Introduction

Antiferromagnetic (AFM) spintronics1,2,3, as a frontier area of research, is expected to bring about the revolutionary progress for the next-generation spintronic devices. This is because the antiferromagnets possess various fascinating features, such as robustness against external magnetic field perturbation, absence of parasitic stray field, and ultrafast dynamics4,5,6,7. To utilize AFM materials as the active elements in spintronics, several key issues remain to be resolved, in which the generation and manipulation of half-metallicity or fully spin polarized current are very important aspects8. Achieving the half-metallicity through the electric field has been pursued recently9, due to the superiority of low power and fast response, and it is conducive to the implementation of fully electrical reading/writing10. Recently, the long sought electric field controlled half-metallicity was predicted in two-dimensional (2D) A-type AFM VSe2 bilayer which features with intralayer ferromagnetic (FM) and interlayer AFM couplings11. However, the achieved half-metallicity is volatile since the fully spin polarized conduction electron would dissipate with the removal of the electric field, which is less desirable for memory and logic devices. As a result, it is urgently required a practical scheme for a nonvolatile electrical controlled half-metallicity.

Recently, van der Waals (vdW) heterostructure has attracted extensive attention for both fundamental science and technological application12,13,14, which offers a platform to realize intriguing physics and functionalities by flexibly stacking layered material with various properties. One of the most representative examples is the multiferroic vdW heterostructure constructed based on 2D FM and ferroelectric (FE) materials, which shows a strong interfacial magnetoelectric effect, such as FE controlled half-metallicity and magnetic order15,16,17,18,19,20. The FE layer, on the one hand, is to provide a spontaneous polarization field, which enables the control of the electronic or magnetic properties of FM layer. On the other hand, the FE layer holds different work functions at two surfaces, which diversifies the interfacial charge transfer with the reversal of the electric polarization, providing an effective avenue for band structure engineering. Motivated by such a principle, here we propose that the half-metallicity in 2D A-type antiferromagnet can be achieved by introducing a FE substrate with out-of-plane electric polarization to construct a multiferroic heterostructure. Figure 1a presents a schematic illustration of spin- and layer-projected density of state (DOS) for an A-type AFM bilayer. Although there is no spin polarization in the total DOS, the inherent ferromagnetism of monolayer makes the different spin subbands locate on different monolayer spatially. Such a characteristic provides an opportunity to realize the half-metallicity by breaking the inversion symmetry. When the 2D A-type antiferromagnet is deposited on a FE substrate, shown in Fig. 1b, the presence of the polarization field and possible interfacial charge transfer due to work function difference are expected to trigger the different electrostatic potential between two FM layers. In this context, the DOS associated with layer-1 will be shifted downwards with respect to that of layer-2. The ultimate result of this phenomenon is likely to lead to a metallic band with single spin polarization at the Fermi level (EF), as depicted in Fig. 1c, and thus the half-metallicity emerges. Furthermore, it is possible to switch the half-metallicity by reversing the FE polarization of the substrate.

Fig. 1: Principle for realizing half-metallicity.
figure 1

a Schematic illustration of spin- and layer-projected DOS for a bilayer of A-type antiferromagnet. b Diagram of 2D A-type antiferromagnet on FE substrate. c Spin- and layer-projected DOS with half-metallicity.

Full size image

Hitherto, tremendous progress in the preparation of vdW magnetic materials has provided an opportunity for exploring and utilizing the 2D A-type AFM materials21,22,23,24. Very recently, the NiI2 bilayer (bi-NiI2) has been successfully fabricated on the h-BN substrate, which was predicted as an A-type AFM material25. In this work, we adopt bi-NiI2 as the active antiferromagnet to demonstrate our above proposal. By combining bi-NiI2 with FE In2Se3 with different thickness to design vdW heterostructure, the feasibility of realizing and controlling the half-metallicity in bi-NiI2 by electric polarization flipping is investigated. It is found that the In2Se3 bilayer (bi-In2Se3) can successfully give rise to half-metallicity in bi-NiI2. With the reversal of polarization from upward to downward for bi-In2Se3, the bi-NiI2 undergoes a transformation from half-metal to semiconductor, accompanied by a switch of easy magnetization axis from in-plane to out-of-plane direction. The nonvolatile electrical control of half-metallicity in bi-NiI2 is the result of a combination of band shifts induced by the polarization field and selective charge transfer at the interface. Moreover, the strain is demonstrated as an additional route to modulate the half-metallic property and magnetic anisotropy energy (MAE). Two conceptual advanced nanodevices, a FE memory device, and a spin field effect transistor (SFET), are proposed based on the vdW heterostructure. These results provide an avenue to generate the switchable fully spin polarized current in AFM material, which would greatly promote the development of AFM spintronics.

