Introduction

The discovery of ferromagnetism in two-dimensional (2D) ultrathin crystals1,2,3,4 has attracted prodigious research interest in recent years since it provides a remarkable opportunity to explore intriguing physical phenomena and develop innovative spintronic devices. Currently, most of the attention has been focused on 2D ferromagnets with perpendicular magnetic anisotropy (PMA), such as CrI3 (Ising ferromagnet) and Cr2Ge2Te6 (Heisenberg ferromagnet)5,6,7,8, whose long-range ferromagnetic (FM) ordering can be observed experimentally. In fact, certain progress has also been achieved in experimental studies on 2D XY ferromagnets, which are characterized by easy-plane magnetization9,10,11,12,13. Nevertheless, the easy-plane magnetization is susceptible to thermal fluctuations, thereby prohibiting long-range FM ordering at any finite temperature according to the Mermin-Wagner theorem14, which partially restricts the application of 2D XY ferromagnets in spintronics. In this scenario, the realization of switching the easy magnetization axis from in-plane to out-of-plane directions in a 2D XY ferromagnet holds significant implications for both fundamental research and practical applications.

Various approaches have been proposed up till now to achieve this goal15,16,17,18,19, with the purely electrical control of magnetic anisotropy being the most desirable due to its compatibility with the development requirements of next-generation magnetic storage technology. It has been reported that by increasing the electric field, the easy magnetization axis of the VSi2P4 monolayer can be switched from in-plane to out-of-plane directions15, suggesting the possibility of electrically controlled magnetic anisotropy in 2D XY ferromagnets. However, the volatility in the manipulation of magnetic anisotropy remains a fundamental question that needs to be resolved. In other words, maintaining the induced state requires a persistent electric field, which will inevitably result in increased energy consumption. This presents a significant challenge to the advancement of energy-efficient memory and logic devices.

With the successful fabrication of 2D ferroelectrics20,21,22,23,24,25, constructing multiferroic van der Waals (vdW) heterostructures based on 2D magnets and ferroelectrics provides a practicable strategy for addressing the aforementioned confusion. The ideal magnetoelectric coupling in heterostructures enables the magnetic behavior in magnets to be tailored by reversing the electric polarization of ferroelectrics. More importantly, considering that the spontaneous polarization of ferroelectric is retained even when the externally applied electric field is removed, nonvolatile electrical control of magnetism is accessible in multiferroic vdW heterostructures. To date, the nonvolatile tuning of magnetic ordering and phase transition between half-metal and semiconductor via switching the ferroelectric polarization have been predicted in diverse multiferroic vdW heterostructures, including CrI3/Sc2CO226, CrI3/In2Se327, FeI2/In2Se328, NiI2/In2Se329, and Sc2CO2/VSe230. In view of this, we propose a scheme that aims to realize the transition of the easy magnetization axis from in-plane to out-of-plane directions in a 2D XY ferromagnets by designing a multiferroic vdW heterostructure, as illustrated in Fig. 1. Owing to the broken spatial inversion symmetry in the ferroelectric substrate, polarization flipping holds promise for inducing atomic orbital redistribution in the XY ferromagnet, which makes possible the electrically controlled alteration of magnetic anisotropy. Accordingly, the switching on-off of long-range FM ordering and the transformation between 2D XY and Heisenberg ferromagnets become achievable. Beyond that, as the polarization of the ferroelectric is reversed, different interfaces can be obtained in the heterostructure, leading to distinct band alignment and interfacial charge transfer. This provides an opportunity to realize the conversion between half-metal (or metal) and semiconductor states for the 2D ferromagnet while tuning the easy magnetization axis. If realized, both the polarization direction of the ferroelectric and the magnetic anisotropy of the ferromagnet can be directly detected by electrical signals, which would greatly benefit data reading processes in storage devices.

Fig. 1: Schematic representation of transition between 2D XY and Heisenberg models.
figure 1

The upper panels depict the reversal of the easy magnetization axis induced by polarization flipping, while the lower panels illustrate the magnetic anisotropy, Curie temperature, and electronic properties for 2D XY and Heisenberg models, respectively.

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Recently, the 2D VBi2Te4 monolayer has been predicted as a member of the MnBi2Te4-family materials31. The favorable dynamical stability of the VBi2Te4 monolayer suggests that it can possibly be synthesized through experiments. Different from the MnBi2Te4 monolayer, which has an out-of-plane easy magnetization axis, the VBi2Te4 monolayer exhibits the easy-plane magnetization characteristic of a typical 2D XY ferromagnet31,32,33. To validate our conception, we propose a multiferroic vdW heterostructure composed of FM VBi2Te4 and ferroelectric In2Se3 monolayers. As the electric polarization of the In2Se3 is reversed from upward to downward, the VBi2Te4 undergoes a transition from 2D XY to Heisenberg ferromagnets, featured by the switching of the easy magnetization axis from in-plane to out-of-plane directions. The Curie temperature (TC) of the VBi2Te4 monolayer, which behaves as a Heisenberg ferromagnet, is evaluated to be 76 K based on Monte Carlo (MC) simulation. In addition to the tuning of magnetic anisotropy, electrically controlled transformation from a semiconductor to a half-metal state is also achieved for the VBi2Te4 monolayer, which can be comprehended by band alignment and interfacial charge transfer. Based on the multiferroic vdW heterostructure, a conceptual memory device for high-density data storage is designed. The half-metallic property and magnetocrystalline anisotropy energy (MAE) of the VBi2Te4 monolayer in the heterostructure are also tunable by strain engineering. Our achieved results provide promising platforms for the exploration of advanced spintronic devices.

Results and discussion

VBi2Te4/In2Se3 heterostructure

Let us commence with the fundamental properties of individual VBi2Te4 and In2Se3 monolayers. The VBi2Te4 monolayer crystallizes in the R\(\bar{3}\)m space group with a triangular lattice, as demonstrated in Fig. 2a, and its optimized lattice constant is 4.36 Å. The calculated phonon dispersions presented in Supplementary Fig. 1 indicate that the VBi2Te4 monolayer is dynamically stable, as no imaginary modes are observed across the entire Brillouin zone. The magnetic ground state of the VBi2Te4 monolayer is determined by constructing both FM and antiferromagnetic (AFM) configurations, as shown in Supplementary Fig. 2. Based on the relative energy of these magnetic configurations listed in Supplementary Table 1, it is found that the VBi2Te4 monolayer prefers FM coupling with a magnetic moment of 3.0 μB per V atom. The MAE of the VBi2Te4 monolayer is also calculated, which is defined as the energy difference between the spin moments along the in-plane and out-of-plane directions, namely, EMAE = Ein-plane − Eout-of-plane. The EMAE is found to be −0.24 meV per unit cell, which closely agrees with previously reported values31,33, revealing that the VBi2Te4 monolayer is a 2D XY ferromagnet. Supplementary Fig. 3a presents the band structure of the VBi2Te4 monolayer, in which a semiconducting nature with an indirect band gap of 0.93 eV can be observed. On the other hand, the free-standing In2Se3 monolayer exhibits a hexagonal structure with a lattice constant of 4.10 Å, see Fig. 2b. Our calculations predict an out-of-plane polarization of 0.16×10–10 C m−1 for this monolayer. According to the band structure presented in Supplementary Fig. 3b, the In2Se3 monolayer behaves as a semiconductor with an indirect band gap of 0.78 eV. All these results are consistent with previous calculations34,35.

