–correlation effects were described using the generalized gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof (PBE). [30, 31]. A plane-wave cutoff energy of 450 eV was adopted, and a 10 Å vacuum layer was applied perpendicular to the slab to minimize the interaction between adjacent periodic images. Atomic coordinates were optimized until the atomic forces converged to 0.02 eV·Å⁻¹, respectively. Long-range dispersion forces were treated with the DFT-D3 correction scheme [32]. A 4 × 4 × 1 Monkhorst−Pack k-point grid was employed for Brillouin-zone integration. Spin-dependent transport through the Fe₃GaTe₂/α-In₂Se₃/CuInP₂S₆/Fe₃GaTe₂ heterostructure was evaluated using the Nanodcal code [33, 34], which combines DFT with the NEGF formalism. The Brillouin zone for transport calculations was sampled using a 3 × 3 × 101 Monkhorst−Pack grid. The atomic basis was truncated with a cutoff energy of 80 Hartree for the transport calculations. The total energy was converged to within 10⁻⁶ eV.

The transmission coefficient can be expressed as

(1)T_{\sigma }={{\displaystyle \sum }}_{{\mathit{k}}_{//}}{T}_{\sigma }\left({\mathit{k}}_{//},E_{\mathrm{F}}\right),

where T_{\sigma }\left({\mathit{k}}_{//},E_{\mathrm{F}}\right) is the transmission coefficient for a spin σ in the transverse Bloch wave vector {\mathit{k}}_{//} which can be given by

(2)\begin{array}{rl}& T_{\sigma }\left({\mathit{k}}_{//},E_{\mathrm{F}}\right)\\ & =Tr\left[{\Gamma }_L\left({\mathit{k}}_{//},E_{\mathrm{F}}\right)G^r\left({\mathit{k}}_{//},E_{\mathrm{F}}\right){\Gamma }_R\left({\mathit{k}}_{//},E_{\mathrm{F}}\right)G^a\left({\mathit{k}}_{//},E_{\mathrm{F}}\right)\right].\end{array}

Here, G^rand G^a represent the retarded and advanced Green’s functions respectively, while {\Gamma }_L and {\Gamma }_R are the linewidth functions.

The TMR ratio under equilibrium (no bias voltage) is calculated using

(3)\mathrm{T}\mathrm{M}\mathrm{R}={\displaystyle \frac{T_{\mathrm{P}}-T_{\mathrm{A}\mathrm{P}}}{T_{\mathrm{A}\mathrm{P}}}},

where T_P and T_AP denote the total transmission of the MFTJ for parallel (P) and antiparallel (AP) alignment of the electrode magnetizations, respectively. Similarly, the TER ratio was evaluated from the total transmission coefficients under different FE states:

(4)\mathrm{T}\mathrm{E}\mathrm{R}={\displaystyle \frac{T_{max}-T_{min}}{T_{min}}},

where T_max and T_min are the total transmission coefficients of MFTJ with different FE polarization states, achieved by reversing the polarization of the barrier layer.

3 Results and discussion

The structural and electronic properties of the FE barrier layers, α-In₂Se₃ and CuInP₂S₆, were first investigated. Among representative two-dimensional FEs, both materials exhibit robust out-of-plane spontaneous polarization [22, 23], making them promising candidates for FE barriers. CuInP₂S₆ crystallizes in a van der Waals monolayer structure consisting of a sulfur framework, with Cu and In atoms occupying octahedral sites and P–P dimers arranged in a triangular lattice [Fig. 1(a)]. The two FE phases with opposite polarizations are depicted in Fig. 1(b). The ferroelectricity of CuInP₂S₆ arises primarily from the displacement of Cu atoms from their octahedral centers, giving rise to spontaneous polarization. The electronic band structure of the monolayer, obtained within the PBE approximation, is shown in Fig. 1(c). The conduction-band minimum (CBM) and valence-band maximum (VBM) are both located at the Γ point, resulting in a direct band gap of 1.59 eV. Moreover, the work functions of the two polar surfaces differ significantly [Fig. 1(d)], suggesting distinct band alignments and interfacial contact properties when coupled to other materials.