Results and discussion

Physical properties of bi-NiI2/In2Se3 heterostructure

We first explore the property of pristine bi-NiI2. To evaluate the optimized structure, six stacking patterns were constructed for bi-NiI2, shown in Supplementary Fig. 1a, in which the interlayer AFM and FM couplings were separately considered. The energy difference in Supplementary Table 1 reveals that the AB1 configuration with A-type AFM coupling is the most energetically stable. The optimized lattice constant and interlayer distance are 3.93 and 3.45 Å, respectively. We find that the spin moment is mainly contributed by the Ni atom, and the local magnetic moment of each Ni atom is about 2μB. Supplementary Fig. 1b presents the band structure of the bi-NiI2, in which a semiconductor characteristic with an indirect bandgap of 1.27 eV can be observed. The conduction band minimum (CBM) and valence band maximum (VBM) are mainly dominated by the Ni-d and I-p orbitals, respectively. From the spin- and layer-projected DOS in Supplementary Fig. 1b, the spin subbands from the bottom NiI2-1 layer and upper NiI2-2 layer are strictly complemented, demonstrating the A-type AFM characteristic of the bi-NiI2. A monolayer of In2Se3 was initially considered as the FE substrate due to its intrinsic out-of-plane FE nature. It shows a hexagonal structure with a lattice constant of 4.10 Å. The bistable polarized states are presented in Supplementary Fig. 2a, b, marked P↑ and P↓, which can be easily switched by a vertical electric field. The calculated band structure in Supplementary Fig. 2c demonstrates the semiconductor characteristic of the In2Se3 monolayer, accompanied by a bandgap of 0.78 eV. The VBM is mainly derived from the Se-p orbitals, while the CBM is jointly contributed by the In-s and the Se-p orbitals, which is consistent with the previous studies26.

A small lattice mismatch of 4.1% between the bi-NiI2 and the In2Se3 monolayer suggests a good quality vdW heterostructure can be easily constructed, which is denoted as bi-NiI2/In2Se3. Here, three stacking patterns were designed for two opposite polarized states, shown in Fig. 2a. Supplementary Table 2 lists the relative energies of different structures. It shows the DN-II and UP-II configurations, in which the Ni atom in the NiI2-1 layer is located above the upper In atom of the adjacent In2Se3 monolayer, are energetically lower than the other configurations. More importantly, the A-type AFM coupling of bi-NiI2 is maintained in the vdW heterostructure. The obtained interlayer distances between bi-NiI2 and In2Se3 monolayer are 3.20 and 3.16 Å for P↑ and P↓ cases, respectively. This small difference implies that polarization switching has a negligible effect on the interlayer distance. Besides, the structural stability of vdW heterostructure was evaluated by the calculation of the formation energies, which is defined as Eform = E(bi-NiI2/In2Se3) − E(bi-NiI2) − E(In2Se3), where the E(bi-NiI2/In2Se3), E(bi-NiI2), and E(In2Se3) are total energies of bi-NiI2/In2Se3 heterostructure, individual bi-NiI2 and In2Se3 monolayer, respectively. The calculated formation energy is about −1.40 eV, suggesting the feasibility of experimental preparation of such vdW heterostructure. Based on the formation energy and interlayer distance, the interlayer vdW interaction in heterostructure is further demonstrated.

Fig. 2: Basic properties of bi-NiI2/In2Se3 heterostructure.
figure 2

a Structural diagram of different stacking patterns for bi-NiI2/In2Se3 heterostructure in the P↑ and P↓ configurations. b, c Calculated band structures and DOS of bi-NiI2/In2Se3 heterostructure in the P↑ and P↓ configurations, respectively. The red and blue lines in the band structure represent spin-up and spin-down states, respectively.