Fig. 2: Geometric structures of free-standing monolayers and heterostructures.
figure 2

a, b Top views of 2D VBi2Te4 and In2Se3 monolayers. c, d Side views of optimal configuration for the VBi2Te4/In2Se3 heterostructure with P↑ and P↓ states.

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The multiferroic vdW heterostructure is then constructed by vertically stacking the VBi2Te4 monolayer on the In2Se3 monolayer, denoted as VBi2Te4/In2Se3. Here, the lattice constant of the VBi2Te4 monolayer remains fixed in the heterostructure to preserve its physical properties and minimize strain-induced alterations, while the In2Se3 monolayer is stretched by 5.73% to match that of the VBi2Te4. Despite being stretched, the semiconducting nature of the In2Se3 monolayer is maintained, with a decreased band gap of 0.34 eV and a shifted valence band maximum (VBM) to the K point, as illustrated in Supplementary Fig. 3c. Meanwhile, the magnitude of out-of-plane polarization for the stretched In2Se3 monolayer is also decreased to 0.10×10–10 C m−1. Since the In2Se3 monolayer possesses two bistable polarization states, the heterostructure has two polarization configurations (i.e., P↑ and P↓). To determine the optimal geometric structure of P↑ and P↓ configurations, six highly-symmetric stacking patterns between VBi2Te4 and In2Se3 are taken into account, as illustrated in Supplementary Fig. 4. According to the relative energy listed in Supplementary Table 2, we find that the Dn-I and Up-I configurations, with the V atom located above the lower In atom, are the most robust, see Fig. 2c, d. Further research studies will be conducted on these two configurations in the following sections. After structural relaxation, the optimized interlayer distances are found to be 2.66 and 2.47 Å for P↑ and P↓ configurations, respectively. Notably, the minimum atomic distance (Te-Se) at the interface is approximately 3.60 Å, which is much larger than the sum of their covalent radii, suggesting that the interlayer coupling is chiefly governed by vdW interactions. The binding energy (Eb) of the VBi2Te4/In2Se3 heterostructure is also evaluated using the formula of \(E_b=(E_{{\mathrm{VBi}}_2{\mathrm{Te}}_4/{\mathrm{In}}_2{\mathrm{Se}}_3} - E_{{\mathrm{VBi}}_2{\mathrm{Te}}_4} - E_{{\mathrm{In}}_2{\mathrm{Se}}_3})/S\). Here, \(E_{{\mathrm{VBi}}_2{\mathrm{Te}}_4/{\mathrm{In}}_2{\mathrm{Se}}_3}\) is the total energy of VBi2Te4/In2Se3, while \(E_{{\rm{VBi}}_2{\rm{Te}}_4}\) and \(E_{{\rm{In}}_2{\rm{Se}}_3}\) represent the energies of individual VBi2Te4 and In2Se3 monolayers, respectively, and S refers to the surface area. The resultant Eb is about −0.20 eV Å−2, indicating that the VBi2Te4/In2Se3 is a vdW heterostructure, and the negative value implies that the heterostructure is energetically stable and promising for experimental fabrication. Besides, the feasibility of ferroelectricity in the VBi2Te4/In2Se3 heterostructure is explored. The transition path from P↑ to P↓ states is illustrated in Supplementary Fig. 5, which involves passing through a paraelectric state. The energy barrier for this path is found to be 0.47 eV per unit cell, indicating the potential accessibility of ferroelectricity in the heterostructure.

Next, we put our emphasis on the magnetic properties of the VBi2Te4/In2Se3. We first examine the magnetic ground state of the VBi2Te4 monolayer in the heterostructure. Similar to the free-standing VBi2Te4 monolayer, both FM and AFM states are considered for P↑ and P↓ configurations, as illustrated in Supplementary Fig. 2. The relative energies of different magnetic states are listed in Supplementary Table 1, where it is observed that the FM state is energetically lower than the AFM states, revealing that the VBi2Te4 monolayer retains its original FM ground state. The response of magnetic anisotropy in the VBi2Te4 monolayer to polarization switching of the In2Se3 monolayer is also studied. Figure 3a, b presents the dependence of the MAE on the polar angle (θ) for P↑ and P↓ configurations. It shows that in the P↑configuration, the 2D VBi2Te4 maintains its easy-plane magnetization characteristic, and the EMAE decreases to −0.20 meV per unit cell due to the proximity effect. Intriguingly, for the P↓ configurations, the easy magnetization axis of the VBi2Te4 monolayer is switched to the out-of-plane direction, along with a EMAE of 0.01 meV per unit cell. The presence of PMA can overcome the Mermin-Wagner constraint and counteract thermal fluctuations, thereby giving rise to long-range FM ordering in the VBi2Te4 monolayer. In other words, the polarization flipping of the In2Se3 monolayer is capable of driving the 2D VBi2Te4 to experience a transition between 2D XY and Heisenberg ferromagnets (i.e., switching on-off of the long-range FM ordering). It also confirms that the VBi2Te4/In2Se3 heterostructure harbors a strong magnetoelectric coupling effect, enabling the nonvolatile electrical control of magnetic anisotropy in the VBi2Te4 monolayer.

Fig. 3: Magnetic properties of the VBi2Te4/In2Se3.
figure 3

a, b Dependence of the MAE on the polar angle θ for the VBi2Te4/In2Se3 heterostructure in P↑ and P↓ configurations. c Simulated specific heat CV in terms of the temperature for the VBi2Te4/In2Se3 heterostructure with the P↓ state.