In contrast, monolayer α-In₂Se₃ is composed of five atomic planes [Figs. 2(a) and (b)]. The non-centrosymmetric arrangement of Se atoms in the middle plane lifts inversion symmetry, yielding two energetically degenerate states with opposite polarization orientations. Unlike CuInP₂S₆, the CBM of α-In₂Se₃ is located at the Γ point, while the VBM lies along the Γ–M line, giving rise to an indirect band gap of 1.13 eV [Fig. 2(c)]. Similar to CuInP₂S₆, the two polar surfaces of α-In₂Se₃ exhibit different work functions [Fig. 2(d)], implying asymmetric interfacial band alignment when integrated with other materials.

The optimized lattice constants of CuInP₂S₆ and monolayer α-In₂Se₃ are 6.108 Å and 4.070 Å, respectively. To construct the CuInP₂S₆/α-In₂Se₃ heterostructure, the CuInP₂S₆ lattice was reconstructed into a 2 × 2 supercell and similarly the α-In₂Se₃ lattice into a 3 × 3 supercell, yielding a negligible lattice mismatch of only 0.05%. With monolayer α-In₂Se₃ being stacked on CuInP₂S₆, four distinct FE polarization configurations emerge, defined by the relative orientation of the FE vectors in both layers as FE-left, FE-right, AFE-head (antiferroelectric polarization head-to-head configuration) and AFE-tail (antiferroelectric polarization Tail-to-Tail configuration) (Fig. 3). In addition, to evaluate the polarization stability and switching barrier of the CuInP₂S₆/α-In₂Se₃ heterostructure in different polarization states, we performed nudged elastic band (NEB) calculations to simulate the kinetic pathway of polarization switching between these states [35]. During the ferroelectric polarization switching process, the primary motion involves the Cu atomic layer and the intermediate Se atomic layer. The activation barrier against direct shifting of Cu atoms are 0.226 eV per Cu atom or 0.247 per Cu atom, and the activation barrier of the central Se layer are 0.721 eV per Se atom, which are consistent with those reported in the literature [36, 23]. These polarization states critically shape the electronic structure of the whole junction, altering both band alignment and the evolution of the electrostatic potential. As shown by the projected band structures in Fig. 4, the relative positions of the conduction and valence bands vary substantially across the four configurations, producing distinct interfacial band offsets. Taking the distribution of the conduction bands as an example, we note that in the FE-left ferroelectric polarization state, the conduction band minimum of CuInP₂S₆ lies 0.35 eV below that of In₂Se₃. Upon switching the ferroelectric polarization to FE-right, AFE-head, and AFE-tail, the band alignment flips, and the conduction band minimum of CuInP₂S₆ is located 0.96 eV, 0.55 eV, and 0.71 eV below that of In₂Se₃, respectively. Such polarization-induced band offset is expected to significantly modify the tunneling barriers when combined with the electrodes on both sides, thereby exerting a decisive influence on the spin-dependent transport properties of the device.

Based on the excellent magnetic properties of Fe₃GaTe₂ and the robust FE properties of CuInP₂S₆ and monolayer α-In₂Se₃, we designed a vdW MFTJ with the integrated structure of Fe₃GaTe₂/α-In₂Se₃/CuInP₂S₆/Fe₃GaTe₂ (Fig. 5). The electrodes on both sides are symmetric Fe₃GaTe₂ layers, while the central scattering region comprises the α-In₂Se₃/CuInP₂S₆ FE heterojunction, together with two slabs of Fe₃GaTe₂ buffer layer. The FE polarization of α-In₂Se₃/CuInP₂S₆ FE heterojunction can be switched by external electric field, while the magnetization of Fe₃GaTe₂ electrodes can be reversed via external magnetic field. Owing to the intrinsic electronic differences between α-In₂Se₃ and CuInP₂S₆, the two FE barriers generate a markedly asymmetric Coulomb potential across the junction (Fig. 5). The continuous modulation of the built-in electric field by FE polarization, illustrated by the red dashed line in Fig. 6, directly alters the tunneling characteristics of the barrier. This polarization-driven control of the electrostatic landscape enables multiple non-volatile resistive states in the proposed vdW MFTJ.