Full size image

Then the electronic properties of bi-NiI2/In2Se3 vdW heterostructures were investigated. Figure 2b, c present the calculated band structures and DOS of heterostructure. For the P↑ configuration, the band degeneracy of the bi-NiI2 is removed due to different degrees of energy level shift for the NiI2-1 and the NiI2-2 layers, in which the spin splitting reaches up to about 73.4 meV. The heterostructure shows a semiconductor characteristic with an indirect bandgap of 476.6 meV. The CBM and VBM are dominated by the bi-NiI2 and In2Se3 monolayer, respectively, indicating that the bi-NiI2/In2Se3 belongs to a typical staggered-gap (type II) heterostructure. In the light of the orbital-projected band structure [see Supplementary Fig. 3a, b], the electronic states nearest to the EF in conduction and valence bands are separately stemmed from the Ni-dyz/dxz and Se-px/py orbitals. Once the polarization is reversed to the P↓ case, the band structure of the heterostructure undergoes a dramatic change, shown in Fig. 2c. Although the type-II band alignment behavior is preserved, the domination components for the CBM and VBM are changed due to the relative displacement between the energy levels of the bi-NiI2 and the In2Se3 monolayer. Under this circumstance, the conduction and valence band edges are originated from the In-s/Se-pz and I-px/py orbitals, respectively [see Supplementary Fig. 3c, d]. In addition, the indirect bandgap of the heterostructure is increased to 802.4 meV, while the spin splitting of the bi-NiI2 is reduced to about 51.5 meV. Generally, despite the spin splitting induced by the FE polarization, the energy bands contributed by the bi-NiI2 and the In2Se3 monolayer in the vdW heterostructure are very similar to their pristine cases, which indicates that there is no obvious hybridization between the AFM bilayer and FE substrate.

The origin of the variation of band structure caused by the polarization flipping was also explored. The In2Se3 monolayer with out-of-plane FE polarization can produce an external polarization field. When the bi-NiI2 is deposited on the In2Se3 monolayer, the polarization field would act upon the AFM bilayer. For the P↑ case, the polarization field drives the energy levels of bi-NiI2 to shift downward, which results in the CBM and VBM of bi-NiI2 being lower than the CBM and VBM of In2Se3 monolayer [see Supplementary Fig. 4]. As a consequence, the CBM of the heterostructure is associated with the bi-NiI2, while the VBM comes from the In2Se3 monolayer. It is important to point out that the distinct spatial position of NiI2-1 and NiI2-2 layers determines that their potential energies are different. As shown in Supplementary Fig. 5a, the potential energy difference between two NiI2 layers turns out to be 0.24 eV, and thus two NiI2 layers exhibit unequal energy level shift, which gives rise to the band spin splitting. However, for the heterostructure in the P↓ configuration, the energy bands of bi-NiI2 shift to higher energy since the polarization field is reversed. This shift of energy level finally leads to the CBM dominated by the In2Se3 monolayer and the VBM dominated by the bi-NiI2 [see Supplementary Fig. 4], in contrast with the P↑ case. Furthermore, the potential energy difference between two NiI2 layer is decreased to 0.16 eV in this situation, shown in Supplementary Fig. 5b, which contributes to a smaller spin splitting for the bi-NiI2. In a word, although the In2Se3 monolayer would not bring about qualitative change for the electronic property of bi-NiI2, the generated electric polarization indeed drives the downward shift of energy level of bi-NiI2, which offers an opportunity to further manipulate the electronic property by enhancing polarization field.

Physical properties of bi-NiI2/bi-In2Se3 heterostructure

To verify the above conception, one more In2Se3 layer was added at the bottom of bi-NiI2/In2Se3. This vdW heterostructure is named bi-NiI2/bi-In2Se3. Here, for simplicity, two different polar configurations were taken into account for the bi-In2Se3, i.e., the polarization directions of FE layers were both pointing upward (P↑↑) or downward (P↓↓). The stacking pattern of the bi-In2Se3 was also optimized and shown in Supplementary Fig. 2d. It reveals that in the most stable configuration, the upper In atom in the In2Se3-1 layer is vertically aligned with the upper Se atom in the In2Se3-2 layer. Figure 3a, b show the geometric structures of bi-NiI2/bi-In2Se3 in the P↑↑ and P↓↓ configurations. The calculated formation energy of the bi-NiI2/bi-In2Se3 is about -0.09 eV, suggesting that such a complex heterostructure is promising to be produced. The interlayer distance at the NiI2–In2Se3 interface is insensitive to the addition of the second In2Se3 layer, and it is found to be 3.20 and 3.19 Å for the P↑↑ and P↓↓ cases, respectively. Remarkably, the A-type AFM ground state of the bi-NiI2 is persisted, which is immune to the polarization direction of the substrate, and the energy differences between AFM and FM states for the P↑↑ and P↓↓ cases are 9.68 and 10.68 meV per unit cell, respectively.