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In the heterostructure with the P↓ state, the VBi2Te4 monolayer transforms into a 2D Heisenberg ferromagnet. The key parameter TC is therefore evaluated through MC simulation. Here, considering the disruption of spatial inversion symmetry in the VBi2Te4 monolayer caused by the ferroelectric polarization of the In2Se3 monolayer, we incorporate the Dzyaloshinskii-Moriya interaction (DMI). The model Hamiltonian can be described as:

$${\rm{H}}=-{\text{J}}_{1}\sum _{\text{i},\text{j}}{\text{S}}_{\text{i}}\cdot {\text{S}}_{\text{j}}-{\text{J}}_{2}\sum _{\text{k},\text{l}}{\text{S}}_{\text{k}}\cdot {\text{S}}_{\text{l}}-{\text{J}}_{3}\sum _{\text{m},\text{n}}{\text{S}}_{\text{m}}\cdot {\text{S}}_{\text{n}}-{\rm{K}}\sum _{\text{i}}{({\text{S}}_{\text{i}}^{\text{z}})}^{2}-{\rm{D}}\sum _{\text{i},\text{j}}\left({\text{S}}_{\text{i}}\times {\text{S}}_{\text{j}}\right).$$
(1)

Here, J1, J2, and J3 are the nearest, next-nearest-, and next-next-nearest-neighbor exchange coupling parameters, respectively; Si denotes the spin vector at the i-th V site; \({S}_{i}^{z}\) represents the spin component parallel to the z direction; K is the single-ion anisotropy and D is the DM vector. The detailed calculations for J1, J2, J3, K, and D are available in Appendix I of the Supplementary Material. In MC simulation, a 100×100×1 supercell with periodic boundary conditions is adopted, and a total of 1×106 MC steps are employed for each temperature point. The value of TC can be determined by locating the peak position in the specific heat CV curve, while the specific heat capacity is evaluated by \({C}_{\text{v}}=\frac{\left(\left\langle {E}^{2}\right\rangle -{\left\langle E\right\rangle }^{2}\right)}{{k}_{B}{T}^{2}}\). Figure 3c displays the simulated CV curve, and the TC is predicted to be 76 K, which is higher than that of previously reported 2D ferromagnets, e.g., CrI3 (45 K)1, CrBr3 (34 K)36, and CrGeTe3 (30 K)2. Therefore, the introduction of the ferroelectric In2Se3 monolayer enhances the potential applications of the VBi2Te4 monolayer in spintronics.

The influence of the ferroelectric proximity effect on the electronic properties of the VBi2Te4 monolayer is then explored. The band structures of two polarization configurations are shown in Fig. 4a, b. For the P↑ case, a semiconducting nature is obtained with an indirect band gap of 0.52 eV. The VBM and conduction band minimum (CBM) are essentially governed by the monolayers of VBi2Te4 and In2Se3, respectively, resulting in a type-II band alignment (see Fig. 4a). According to the density of states (DOS) in Supplementary Fig. 7a, the VBM mainly originates from the \(V-d_{z^2}\) orbital, while the CBM is contributed by the In-s and Se-px,y orbitals. It is also noteworthy that the lowest conduction band shows a slight spin splitting, indicating that the In2Se3 monolayer becomes magnetized due to the magnetic proximity effect. When the polarization of the In2Se3 monolayer is switched to the P↓ state, the Fermi level intersects with the energy bands, leading to hole and electron pockets for VBi2Te4 and In2Se3, respectively (see Fig. 4b). More interestingly, at the Fermi level, the energy band stemming from the VBi2Te4 monolayer is completely dominated by the spin-up state. Due to the spatial separation of hole and electron pockets, the VBi2Te4 monolayer exhibits a half-metallic property, whereas the In2Se3 monolayer displays metallic behavior, as shown in Supplementary Fig. 7b. Therefore, reversing the polarization of the In2Se3 monolayer from upward to downward can induce a transition from a semiconductor to a half-metal for the 2D VBi2Te4. When considering the spin-orbit coupling (SOC) effect, it is observed that neither the electronic properties of P↑nor those of P↓ configurations undergo a significant change in nature, except for a decrease in band gap for the former, as illustrated in Supplementary Fig. 8. The phase transition from a semiconductor to a half-metal is also well preserved in the VBi2Te4 monolayer. While previous studies have demonstrated the feasibility of individually controlling half-metallicity or magnetic anisotropy in multiferroic heterostructures, such as CrI3/Sc2CO226, MnCl3/CuInP2S637, Cr2Ge2Te6/Sc2CO238, and Cr2Ge2Te6/In2Se339, our VBi2Te4/In2Se3 heterostructure offers a particular opportunity for simultaneous control over both half-metallicity and magnetic anisotropy. The realization of multidimensional regulation within this heterostructure will significantly enhance the functionality of electronic devices. Considering that the VBi2Te4 and MnBi2Te4 monolayers belong to the same material family, we have also constructed the MnBi2Te4/In2Se3 multiferroic heterostructure to validate the possibility of magnetoelectric coupling effect. As shown in Supplementary Fig. 9, the MnBi2Te4 monolayer solely exhibits an electrically controlled phase transition from a semiconductor to a half-metal, whereas its PMA remains unaffected by the polarization switching of the In2Se3 monolayer, which is consistent with previous research findings40.

Fig. 4: Electronic properties and MAE contribution of the VBi2Te4/In2Se3.
figure 4

a, b Calculated band structures of the VBi2Te4/In2Se3 heterostructure with P↑ and P↓ states. The red and blue lines represent the spin-up and spin-down states, respectively. c Atom-resolved MAE of the VBi2Te4/In2Se3 heterostructure with P↑ and P↓ states.

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Having established the nonvolatile electrical control of magnetic and electronic properties in the VBi2Te4/In2Se3 heterostructure, our focus now shifts to elucidating the origin of MAE in this heterostructure. Figure 4c illustrates the atom-resolved MAE of two polarization configurations. It is evident that the VBi2Te4 monolayer primarily contributes to the MAE, while the contribution of the In2Se3 monolayer is almost negligible. For the P↑ configuration, the Te1 and Te4 atoms contribute to the PMA, whereas the Te2, Bi1, V, Bi2, and Te3 atoms are responsible for the in-plane magnetic anisotropy (IMA). It should be noted that the contribution of the latter is remarkably larger than that of the former, resulting in easy-plane magnetization for the VBi2Te4 monolayer in the heterostructure. As the In2Se3 monolayer is switched to the P↓ state, a sign reversal occurs in the MAE contribution from Bi1, Te2, and Te3 atoms. Accompanied by a significant decrease in MAE contribution from V and Bi2 atoms, the overall MAE contribution becomes positive, indicating that the VBi2Te4 monolayer exhibits the PMA. Therefore, the sign change in MAE for Bi1, Te2, and Te3 atoms plays a decisive role in the transition of magnetic anisotropy in the VBi2Te4 monolayer. To further elucidate this point, we calculate the orbital-resolved MAE of these atoms in the heterostructure with different polarized states, see Supplementary Fig. 10. In the P↑ configuration, the MAE contribution from the Bi1 atom arises from the hybridizations between px and py orbitals, as well as between py and pz orbitals, which exhibit positive and negative values, respectively. Obviously, the magnitude of the former is smaller than that of the latter, thereby establishing the contribution of the Bi1 atom to the IMA. However, for Te2 and Te3 atoms, the hybridization between px and py orbitals contribute to the IMA, while that between py and pz orbitals contribute to the PMA. The contribution from the former is predominant, ultimately leading to the overall IMA. When the ferroelectric polarization of the In2Se3 monolayer is reversed, the MAE contribution from the Bi1 atom is determined by the hybridizations between px and py orbitals, as well as between px and pz orbitals. Both contributions are positive, implying that the Bi1 atom contributes to the PMA. Besides, the signs of hybridizations between px and py orbitals, as well as between px and pz orbitals, for both Te2 and Te3 atoms are reversed accordingly. The MAE are dominated by the former, which provides a positive contribution. Hence, both Te2 and Te3 atoms also exhibits the PMA contribution.