The two Fe₃GaTe₂ electrodes adopt two configurations with relative alignment of P and AP magnetization, while the α-In₂Se₃/CuInP₂S₆ bilayer accommodates four polarization states, FE-left, FE-right, AFE-head, and AFE-tail. The combination of ferroic orders yields eight distinct switching states in the MFTJ. The calculated electron transmittance, TMR, and TER for these states are summarized in Table 1. Across all polarization states, the transmittance in the P configuration is significantly higher than in the AP configuration, giving rise to exceptionally large TMR ratios. Notably, the AFE-tail state delivers the maximum TMR of 5.8 × 10⁶ %, while the AFE-head state yields the minimum value of 4.4 × 10⁴ %. This giant TMR originates from the high spin polarization of bulk Fe₃GaTe₂. In the AFE-tail state, the transmission coefficient is minimal for both P and AP magnetizations, and it was chosen as the reference for TER evaluation. By comparison, the AFE-head state shows the highest transmittance, resulting in TER ratios of 372% (P) and 6.2 × 10⁴ % (AP). Crucially, reversible switching between different states via an external electric field enables dynamic control of the transport response. The coexistence of giant TMR and TER for fully vdW MFTJ underscores its potential as a platform for next-generation spintronic devices.

To investigate how FE polarization and magnetization affect electron transport, the k-resolved transmission coefficient are calculated in the two-dimensional Brillouin zone for the Fe₃GaTe₂/α-In₂Se₃/CuInP₂S₆/Fe₃GaTe₂ MFTJ. Figures 7(a)–(h) show the transmission maps for the P configuration, while Figs. 7(i)–(p) present the spin-resolved spectra for the AP configuration. At the P state, the spin-up channel exhibits a broad region of high transmission throughout the Brillouin zone, in stark contrast to the spin-down channel and both spin channels at the AP state, which are dominated by low-transmission regions. As a result, electron tunneling is strongly suppressed at the AP state, accounting for the giant TMR observed. Comparison among the FE polarization states reveals pronounced asymmetry, the AFE-head configuration supports the broadest and strongest transmission distribution over the whole 2D Brillouin zone, whereas the AFE-tail configuration produces the narrowest and weakest, leading to the maximum TER effect. These results reveal that electron transport in the junction can be effectively tuned through electric-field-controlled switching of the α-In₂Se₃/CuInP₂S₆ bilayer polarization.

To analyze the spatial and energy distribution of states in the central scattering region, we calculated the projected density of states (PDOS) on the (E,z) plane, with E and z denoting energy and position along the transport direction, respectively. As shown in Fig. 8 and Fig. 9, the PDOS located at the middle barrier formed by monolayers α-In₂Se₃ and CuInP₂S₆ is nearly zero around the Fermi level, confirming that both FE layers act as excellent insulators and form an ideal tunnel barrier. This suppresses parasitic conduction channels and establishes the essential condition for realizing TER and TMR. Specifically, the polarization switching in the α-In₂Se₃ and CuInP₂S₆ layers further modulates the band structure of the FE barrier. While the DOS profiles of the Fe₃GaTe₂ electrodes remain nearly unchanged across the four polarization states, the DOS distribution within the α-In₂Se₃/CuInP₂S₆ bilayer is strongly altered. The polarization reversal modifies the band alignment of α-In₂Se₃/CuInP₂S₆ bilayer, thereby tuning the effective barrier height for carriers. For example, in the AFE-head state [Fig. 8(e)], the Fermi level lies closer to the CBM, giving rise to a lower barrier and higher transmission. In the AFE-tail state [Fig. 8(g)], the Fermi level shifts farther away, effectively increasing the barrier height and reducing the tunneling probability, which produces the pronounced TER effect. Similarly, the FE-left configuration exhibits a lower potential barrier than the AFE-Tail state, yielding higher transmission in the FE-left case. Hence, the PDOS reveals that ferroelectric polarization switching shifts the Fermi level relative to the ferroelectric conduction-band edge, leading to distinct barrier heights for the four configurations. In particular, the FE-left and AFE-head states exhibit a markedly lower Schottky barrier, which reduces the effective tunnel resistance and enhances the transmission coefficient. Conversely, the FE-right and AFE-tail states show a higher barrier, suppressing electron tunneling. This polarization-dependent barrier variation will also directly influences the spin-polarized current, as a lower barrier allows more efficient injection of spin-polarized carriers from the Fe₃GaTe₂ electrodes.