Fig. 3: Basic properties of bi-NiI2/bi-In2Se3 heterostructure.
figure 3

a, b Structural diagrams, c, d calculated band structures and DOSs, and e, f differential charge distributions of bi-NiI2/bi-In2Se3 heterostructure in the P↑↑ and P↓↓ configurations, respectively. The red and blue lines in band structures represent spin-up and spin-down states, respectively.

Full size image

The effect of the bi-In2Se3 on the electronic property of the bi-NiI2 was also investigated. The layer- and spin-projected band structures and DOS of bi-NiI2/bi-In2Se3 heterostructures are plotted in Fig. 3c, d. For the P↑↑ configuration, the spin splitting of the energy band for the bi-NiI2 is increased to 138.7 meV because of the enhanced polarization field from the FE substrate, which is about double that of bi-NiI2/In2Se3. More interestingly, the EF passes through the spin-down conduction band edge, which forms an interesting band structure with half-metallicity, shown in Fig. 3c. From the DOS analysis, the electronic states at the EF are contributed by the NiI2-1 layer, while the NiI2-2 layer remains the semiconducting property. To be brief, the bi-NiI2 possesses the AFM half-metallicity under the action of the upward FE polarization from the substrate, which makes the generation of fully polarized current possible. By flipping the electric polarization of bi-In2Se3, we find that the energy bands associated with the bi-NiI2 shift upward relative to the EF, and the intersection between them is vanished, implying that the bi-NiI2 restores the semiconducting nature, as depicted in Fig. 3d. Meanwhile, the spin splitting is decreased to 98.9 meV. However, for the heterostructure, it exhibits a metallic characteristic since the EF cuts through the energy band contributed by the bi-In2Se3. Despite the presence of the conductive state for both P↑↑ and P↓↓ cases, the produced currents in heterostructure are distinctly different: the former is fully spin polarized and localized in the bi-NiI2, while the latter is spin depolarized and existed in the bi-In2Se3 substrate.

Next, we discuss the underlying physics for the electrically controlled half-metallicity in the AFM bi-NiI2. With the increase of the thickness of FE layer, the generated polarization field is enhanced correspondingly, which further improves the degrees of band shift and spin-splitting of bi-NiI2. For the P↑↑ case, the enhanced polarization field offers a prerequisite to realizing the half-metallicity for bi-NiI2, while the charge transfer at the NiI2-In2Se3 interface plays a decisive role. Figure 3e, f present the three-dimensional (3D) and plane-integrated differential charge distribution of bi-NiI2/bi-In2Se3. It can be seen that the charge transfer is mainly located at the NiI2-In2Se3 and the In2Se3-In2Se3 interfaces, whereas it is almost negligible between the NiI2-1 and the NiI2-2 layers. This can be explained by comparing the work functions of the In2Se3 and the NiI2 pristine layers. Since the In2Se3 layer is highly polarized, the calculated work functions on the two sides of the sample are different, i.e., W1 = 5.24 eV for the Se+ surface and W2 = 6.03 eV for the Se− surface. However, for the nonpolar NiI2 monolayer, the work function shows a single value of W = 5.62 eV. Hence, the obtained work functions satisfy the relationship of W1 < W < W2. With an upward polarization direction, the electrons would transfer from the In2Se3-1 to the NiI2-1, shown in Fig. 3e. The charge transfer will result in the electrons depletion at the upper surface of In2Se3-1 and the electron accumulation at the lower surface of NiI2-1, respectively. The extra electrons in the NiI2-1 layer will partially occupy the conduction band edge, leading to the phenomenon of electron doping. Therefore, the half-metallicity in the bi-NiI2 is the synergistic result of the polarization field induced variation of band alignment and charge redistribution induced electron doping. With the reversal of the electric polarization, the electrons in the NiI2-1 layer tend to transfer to the In2Se3-2 layer due to W < W2 [see Fig. 3f], which endows the bi-In2Se3 substrate with electron doping and conductive state. On the other hand, the work function at the In2Se3-In2Se3 interface is invariably different, and thus the charge transfer associated with the polarization direction is inevitable. The inappreciable interlayer charge transfer between the NiI2 layers can be attributed to the identical work function between the two layers.