Furthermore, we qualitatively interpret the ferroelectricity-dependent magnetic anisotropy in the VBi2Te4/In2Se3 heterostructure based on second-order perturbation theory41,42. According to the theory, the MAE can be expressed as:

$$MAE=\sum _{\sigma \sigma {\prime} }{E}^{\sigma \sigma {\prime} }(x)-{E}^{\sigma \sigma {\prime} }(z)=\sum _{\sigma \sigma {\prime} }(2{\delta }_{\sigma \sigma {\prime} }-1){\xi }^{2}\sum _{{o}^{\sigma }{u}^{\sigma {\prime} }}\frac{|{o}^{\sigma }|{L}_{z}{|{u}^{\sigma {\prime} }|}^{2}-|{o}^{\sigma }|{L}_{x}{|{u}^{\sigma {\prime} }|}^{2}}{{E}_{u}^{\sigma {\prime} }-{E}_{o}^{\sigma }}$$
(2)

where ξ represents the SOC amplitude, while \({E}_{u}^{\sigma {\prime} }\) and \({E}_{o}^{\sigma }\) are the energy levels of unoccupied states with spin σ′ and occupied states with spin σ, respectively. (2δσσ‘ − 1)(|oσ|Lz|uσ‘|2 − |oσ|Lx|uσ‘|2) is the difference of spin-orbital angular momentum matrix elements, which is shown in Supplementary Table 3. The equation suggests that the MAE is primarily determined by the matrix element differences and energy differences. In particular, the electronic states near the Fermi level play a dominant role in contributing to the MAE due to their small energy separation (\({E}_{u}^{\sigma {\prime} }-{E}_{o}^{\sigma }\)) in the denominator of the equation. Additionally, the total MAE may also be affected by the intensity of DOS as it is the integral of all occupied and unoccupied states42,43,44. Supplementary Fig. 11 shows the projected DOS of p orbitals for Bi1, Te2, and Te3 atoms in the VBi2Te4/In2Se3 heterostructure with opposite polarizations. In the P↑ configuration, for the Bi1 atom, the main occupied and unoccupied states near the Fermi level are governed by the spin-up state, see Supplementary Fig. 11a. This indicates that the SOC-induced total energy changes are determined by the hybridization between spin-up occupied and unoccupied states. Supplementary Table 3 lists the matrix element differences between spin-up occupied and unoccupied p states (po+ and pu+) in Eq. (2). From Supplementary Fig. 11a, one can observe that the main occupied states near the Fermi level originate from degenerate spin-up px and py states (\({p}_{x}^{o+}\) and \({p}_{y}^{o+}\)). Based on the data in Supplementary Table 3, the contribution to MAE can be obtained from hybridizations between spin-up unoccupied pz states (\({p}_{z}^{u+}\)) and \({p}_{y}^{o+}\), between spin-up unoccupied py states (\({p}_{y}^{u+}\)) and \({p}_{x}^{o+}\), as well as between spin-up unoccupied px states (\({p}_{x}^{u+}\)) and \({p}_{y}^{o+}\). Supplementary Table 3 also indicates that the matrix element difference between \({p}_{z}^{u+}\) and \({p}_{y}^{o+}\) is −1, implying a negative contribution to MAE from the py and pz hybridization. On the other hand, the matrix element difference between \({p}_{y(x)}^{u+}\) and \({p}_{x(y)}^{o+}\) equals 1, resulting in a positive contribution to MAE from the px and py hybridization. Considering that the energy difference between \({p}_{z}^{u+}\) and \({p}_{y}^{o+}\) (Δyz) is smaller than that between \({p}_{y(x)}^{u+}\) and \({p}_{x(y)}^{o+}\) (Δxy), as shown in Supplementary Fig. 11a, according to Eq. (2), the negative contribution to MAE outweighs the positive one, which is consistent with the orbital-resolved MAE of the Bi1 atom. Since the Te2 and Te3 atoms have similar DOS distributions, as illustrated in Supplementary Fig. 11b, c, we chose the Te2 atom as the representative for our investigation. The main unoccupied and occupied states near the Fermi level are determined by spin-up and spin-down states, respectively. Notably, the spin-up unoccupied state is mainly dominated by the \({p}_{x(y)}^{u+}\), and thus its hybridizations between spin-down occupied pz and px,y states (\({p}_{z}^{o{-}}\) and \({p}_{y(x)}^{o{-}}\)) can contribute to the MAE. As listed in Supplementary Table 3, matrix element differences between \({p}_{y}^{u+}\) and \({p}_{z}^{o{-}}\), as well as between \({p}_{x(y)}^{u+}\) and \({p}_{y(x)}^{o{-}}\), are equal to 1 and −1, respectively. The energy differences between \({p}_{y}^{u+}\) and \({p}_{z}^{o{-}}\), as well as between \({p}_{x(y)}^{u+}\) and \({p}_{y(x)}^{o{-}}\) are similar. However, as indicated by the DOS, the strength of \({p}_{y(x)}^{o{-}}\) is greater than that of \({p}_{z}^{o{-}}\), and thus the hybridization between \({p}_{x(y)}^{u+}\) and \({p}_{y(x)}^{o{-}}\) plays a major role. As a result, both Te2 and Te3 atoms contribute to the IMA, as illustrated in Supplementary Fig. 10b, c.