Furthermore, the spin-up PDOS dominates near the Fermi level in both electrodes for the P configuration, making spin-up electrons the primary tunneling carriers. Owing to spin conservation during tunneling, these majority carriers encounter matched spin polarization across the barrier, resulting in efficient transmission. By contrast, spin-down electrons form the minority channel, where the PDOS mismatch strongly suppresses tunneling. At the AP configuration (Fig. 9), the majority and minority spin states are opposite in the two electrodes, hence electrons of either spin experience a mismatch. This leads to a dramatic suppression of transmission compared to the P state. These results indicate that the pronounced difference in spin-resolved DOS between the P and AP configurations gives rise to the giant TMR, where efficient tunneling of spin-up electrons in the P state versus simultaneous suppression of both spin channels in the AP state.

Previous work on CrSe₂/monolayer CuInP₂S₆/CrSe₂ tunnel junctions demonstrated a TER exceeding 120% upon switching between FE and anti-FE states of CuInP₂S₆ [37]. However, because its polarization reversal induces only minor changes in the interfacial band structure, the attainable TER is intrinsically limited , making it difficult to achieve large resistance modulation with a single FE barrier. To address this challenge, a six-state MFTJs based on bilayer α-In₂Se₃ are proposed based on the ferroelectric transitioning from antiferroelectric to ferroelectric phase [38−40]. By controlling the magnetic alignment of Fe₃GaTe₂ electrodes, they reported a giant TMR , together with a high TER arising from polarization switching of the bilayer α-In₂Se₃. It should be noted that the structural symmetry, however, constrained the TER. Introducing interfacial asymmetry with a single h-BN spacer increased the TER to 1.5 × 10³ %. To actively engineer interfacial asymmetry for enhanced TER in practical devices, one must manipulate the electrostatic boundary conditions at the top and bottom electrode/barrier interfaces. In our previous work [13], an asymmetric Fe₃GaTe₂/bilayer α-In₂Se₃/Fe₃GeTe₂ junction achieved a TER of 1.2 × 10³ %, which was further enhanced threefold to ~3.0 × 10³ % by inserting an h-BN layer. Here, we demonstrate a qualitatively different approach by employing dual-type 2D FE monolayer of α-In₂Se₃ and CuInP₂S₆ to form a FE heterobarrier. This design yields an ultra-high TER of 6.2 × 10⁴ % and a giant TMR of 5.8 × 10⁶ %, giving access to eight distinct resistance states, exceeding the performance of previously reported devices by more than an order of magnitude. The dramatic improvement originates from the strongly asymmetric electrostatic potential inherent to the α-In₂Se₃/CuInP₂S₆ heterojunction. When coupled with FE polarization switching, this built-in asymmetry drives large modulations of the effective barrier height, enabling a step-change increase in TER and establishing a robust route toward high-performance vdW spintronic devices. The MFTJ can be experimentally constructed by layer-by-layer stacking of Fe₃GaTe₂/α-In₂Se₃/CuInP₂S₆/Fe₃GaTe₂ multilayered heterojunctions via mechanical exfoliation and transfer methods, with BN as the protective layer [41]. Fe₃GaTe₂-based magnetic tunnel junctions show experimental TMR of 122%–210% far below theoretical predictions [42, 43] and TER up to 10⁷ far higher than theoretical predictions [24]. This gap is attributed to idealized interfaces in models. The real defects and roughness break tunneling coherence and reduce spin-polarized transport. Moreover, actual electrode spin polarization is likely lower than theory. Nevertheless, such imperfections can induce asymmetric potentials that enhance TER.

Fe₃GaTe₂ is a transition-metal-based material that exhibits relatively strong spin−orbit coupling (SOC). As shown in Table 3, including SOC has little effect on transmission in the parallel magnetic configuration. In the antiparallel magnetic configuration, however, transmission increases significantly. This enhancement can be attributed to spin-flip processes induced by SOC within the barrier layer, which open additional transmission channels in vdW MTJs under antiparallel alignment. Consequently, the TMR as listed in Table 3 decreases by there orders of magnitude but remains very high, up to 10³ %. Meanwhile, although the TER decreased by just one order of magnitude, it remains at the exceedingly high level of 8.48×10³ %, indicating that SOC does not affect the main conclusions of this study.