For the AFM materials, the manipulation of easy magnetization axis is of significance and has attracted great attention27,28,29,30,31,32. Thus it is important to identify the response of the easy magnetization axis of bi-NiI2 to the polarization switching. Then the MAE of the bi-NiI2/bi-In2Se3 heterostructure was calculated. The result indicates that the MAE of the bi-NiI2 is isotropic within the xy plane, regardless of the polarization direction of the FE substrate. Figure 4a, b show the MAE associated with polar angle θ. It is observed that the easy magnetization axis for the P↑↑ and P↓↓ cases are in-plane and out-of-plane, respectively. Hence, the polarization flipping of substrate can effectively switch the easy magnetization axis of the bi-NiI2. The magnitude of MAE for the bi-NiI2/bi-In2Se3 is considerably larger than those of Sc2CO2/VSe2 and bi-CrI3/Sc2CO2 heterostructures33,34. From the layer-resolved MAE in Supplementary Fig. 6a, one can see that the MAE of heterostructures is mainly contributed by the I atoms in the bi-NiI2, while the contribution of the bi-In2Se3 can be almost ignored. With regard to the I atom, the hybridization between px and py orbitals as well as the hybridization between py and pz orbitals jointly constitute the MAE, in which the former and the latter are responsible for the in-plane and the out-of-plane magnetic anisotropy, respectively, as illustrated in Supplementary Fig. 6b, c. The reversal of easy magnetization axis in the bi-NiI2 triggered by the polarization switching of the substrate can be understood by the competition between these two hybridizations. When the electric polarization of bi-In2Se3 is upward (downward), the px and py (py and pz) hybridization is stronger than the py and pz (px and py) hybridization, which leads to the in-plane (out-of-plane) magnetic anisotropy [see Supplementary Fig. 6b, c]. Moreover, we notice that the bi-NiI2 shows an easy-plane magnetization when the substrate is in the P↑↑ configuration. Very recently, the antiferromagnetism and the magnetic transition temperature have been demonstrated experimentally in the bi-CrCl3 which also has an easy magnetization plane35,36. Therefore, the long-range AFM order and half-metallicity in bi-NiI2 are expected to be existent at finite temperature. With these outstanding advantages, the bi-NiI2/bi-In2Se3 heterostructure shows promising potential for the application as an efficient nonvolatile memory.

Fig. 4: MAE of bi-NiI2/bi-In2Se3 heterostructure.
figure 4

a, b Polar angle θ dependence of MAE with a–c plane for P↑↑ and P↓↓ cases, respectively. c Variation of EMAE as a function of biaxial strain for P↑↑ and P↓↓ cases.