When the In2Se3 monolayer is flipped to the P↓ state, considerable charge transfer from VBi2Te4 to In2Se3 (details below) can induce a shift of p orbital occupied states towards the Fermi level for Bi1, Te2, and Te3 atoms. This results in a redistribution of the DOS, see Supplementary Fig. 11, which has the potential to alter the MAE of these atoms. For the Bi1 atom, the SOC-induced total energy variations are primarily governed by the hybridization between spin-down occupied and unoccupied states. According to Supplementary Table 3, the matrix element difference between spin-down unoccupied px,y state (\({p}_{x\left(y\right)}^{u-}\)) and \({p}_{y\left(x\right)}^{o-}\) remains equal to 1, suggesting a positive contribution to MAE from the hybridization between px and py orbitals. Notably, Supplementary Fig. 10d reveals a disappearance of the hybridization between py and pz orbitals, which is replaced by a positive contribution from the px and pz hybridization, contradicting the data presented in Supplementary Table 3. The explanation of this phenomenon may necessitate the incorporation of higher-order terms in Eq. (2). Since the hybridization between px and pz orbitals does not affect our conclusions, we will not discuss it here. In this context, the Bi1 atom exhibits a positive MAE contribution, thereby contributing to the PMA. For the Te2 atom, the spin-up electronic states intersect with the Fermi level, and the pu+ state closest to the Fermi level play a significant role in contributing to the MAE when interacting with the po+ state. As listed in Supplementary Table 3, matrix element differences between \({p}_{y}^{u+}\) and \({p}_{z}^{o+}\), as well as between \({p}_{x(y)}^{u+}\) and \({p}_{y(x)}^{o+}\), can be obtained, featuring −1 and 1, respectively. However, the energy difference between \({p}_{x(y)}^{u+}\) and \({p}_{y(x)}^{o+}\) is smaller than that between \({p}_{y}^{u+}\) and \({p}_{z}^{o+}\), resulting in a stronger contribution of PMA over IMA, as shown in Supplementary Fig. 10e. The Te3 atom demonstrates similar results to the Te2 atom, see Supplementary Figs. 10f and 11c. Consequently, the transition of magnetic anisotropy in the VBi2Te4 monolayer caused by the polarization reversal of the In2Se3 monolayer can be attributed to the changes in hybridizations between p orbitals of Bi1, Te2, and Te3 atoms.

Furthermore, the alteration of electronic properties in the heterostructure induced by polarization switching is further explained by considering the band alignment between two monolayers and the interfacial charge transfer. As shown in Supplementary Fig. 12a, b, the VBi2Te4 monolayer is symmetric with an identical electrostatic potential on both sides. In contrast, the In2Se3 monolayer displays an asymmetric structure with noticeable differences in electrostatic potential along the out-of-plane direction, resulting in a 1.2 eV discrepancy in work function between its two sides. Through integrating 2D VBi2Te4 and In2Se3 into the vdW heterostructure, the spatial inversion symmetry is broken because of the presence of ferroelectricity. Therefore, different band alignments are generated for the two opposite polarized states. For the P↑ configuration, as depicted in Fig. 5a, the valence band of the VBi2Te4 monolayer in both spin-up and spin-down channels are energetically lower than the conduction band of the In2Se3 monolayer, which hinders charge transfer between VBi2Te4 and In2Se3. Despite this fact, a weak charge transfer and redistribution occur at the interface due to the small electrostatic potential difference (ΔV) and associated built-in electric field at the interface, see Fig. 5c and Supplementary Fig. 12c. However, this subtle effect is insufficient to induce any qualitative changes in the electronic properties; hence, both VBi2Te4 and In2Se3 monolayers tend to retain their intrinsic semiconducting nature. By switching the In2Se3 monolayer to the P↓ state, the conduction band edge of the In2Se3 becomes lower than the spin-up valence band of the VBi2Te4, while still remaining higher than its spin-down valence band, see Fig. 5b. Accompanied by a significant increase in interfacial ΔV, a large amount of charge transfer takes place at the interface, as depicted in Fig. 5d and Supplementary Fig. 12d. This charge transfer is chiefly characterized by the injection of electrons from the spin-up channel of the VBi2Te4 monolayer into the In2Se3 monolayer, which results in partial filling of the spin-up subband and yields fully spin-polarized hole pockets for the VBi2Te4 monolayer. In this context, the VBi2Te4 monolayer exhibits metallic and semiconducting characters in spin-up and spin-down channels, respectively, giving rise to a half-metallic characteristic. The 2D In2Se3 behaves as a metal due to the electron injection. Therefore, the phase transition from a semiconductor to a half-metal for the VBi2Te4 monolayer within the heterostructure arises synergistically from the polarization switching-induced alteration of band alignment and the charge transfer occurring at the interface. In brief, even within the framework of weak vdW interlayer interaction, the VBi2Te4/In2Se3 heterostructure can still achieve the seemingly counter-intuitive phenomenon of strong magnetoelectric coupling.

Fig. 5: Origin of phase transition and device prototype.
figure 5

a, b Band alignment of the VBi2Te4/In2Se3 heterostructure with P↑ and P↓ states. c, d Plane-averaged charge density difference and differential charge density distributions of the VBi2Te4/In2Se3 heterostructure with P↑ and P↓ states. The isosurface value is 0.0003 eÅ-3. e, f Schematic representation of multiferroic memory device designed based on the VBi2Te4/In2Se3 heterostructure. The data writing process relies on the ferroelectric In2Se3, while the data reading process is realized by detecting the electric or optical signal of the VBi2Te4 monolayer.

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Recently, ferroelectric memory has garnered significant attention as a highly promising member within the realm of memory technologies. Compared to other types of storage devices, such as magnetic memory, ferroelectric memory exhibits superiority in the data writing process achieved by changing the polarized state of ferroelectrics. Nevertheless, the data reading process in ferroelectric memory is destructive, which poses great challenges to the flexibility and service life of storage devices. To address this drawback, a prototype of a memory device based on the VBi2Te4/In2Se3 multiferroic vdW heterostructure for high-density data storage is proposed, as depicted in Fig. 5e, f. In this conceptual device, data writing is achieved by flipping the electric polarization of the ferroelectric In2Se3, which retains the advantage of ferroelectric memory in data writing. The ferroelectric control of electronic properties in the VBi2Te4 monolayer provides a remarkable avenue for realizing data reading. When the electric polarization of the In2Se3 monolayer is upward, the VBi2Te4 monolayer behaves as a semiconductor and no electric signal is detected. We denote this state as the ‘OFF’ or ‘0’ state of the device. In contrast, when the 2D In2Se3 is driven into the P↓ state, the VBi2Te4 monolayer becomes conductive due to its half-metallicity, allowing spin-polarized holes to propagate through the channel layer. This corresponds to the ‘ON’ or ‘1’ state. Thus, in this multiferroic memory, the data reading process is achieved by converting the polarized states of the In2Se3 monolayer into the conducting state of the VBi2Te4 monolayer and checking it, which effectively avoids the destructive effect caused by detecting ferroelectric polarization. Additionally, since 2D XY and Heisenberg ferromagnets exhibits distinct optical signals, data reading in the device can also be achieved by checking the magnetoelectric coupling-induced signal differences in the VBi2Te4 monolayer. As a matter of fact, the proposed device prototype is also applicable for designing high-performance field effect transistor (FET). The ability to readily control the conducting state in the VBi2Te4/In2Se3 heterostructure is likely to result in a high on-off ratio for the FET, and more importantly, the whole regulation process is nonvolatile. The interfacial magnetoelectric coupling also endows the VBi2Te4/In2Se3 heterostructure with great potential for exploring modern magnetic and resistive memories.