4 Conclusion

In summary, we have designed and theoretically investigated a fully vdW MFTJ composed of Fe₃GaTe₂ ferromagnetic electrodes and an α-In₂Se₃/CuInP₂S₆ FE heterojunction barrier, using first-principles calculations combined with NEGF methods. The α-In₂Se₃/CuInP₂S₆ interface introduces a pronounced intrinsic asymmetry in the electrostatic potential, which enables substantial modulation of the tunneling barrier upon polarization reversal. This results in an unprecedented TER ratio of 6.2 × 10⁴ %, far exceeding that of conventional single-barrier FTJ. Simultaneously, the strong spin polarization of Fe₃GaTe₂ gives rise to a colossal tunneling magnetoresistance (TMR) of 5.8 × 10⁶ % between the P and AP magnetization configurations. The coexistence of four FE and two magnetic configurations yields eight distinct and stable resistance states, demonstrating the feasibility of multilevel, non-volatile data storage within a single vdW junction. Compared with previously reported vdW MFTJs, this heterostructure achieves more than an order-of-magnitude enhancement in TER, highlighting the critical role of FE heterojunction engineering in boosting device performance. Our results establish FE heterobarriers as an effective route to engineer asymmetric potential landscapes and achieve coupled electric–magnetic control of charge transport in vdW spintronic devices, providing a promising pathway toward next-generation high-density, multifunctional, and low-power nonvolatile memory and spintronic devices.

References

[1] M. Y. Zhuravlev , R. F. Sabirianov , S. S. Jaswal , and E. Y. Tsymbal , Giant electroresistance in ferroelectric tunnel junctions, Phys. Rev. Lett. 94(24), 246802 (2005)

[2] M. Gajek , M. Bibes , S. Fusil , K. Bouzehouane , J. Fontcuberta , A. Barthélémy , and A. Fert , Tunnel junctions with multiferroic barriers, Nat. Mater. 6(4), 296 (2007)

[3] J. P. Velev , C. G. Duan , J. D. Burton , A. Smogunov , M. K. Niranjan , E. Tosatti , S. S. Jaswal , and E. Y. Tsymbal , Magnetic tunnel junctions with ferroelectric barriers: Prediction of four resistance states from first principles, Nano Lett. 9(1), 427 (2009)

[4] V. García , S. Fusil , K. Bouzehouane , S. Enouz-Vedrenne , N. D. Mathur , A. Barthélémy , and M. Bibes , Giant tunnel electroresistance for non-destructive readout of ferroelectric states, Nature 460(7251), 81 (2009)

[5] E. Y. Tsymbal and H. Kohlstedt , Tunneling across a ferroelectric, Science 313(5784), 181 (2006)

[6] M. Y. Zhuravlev , S. Maekawa , and E. Y. Tsymbal , Effect of spin-dependent screening on tunneling electroresistance and tunneling magnetoresistance in multiferroic tunnel junctions, Phys. Rev. B 81(10), 104419 (2010)

[7] D. Pantel and M. Alexe , Electroresistance effects in ferroelectric tunnel barriers, Phys. Rev. B 82(13), 134105 (2010)

[8] A. Chanthbouala , A. Crassous , V. Garcia , K. Bouzehouane , S. Fusil , X. Moya , J. Allibe , B. Dlubak , J. Grollier , S. Xavier , C. Deranlot , A. Moshar , R. Proksch , N. D. Mathur , M. Bibes , and A. Barthélémy , Solid-state memories based on ferroelectric tunnel junctions, Nat. Nanotechnol. 7(2), 101 (2012)

[9] A. Crassous , V. Garcia , K. Bouzehouane , S. Fusil , A. H. G. Vlooswijk , G. Rispens , B. Noheda , M. Bibes , and A. Barthélémy , Giant tunnel electroresistance with PbTiO₃ ferroelectric tunnel barriers, Appl. Phys. Lett. 96(4), 042901 (2010)

[10] Z. Xi , J. Ruan , C. Li , C. Zheng , Z. Wen , J. Dai , A. Li , and D. Wu , Giant tunnelling electroresistance in metal/ferroelectric/semiconductor tunnel junctions by engineering the Schottky barrier, Nat. Commun. 8(1), 15217 (2017)