Full size image

Effect of strain on bi-NiI2/bi-In2Se3 heterostructure

As mentioned above, the upward FE polarization can induce the electron doping for bi-NiI2, while the downward FE polarization drives the valence band edge of the bi-NiI2 extremely close to the EF. Such electronic properties suggest that external means, such as in-plane biaxial strain, may further tailor the electronic behavior of the heterostructure. Supplementary Fig. 7 shows the band structures of heterostructure under different biaxial strains. When the compressive strain is applied, the energy band dispersion becomes more extended because of bond length shortening. For the heterostructure in the P↑↑ configuration, this would enhance the electron doping in the bi-NiI2, which in turn increases the conductivity of the half-metallic bi-NiI2. Meanwhile, for the P↓↓ case, the valence band edge of the bi-NiI2 shifts upward continuously with the increase of the compressive strain, and finally intersects with the EF at −3% of strain, leading to a hole doping induced half-metallicity. Such half-metallicity is also stemmed from the NiI2-1 layer, but determined by the spin-up state. Thus, within an appropriate range of the compressive strain, the half-metallicity of the bi-NiI2 becomes independent of polarization flipping, whereas the reversal of the polarization can effectively switch the type of charge carrier and the spin orientation of the fully spin polarized current. On the contrary, the tensile strain would enlarge the bond length and improve the localization of energy bands. Once the tensile strain is implemented, the bi-NiI2 would restore the semiconducting property due to the depletion of the doped electrons [see Supplementary Fig. 7c]. Hence, for developing spintronics applications, the manipulation with compressive strain is more effective for providing better spin control. The effect of biaxial strain on the MAE was also studied. The energy difference between the magnetization in x (100) and z (001) directions was calculated, which is defined as EMAE = E100 − E001. The evolution of EMAE as a function of biaxial strain is displayed in Fig. 4c. For the P↑↑ case, the EMAE is diminished gradually in the strain range of −5–2%. To figure out the mechanism of the MAE change, we further analyze the orbital-resolved MAE of the I atom in the heterostructure under different strain, as depicted in Supplementary Fig. 8. The result reveals that the MAE contribution from the px and py hybridization is decreased significantly in the strain range from −5% to 2%, while the py and pz hybridization is almost unchanged, which results in the decrease of EMAE. More interestingly, the EMAE becomes positive and increases slightly when the tensile strain is larger than 3%, indicating that the easy magnetization axis is switched from in-plane to out-of-plane. This is due to the fact that the continuous decrease of the hybridization between px and py orbitals makes the py and pz hybridization dominate the MAE. It is worth mentioning that the EMAE at the 3% tensile strain is 91 μeV per unit cell (45.5 μeV per Ni atom), comparable to those of monolayers CrSnTe3 (69 μeV per Cr atom) and VSi2N4 (64 μeV per V atom)37,38, suggesting that the heterostructure still holds the potential for magnetoelectronic applications. On the other hand, for the P↓↓ case, the EMAE also shows a decrease trend in the strain range from −5 to 3%. It is caused by the significant enhancement of the px and py hybridization and the slight decrease of the py and pz hybridization [see Supplementary Fig. 9], which is distinct from that of the heterostructure in the P↑↑ configuration. Besides, as the tensile strain is larger than 3%, the EMAE tends to remain constant. To understand this phenomenon, the layer-resolved MAE under the tensile strain is plotted in Supplementary Fig. 10. It shows that the MAE is jointly determined by the I and Ni atoms, in which the former and the latter contribute to the out-of-plane and in-plane magnetic anisotropy, respectively. The overall contributions from the I atoms are enhanced with increasing tensile strain, while the same trend is obtained for the Ni atom. Therefore, the EMAE is hardly changed in this scenario.

FE memory device based on bi-NiI2/bi-In2Se3

The results have demonstrated that the heterostructure possesses the capacity of controlling the half-metallicity by FE polarization, which provides a promising opportunity for designing FE memory devices. Here, a prototype of a memory device is proposed based on the heterostructure, shown in Fig. 5a. The electric polarization in the bi-In2Se3 is switched by an independent voltage VA, and the bi-NiI2 as the conducting channel is contacted with the source/drain. When the FE substrate is in the P↑↑ configuration, the electron would travel through the channel layer with 100% spin polarization, due to the half-metallicity of the bi-NiI2. Such conductive state is denoted “1” or “ON” state of the device, shown in Fig. 5b. By flipping the FE substrate to the P↓↓ configuration, the bi-NiI2 becomes a semiconductor and the traveling of electrons is forbidden. This corresponds to the “0” or “OFF” state of the device, shown in Fig. 5c. In this context, the data reading process is accessible by converting the FE polarization state of bi-In2Se3 into conducting state of bi-NiI2 and detecting it, which can effectively avoid the destructive effect caused by detecting the polarized state. Furthermore, the scheme in Fig. 5a can also be adopted into SFETs. Different from a traditional semiconductor transistor with modulating the charge populations, the working principle of bi-NiI2/bi-In2Se3 heterostructure based SFET is manipulating the band structure of the AFM bilayer via controlling the FE polarization of the substrate. As a result, this SFET not only has the advantage of rapid response but more importantly, the regulation between different states is nonvolatile. Therefore, the SFET can be used in high-performance and low-power consumption devices.

Fig. 5: Device prototype and schematic diagram.
figure 5

a Prototypes of the ferroelectric memory device and spin-field effect transistor based on the bi-NiI2/bi-In2Se3 heterostructure. b, c Operation principle of ferroelectric memory device whose data writing depends on FE bi-In2Se3 and data reading is based on the different electric signal.