Effects of strain and interlayer distance variations

In experimental synthesis or device fabrication, the magnetoelectric coupling of the VBi2Te4/In2Se3 heterostructure may be affected by several factors, such as a small amount of artificial strain. Therefore, investigating the effect of biaxial strain on the magnetic and electronic properties of the heterostructure is of particular interest. Figure 6a displays the variation of EMAE as a function of biaxal strain. For the heterostructure with up-polarized In2Se3, the EMAE slightly increases under compressive strain, but exhibits a decreasing trend under tensile strain. The sign of EMAE remains unchanged, suggesting that the characteristic of 2D XY ferromagnet is sustained for the VBi2Te4 monolayer. By comparison, in the P↓ configuration, biaxial strain can effectively modulate the EMAE. With increasing compressive strain, the EMAE is continuously enhanced, indicating further stabilization of long-range FM ordering in the VBi2Te4 monolayer. However, when tensile strain is adopted, the EMAE first undergoes a sign change and then increases obviously as tensile strain increases, implying that the VBi2Te4 monolayer reverts to a 2D XY ferromagnet. Hence, in the stretched VBi2Te4/In2Se3 heterostructure, the magnetoelectric coupling effect is eliminated since the IMA of the VBi2Te4 becomes immune to polarization switching. To elucidate the sign change of MAE in the P↓ configuration, we plot the atom-resolved MAE of the VBi2Te4 monolayer subjected to different strains in Fig. 6b. One can see that the tensile strain-induced IMA is attributed to the sign reversal of the MAE contributions from Te1, Te2, and Te3 atoms. Besides, both compressive and tensile strains can enhance the MAE contribution of all atoms, providing a reasonable explanation for the observed increase in MAE under strains. Supplementary Figs. 13 and 14 present the band structures of P↑ and P↓ configurations under different strains. The results reveal that the semiconductor property of the P↑ configuration is preserved intact with strain ranging from −4% to 4%. The band gap exhibits an increasing trend under compressive strain and a decreasing trend under tensile strain. In the P↓ configuration, the VBi2Te4 monolayer retains its half-metallicity under compressive strain, and more importantly, the hole doping concentration is enhanced accordingly. This phenomenon is mainly ascribed to the increased charge transfer from VBi2Te4 to In2Se3 monolayers. The employment of compressive strain would shorten the bond length, resulting in more extend energy band dispersions for VBi2Te4 and In2Se3. Under this circumstance, the difference between the spin-up valence band edge of the VBi2Te4 and the conduction band edge of the In2Se3 is enhanced, thereby promoting charge transfer at the interface. In contrast, tensile strain renders a more localized energy band dispersion, which leads to a reduction in interfacial charge transfer. Thus, the hole doping weakens with increasing tensile strain, and the VBi2Te4 monolayer transforms into a semiconductor at a critical strain of 4%. In light of the above findings, the VBi2Te4/In2Se3 heterostructure exhibits favorable characteristics in both equilibrium and compression states, rendering it highly suitable for practical applications.

Fig. 6: Strain-induced change in MAE.
figure 6

a Calculated MAE of the VBi2Te4/In2Se3 heterostructure with P↑ and P↓ states in term of the biaxial strain. b Atom-resolved MAE of the VBi2Te4 monolayer in the heterostructure subjected to various strains.

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To gain insight into the origin of changes in MAE induced by tensile strain for Te1, Te2, and Te3 atoms, we conduct a comparative analysis of orbital-resolved MAE for the P↓ configuration under 0% and 4% tensile strains. As shown in Supplementary Fig. 15, for the Te1 atom in the pristine heterostructure, the contribution of hybridization between p orbitals to MAE is almost negligible. However, when subjected to tensile strain, there is a significantly enhancement of the hybridizations between py and pz orbitals, as well as between px and py orbitals. Notice that the former and latter constitute IMA and PMA, respectively, with the former being strong than the latter, thereby resulting in the contribution of the Te1 atom to the IMA. While the sign change of MAE for the Te2 atom under tensile strain can be attributed to a remarkable increase in the hybridization between py and pz orbitals, accompanied by the sign reversal of the hybridization between px and py orbitals. This latter effect is also responsible for the observed MAE change of the Te3 atom. We further provide a qualitative explanation for the MAE changes of Te1, Te2, and Te3 atoms using second-order perturbation theory. The projected DOS of these Te atoms in the P↓ configuration under a 4% tensile strain is shown in Supplementary Fig. 16. Starting from the Te1 atom, it can be seen that both occupied and unoccupied states near the Fermi level are determined by the spin-up state. This suggests that the hybridization between po+ and pu+ dominates the SOC-induced total energy changes. Therefore, the Te1 atom exhibits a mechanism similar to that of the Bi1 atom in pristine P↑ configuration. For the Te2 atom, tensile strain drives its spin-up occupied pz orbital to move towards the Fermi level, decreasing the energy difference between \({p}_{y}^{u+}\) and \({p}_{z}^{o+}\). This leads to an increase in the hybridization between py and pz orbitals, which contributes to the IMA. In addition, the enhancement of the spin-down occupied state \({p}_{x\left(y\right)}^{o-}\) in both Te2 and Te3 atoms can be observed under tensile strain, which facilitates its interaction with \({p}_{x(y)}^{u+}\). As listed in Supplementary Table 3, the matrix element difference between \({p}_{x\left(y\right)}^{o-}\) and \({p}_{y(x)}^{u+}\) is −1, indicating the px and py hybridization provides a negative MAE contribution, which aligns with the orbital-resolved MAE of Te2 and Te3 atoms.