[11] Z. Ma , Q. Zhang , and N. Valanoor , A perspective on electrode engineering in ultrathin ferroelectric heterostructures for enhanced tunneling electroresistance, Appl. Phys. Rev. 7(4), 041316 (2020)

[12] R. Soni , A. Petraru , P. Meuffels , O. Vavra , M. Ziegler , S. K. Kim , D. S. Jeong , N. A. Pertsev , and H. Kohlstedt , Giant electrode effect on tunnelling electroresistance in ferroelectric tunnel junctions, Nat. Commun. 5(1), 5414 (2014)

[13] R. Zhang , R. Jiao , Z. Fu , H. Yuan , J. He , L. Shen , X. Liao , Y. Zhou , and J. Yuan , Multilevel resistance states in van der Waals multiferroic tunnel junctions with asymmetric electrodes, Phys. Rev. B 111(15), 155414 (2025)

[14] J. D. Burton and E. Y. Tsymbal , Prediction of electrically induced magnetic reconstruction at the manganite/ferroelectric interface, Phys. Rev. B 82(16), 161407(R) (2010)

[15] V. García and M. Bibes , Ferroelectric tunnel junctions for information storage and processing, Nat. Commun. 5(1), 4289 (2014)

[16] K. Ao , L. Kuang , J. Zhe , Y. Li , W. Gan , L. Li , Z. Tao , and C. Yan, , Multifaceted frontiers of two-dimensional materials: from controlled synthesis to multifunctional applications, Nano (2026)

[17] S. Lyu , X. Long , Y. Yang , W. Wei , Y. Chen , H. Xie , B. Nie , B. Wang , Y. Wang , P. Jiang , T. Gong , Y. Wang , and Q. Luo, , Enhanced electro‐resistance and tunable asymmetric depolarization behavior in Hf_0.5Zr_0.5O₂ ferroelectric tunnel junction by bottom oxide interfacial layer, Adv. Electron. Mater. 11(3), 2400466 (2025)

[18] Z. Wen and D. Wu , Ferroelectric tunnel junctions: modulations on the potential barrier, Adv. Mater. 32(27), 1904123 (2020)

[19] Q. Wu , L. Shen , M. Yang , J. Zhou , J. Chen , and Y. P. Feng , Giant tunneling electroresistance induced by ferroelectrically switchable two-dimensional electron gas at nonpolar BaTiO₃/SrTiO₃ interface, Phys. Rev. B 94(15), 155420 (2016)

[20] K. F. Luo , Z. Ma , D. Sando , Q. Zhang , and N. Valanoor , Hybrid ferroelectric tunnel junctions: state of the art, challenges, and opportunities, ACS Nano 19(7), 6622 (2025)

[21] J. Ding , D. F. Shao , M. Li , L. W. Wen , and E. Y. Tsymbal , Two-dimensional antiferroelectric tunnel junction, Phys. Rev. Lett. 126(5), 057601 (2021)

[22] A. Belianinov , Q. He , A. Dziaugys , P. Maksymovych , E. Eliseev , A. Borisevich , A. Morozovska , J. Banys , Y. Vysochanskii , and S. V. Kalinin , CuInP₂S₆ Room Temperature Layered Ferroelectric, Nano Lett. 15(6), 3808 (2015)

[23] W. Ding , J. Zhu , Z. Wang , Y. Gao , D. Xiao , Y. Gu , Z. Zhang , and W. Zhu , Prediction of intrinsic two-dimensional ferroelectrics in In₂Se₃ and other III₂-VI₃ van der Waals materials, Nat. Commun. 8(1), 14956 (2017)

[24] J. Wu , H. Y. Chen , N. Yang , J. Cao , X. Yan , F. Liu , Q. Sun , X. Ling , J. Guo , and H. Wang , High tunnelling electroresistance in a ferroelectric van der Waals heterojunction via giant barrier height modulation, Nat. Electron. 3(8), 466 (2020)

[25] G. Feng , Y. Liu , Q. Zhu , Z. Feng , S. Luo , C. Qin , L. Chen , Y. Xu , H. Wang , M. Zubair , K. Qu , C. Yang , S. Hao , F. Yue , C. Duan , J. Chu , and B. Tian , Giant tunnel electroresistance through a van der Waals junction by external ferroelectric polarization, Nat. Commun. 15(1), 9701 (2024)

[26] W. Yang , Y. Xu , S. Li , J. Han , X. Lin , and W. Zhao , Large and multistate magnetoresistance in 2D van der Waals multiferroic tunnel junctions, Sci. China Mater. 68(5), 1622 (2025)

[27] X. Pan , Y. Li , B. Cheng , S. J. Liang , and F. Miao, , 2D materials for intelligent devices, Sci. China Phys. Mech. Astron. 66(11), 117504 (2023)

[28] A. Xie , H. Hao , C. S. Liu , X. Zheng , L. Zhang , and Z. Zeng , Giant tunnel electroresistance in two-dimensional ferroelectric tunnel junctions constructed with a Sc₂CO₂/In₂Se₃ van der Waals ferroelectric heterostructure, Phys. Rev. B 107(11), 115427 (2023)

[29] P. E. Blöchl , Projector augmented-wave method, Phys. Rev. B 50(24), 17953 (1994)

[30] G. Kresse and D. Joubert , From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59(3), 1758 (1999)

[31] J. P. Perdew , K. Burke , and M. Ernzerhof , Generalized gradient approximation made simple, Phys. Rev. Lett. 77(18), 3865 (1996)

[32] J. Klimeš , D. R. Bowler , and A. Michaelides , Van der Waals density functionals applied to solids, Phys. Rev. B 83(19), 195131 (2011)

[33] J. Taylor , H. Guo , and J. Wang, , Ab initio modeling of quantum transport properties of molecular electronic devices, Phys. Rev. B 63(12), 121104 (2001)

[34] J. Taylor , H. Guo , and J. Wang , Ab initio modeling of open quantum systems, Phys. Rev. B 63(24), 245407 (2001)

[35] G. Henkelman , B. P. Uberuaga , and H. Jónsson , A climbing image nudged elastic band method for finding saddle points and minimum energy paths., J. Chem. Phys. 113(22), 9901 (2000)

[36] N. Sivadas , B. G. Sumpter , and P. Ganesh , Scale-free switching of polarization in the layered ferroelectric material CuInP₂S₆, Phys. Rev. Res. 5(4), 043074 (2023)

[37] H. Bai , X. Li , H. Pan , P. He , Z. Xu , and Y. Lu , Van der Waals antiferroelectric magnetic tunnel junction: A first-principles study of a CrSe₂/CuInP₂S₆/CrSe₂ junction, ACS Appl. Mater. Interfaces 13(50), 60200 (2021)

[38] Z. Yan , Z. Li , Y. Han , Z. Qiao , and X. Xu , Giant tunneling magnetoresistance and electroresistance in α-In₂Se₃-based van der Waals multiferroic tunnel junctions, Phys. Rev. B 105(7), 075423 (2022)

[39] Z. Yan , D. Qiao , W. Lu , X. Dong , and X. Xu , Magnetic order dependent giant tunneling magnetoresistance and electroresistance in van der Waals antiferromagnetic-multiferroic tunnel junctions, Phys. Rev. B 111(4), 045404 (2025)

[40] Y. Zhang , X. Li , J. Sheng , S. Yu , J. Zhang , and Y. Su , Multilevel resistance states in van der Waals multiferroic tunnel junctions above room temperature, Appl. Phys. Lett. 123(19), 192402 (2023)

[41] A. Castellanos-Gomez , M. Buscema , R. Molenaar , V. Singh , L. Janssen , H. S. Van Der Zant , G. A. Steele , Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping, 2D Mater. 1(1), 011002 (2014)

[42] Z. C. Pan , D. Li , X. G. Ye , Z. Chen , Z. H. Chen , A. Q. Wang , M. Tian , G. Yao , K. Liu , and Z. M. Liao , Room-temperature orbit-transfer torque enabling van der Waals magnetoresistive memories, Sci. Bull. (Beijing) 68(22), 2743 (2023)

[43] W. Zhu , S. Xie , H. Lin , G. Zhang , H. Wu , T. Hu , Z. Wang , X. Zhang , J. Xu , Y. Wang , Y. Zheng , F. Yan , J. Zhang , L. Zhao , A. Patane , J. Zhang , H. Chang , and K. Wang , Large room-temperature magnetoresistance in van der Waals ferromagnet/semiconductor junctions, Chin. Phys. Lett. 39(12), 128501 (2022)

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