The preceding discussion has confirmed the sign change of MAE for the VBi2Te4 monolayer upon reversing the polarization of the In2Se3 monolayer from upward to downward. This change is attributed to modifications in interlayer coupling induced by interface alternation. Given the strong correlation between interlayer distance and interlayer coupling strength, it is essential to study the influence of variations in interlayer distance (Δd) on the magnetic anisotropy of the VBi2Te4 monolayer. Prior to that, we first investigate the relationship between amount of electron transfer (Δe) from VBi2Te4 to In2Se3 monolayers and Δd. As shown in Supplementary Fig. 17a, the increase (decrease) in Δe is observed as Δd decreases (increases), regardless of P↑ and P↓ configurations. This phenomenon demonstrates that the reduction (expansion) of interlayer distance enhances (weakens) the interlayer coupling, thereby facilitating (impeding) interfacial electron transfer. Supplementary Fig. 17b presents the variation of EMAE as a function of Δd. For the P↑ configuration, there is a gradual increase in EMAE observed with decreasing interlayer distance. Conversely, when the interlayer distance is increased, the EMAE decreases gradually with a slight fluctuation. Throughout this process, the consistently negative sign of EMAE indicates that the IMA of the VBi2Te4 monolayer is immune to Δd. On the other hand, in the P↓ configuration, an increased interlayer distance leads to a continuous reduction in EMAE, while a decreased interlayer distance initially increases and then diminishes the EMAE. When the interlayer distance is reduced by 0.3 Å, the EMAE can reach up to 0.04 meV per unit cell. Nevertheless, a transition from PMA to IMA can be observed in the VBi2Te4 monolayer when the interlayer distance decreases by more than 0.6 Å, as evidenced by the sign change of EMAE. More importantly, the half-metallicity of the VBi2Te4 monolayer within the P↓ configuration remains unaffected by variations in interlayer distance, as shown in Supplementary Fig. 18. In a word, manipulating the interlayer distance offers a viable strategy to modulate the MAE of the heterostructure.

In2Se3/VBi2Te4/In2Se3 and VBi2Te4/bi-In2Se3 heterostructures

Considering that the VBi2Te4 monolayer has two surfaces, another form of multiferroic vdW heterostructure is proposed by sandwiching it between two ferroelectric In2Se3 monolayers. This heterostructure, denoted as In2Se3/VBi2Te4/In2Se3, is anticipated to provide more opportunities for nonvolatile electrical control over the magnetic and electronic properties of 2D VBi2Te4. Four polarization configurations, namely, P↑↑, P↑↓, P↓↑ and P↓↓, are designed for the In2Se3/VBi2Te4/In2Se3 heterostructure based on the energetically stable stacking pattern between VBi2Te4 and In2Se3 monolayers. The geometric structures and optimized interlayer distances of different configurations are illustrated in Fig. 7a–d. Interestingly, we find a strong correlation between the interface type and the interlayer distance in the heterostructure. For instance, the upper and lower interfaces of the P↑↑ configuration correspond to the interfaces of the VBi2Te4/In2Se3 heterostructure with P↓ and P ↑ states, respectively, while the interlayer distance exhibits the same phenomenon. This fundamental law is also applicable to the P↑↓, P↓↑ and P↓↓ configurations. We then calculate the Eb of the In2Se3/VBi2Te4/In2Se3 heterostructure by \(E_{\rm{b}}=(E_{{\rm{In}}_2{\rm{Se}}_3/{\rm{VBi}}_2{\rm{Te}}_4/{\rm{In}}_2{\rm{Se}}_3}-E_{{\rm{VBi}}_2{\rm{Te}}_4}-2E_{{\rm{In}}_2{\rm{Se}}_3})/S\) and estimate that it is approximately −0.27 eV Å−2, which is smaller than that of the VBi2Te4/In2Se3 heterostructure. In the following, we investigate the magnetic and electronic properties of the In2Se3/VBi2Te4/In2Se3 heterostructure. For the P↑↑ configuration, the value of EMAE is calculated to be 0.02 meV per unit cell, revealing that the VBi2Te4 monolayer in the heterostructure belongs to a 2D Heisenberg ferromagnet. The band structure in Fig. 7e shows that the VBi2Te4 monolayer exhibits a hole doping-induced half-metallic character. The hole doping is primarily attributed to the transfer of massive electrons from the VBi2Te4 monolayer to the top In2Se3 monolayer, see Supplementary Fig. 19a. In contrast, the electron transfer at the lower interface is very limited. As a result, in the In2Se3/VBi2Te4/In2Se3 with the P↑↑ state, the upper interface plays a dominant role in determining the magnetic and electronic properties of the VBi2Te4 monolayer, thereby leading to the PMA in the VBi2Te4 monolayer. Then we turn to the P↑↓ configuration whose upper and lower interfaces coincide with that of the VBi2Te4/In2Se3 heterostructure in the P↑ configuration. The EMAE is calculated to be −0.20 meV per unit cell, demonstrating the IMA in the VBi2Te4 monolayer. A semiconducting property with an indirect band gap of 0.48 eV is obtained for the heterostructure, as presented in Fig. 7f. As expected, there is only a small amount of charge transfer at interfaces, see Supplementary Fig. 19b. In the P↓↑ configuration, both the upper and lower interfaces are identical to that of the VBi2Te4/In2Se3 heterostructure with the P↓ state. It turns out that the value of EMAE is 0.18 meV per unit cell, which is improved by an order of magnitude compared to the VBi2Te4/In2Se3 heterostructure. In this scenario, the VBi2Te4 monolayer transforms into a 2D Heisenberg ferromagnet with a more stable long-range FM ordering. From the band structure given in Fig. 7g, one can see that the VBi2Te4 monolayer possesses half-metallic behavior, and more interestingly, there is a pronounced increase in hole doping concentration. This is because abundant electrons are simultaneously transferred from the VBi2Te4 monolayer to both the top and bottom In2Se3 monolayers, as shown in Supplementary Fig. 19c. When the In2Se3/VBi2Te4/In2Se3 heterostructure is in the P↓↓ configuration, it exhibits the same magnetic and electronic properties as those of the P↑↑ configuration because of the existence of spatial inversion symmetry, as illustrated in Fig. 7h and Supplementary Fig. 19d. Furthermore, the electronic properties of these four polarization configurations remain largely unchanged by the inclusion of SOC effect, with only a slight decrease in band gap for the P↑↓ configuration, see Supplementary Fig. 20. To gain a better understanding of the electronic properties, we plot the band alignments between VBi2Te4 and In2Se3 in Supplementary Fig. 21. To be brief, in the In2Se3/VBi2Te4/In2Se3 heterostructure, the magnetic and electronic properties are predominantly governed by a synergistic interplay between the upper and lower interfaces.

Fig. 7: Basic properties of the In2Se3/VBi2Te4/In2Se3.
figure 7

a–d Geometric structures of the In2Se3/VBi2Te4/In2Se3 heterostructure in P↑↑, P↑↓, P↓↑, and P↓↓ configurations. e–h Calculated band structures of the In2Se3/VBi2Te4/In2Se3 heterostructure in P↑↑, P↑↓, P↓↑, and P↓↓ configurations. The red and blue lines represent spin-up and spin-down states, respectively.

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Additionally, we explore the influence of varying the thickness of ferroelectric In2Se3 on the physical properties of the VBi2Te4 monolayer. To achieve this, we propose a VBi2Te4/bi-In2Se3 heterostructure by introducing an additional In2Se3 monolayer at the bottom of the VBi2Te4/In2Se3. Two opposite polarized states are considered and denoted as bi-P↑↑ and bi-P↓↓, as shown in Fig. S22a, b. The calculated Eb of the VBi2Te4/bi-In2Se3 heterostructure is approximately −0.26 eV Å−2. The MAE calculation results indicate that the VBi2Te4 monolayer exhibits IMA and PMA in bi-P↑↑ and bi-P↓↓ configurations, respectively, accompanied by corresponding EMAE of −0.12 and 0.12 meV per unit cell. This discovery aligns with the observed behavior in the VBi2Te4/In2Se3 heterostructure, revealing that even with an increased number of ferroelectric layers, the easy magnetization axis of the VBi2Te4 monolayer remains robust. The band structures of the VBi2Te4/bi-In2Se3 heterostructure with different polarized states are illustrated in Supplementary Fig. 22 c, d. It can be observed that the bi-P↑↑ configuration exhibits metallic behavior, contributed by the In2Se3 bilayer, as shown in Supplementary Fig. 22c. When the electric polarization of the In2Se3 bilayer is oriented downward, the VBi2Te4/bi-In2Se3 shows similar electronic properties to those of the VBi2Te4/In2Se3 heterostructure with the P↓ state, where the VBi2Te4 monolayer and In2Se3 bilayer possess half-metallicity and metallicity, respectively, see Supplementary Fig. 22d. However, compared to the VBi2Te4/In2Se3 heterostructure, the half-metallicity of the VBi2Te4 monolayer within the VBi2Te4/bi-In2Se3 heterostructure is enhance, characterized by a higher hole doping concentration. This enhancement is attributed to a greater electron transfer from the VBi2Te4 monolayer to the In2Se3 bilayer, which is facilitated by an increased number of ferroelectric layers, as shown in Supplementary Fig. 22e, f. Thus, the VBi2Te4/bi-In2Se3 heterostructure can also achieve synchronous control of both magnetic anisotropy and half-metallicity in the VBi2Te4 monolayer, enabling desirable magnetoelectric coupling.

It is noteworthy that the In2Se3 monolayer (bilayer) exhibits a ferroelectric metal phase in both VBi2Te4/In2Se3, In2Se3/VBi2Te4/In2Se3, and VBi2Te4/bi-In2Se3 heterostructures. The screening effect typically eliminates the possibility of ferroelectric polarization switching in metallic bulk materials; however, this effect becomes negligible in atomically thin films due to the profound penetration of the external electric field. Experimental evidence has successfully demonstrated the switchable behavior in a 2D ferroelectric metal21. Therefore, the polarization reversal in the In2Se3 monolayer (bilayer) within heterostructures can be achieved by applying an external electric field, irrespective of its metallicity.

In summary, we have designed multiferroic vdW heterostructures consisting of FM VBi2Te4 and ferroelectric In2Se3 monolayers, and examined the corresponding magnetoelectric coupling by first-principles calculations. By reversing the electric polarization of the In2Se3 monolayer, the magnetic anisotropy of the VBi2Te4 monolayer can be switched between easy-plane and easy-axis states, enabling transformation of the VBi2Te4 from 2D XY to Heisenberg ferromagnets. More interestingly, with the reversal of easy magnetization axis, the VBi2Te4 monolayer also undergoes a transition from a semiconductor to a half-metal. This fascinating phenomenon is essentially attributed to the band alignment and charge transfer between VBi2Te4 and In2Se3 monolayers. A conceptual memory device is proposed for nonvolatile data storage based on the multiferroic vdW heterostructure. Additionally, biaxial strain has been demonstrated as an effective avenue to tune the half-metallicity and MAE of the VBi2Te4 monolayer in the heterostructure. The present work provides potential candidates for achieving nonvolatile electrical control of magnetic anisotropy and half-metallicity, which paves the way for the exploitation of high-performance nanodevices.

Methods

Geometry optimization and electronic structure calculations

All first-principles calculations were performed using the Vienna ab initio simulation package (VASP) within the framework of density functional theory (DFT)45,46. The electron-ion interaction was described by the projector-augmented wave (PAW) pseudopotentials method47,48, and the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) parametrization was implemented for the exchange correlation functional49. The cutoff energy of the plane-wave basis was set to 400 eV. The first Brillouin zone was sampled by employing a centered 25×25×1 Monkhorst-Pack k-point mesh. To avoid interaction between neighboring periodic images, a vacuum region up to 70 Å was adopted along the z direction. The atomic positions were fully relaxed until the force on each atom was less than 0.001 eV A−1, and the convergence criteria for energy was set as 1×10–5 eV. The GGA + U scheme was utilized to treat the strong exchange correlations of the magnetic atom50, and the Ueff is selected to be 3.0 eV for the V-d orbital, according to previous investigations31,33. The DFT-D3 method of Grimme was adopted to describe the interlayer vdW interactions51,52. To access the reliability of DFT-D3 in comparison with other methods, we also employed DFT-D2 and optPBE-vdW methods to examine the systems investigated in this study53,54. Despite slight variations in interlayer distance under different methods, the calculated magnetic anisotropy and band structure of heterostructure remains nearly identical to those obtained using DFT-D3 method, as shown in Supplementary Table 4 and Fig. 23, thereby validating the reliability of DFT-D3 method. Dipole correction was incorporated in the calculation of the work function, whereas it was omitted from the calculation of heterostructures. This is because even with dipole correction considered, the physical properties of the heterostructure and our main conclusion will not be affected, as illustrated in Supplementary Fig. 24.

Polarization, NEB, and phonon spectrum calculations

The out-of-plane polarization was calculated by directly integrating the charge density over the whole structure in consideration of the presence of a vacuum region. It can be defined as:

$$P=\frac{1}{S}\int z\rho (z)dz$$
(3)

where ρ is the charge density, S represents the plane area of the 2D supercell, and z is the coordinate. The ferroelectric transition path and energy barrier were calculated utilizing the climbing-image nudged elastic band (NEB) method55,56. Phonon dispersions were calculated using the finite displacement method as implemented in the PHONOPY code57, in which a 3 × 3 × 1 supercell was employed.