Full size image

To realize the above device functions, switching the polarization of the FE substrate via external electric field is a very vital tache. However, the result has revealed that the FE bi-In2Se3 is conductive in the heterostructure when the electric polarization is downward. For a metallic FE material, the polarization is difficult to be switched since the required voltage bias will produce a high electrical current rather than changing the structural polarity. Inspired by the recently successful case of the polarization reversal in the FE semimetal WTe239, it is possible to eliminate the electrical current by inserting a dielectric layer into the bi-NiI2/bi-In2Se3 heterostructure, which might be able to achieve the polarization switching via an external electric field. In addition, the FE bistability of bi-NiI2/bi-In2Se3 was also investigated, since it is closely associated with device performance. As a matter of fact, the polarization reversal in the FE In2Se3 layer requires undergoing an intermediate antiferroelectric (AFE) state. Thus the heterostructure in the AFE configuration was constructed, shown in Supplementary Fig. 11. By calculating the total energy, we find that the total energy of the AFE configuration is 2.05 eV per unit cell. higher than the P↑↑ and P↓↓ cases. Therefore, the bi-NiI2/bi-In2Se3 heterostructure offers sufficient bistability for the device application.

Physical properties of bi-NiI2/tri-In2Se3 heterostructure

From the above results, we extract that the electronic property of the bi-NiI2 shows different response to the In2Se3 layer with different thickness. To clarify the thickness effect of the In2Se3, on the basis of bi-NiI2/bi-In2Se3, we further added one more In2Se3 layer to construct the bi-NiI2/tri-In2Se3 heterostructure. After structural optimization, the most stable geometric structures of bi-NiI2/tri-In2Se3 with two opposite polarized configurations are displayed in Supplementary Fig. 12a, b. The formation energy of the heterostructure is evaluated to be about -0.01 meV, and the interlayer distances between the bi-NiI2 and the tri-In2Se3 are 3.24 and 3.22 Å for the P↑↑↑ and P↓↓↓ cases, respectively. By comparing the energy between different magnetic configurations, as listed in Supplementary Table 3, we find that the bi-NiI2 still maintains the A-type AFM coupling in the heterostructure. Supplementary Fig. 12c, d present the calculated band structures of heterostructures. Different from the bi-NiI2/bi-In2Se3, the bi-NiI2/tri-In2Se3 in the P↑↑↑ configuration in general shows a metallic property, which is featured with the intersection between EF and energy bands originated from both bi-NiI2 and tri-In2Se3. Fortunately, the bi-NiI2 still harbors the AFM half-metallicity in this situation, and the fully spin polarized (spin-down) state is come from the NiI2-1 layer, as illustrated in Supplementary Fig. 12c. The effect of the increase of In2Se3 layer is mainly manifested in two aspects: the spin splitting of NiI2 is enhanced to 151.97 meV; the FE substrate becomes metallic. On the other hand, when the electric polarization of the FE substrate is downward, the bi-NiI2/tri-In2Se3 possesses a similar electronic characteristic to that of bi-NiI2/bi-In2Se3. However, there is a significant difference between them. The bi-NiI2 in the bi-NiI2/tri-In2Se3 is also endowed with the half-metallicity since the EF passes through the spin-up state arisen from the NiI2-1 layer, which is distinct from the semiconducting nature in the bi-NiI2/bi-In2Se3. The emergence of such half-metallicity is result from the hole doping in the bi-NiI2. With the increase of In2Se3 layer, the electron transfer from NiI2-1 to In2Se3-1 is enhanced correspondingly. Combined with the upward shift of energy level of the bi-NiI2 induce by the polarization field, the sufficient electron transfer can give rise to the hole doping for the valence band edge, and thus half-metallic property is produced in the bi-NiI2. Besides, the spin splitting of the bi-NiI2 is reduced to 80.72 meV. In brief, when the tri-In2Se3 is employed as the substrate, the bi-NiI2 always shows the AFM half-metallicity, with the fully spin-polarized state being localized at the NiI2-1 layer, while the heterostructure exhibits a metallic band structure. The reversal of electric polarization of the tri-In2Se3 can effectively flip the spin polarity of the half-metallic bi-NiI2.

In summary, we have proposed vdW heterostructures formed by A-type AFM bi-NiI2 and FE In2Se3 with different thickness. With first-principles calculations, the switchable half-metallicity is realized in the bi-NiI2/bi-In2Se3 heterostructure. The polarization flipping of bi-In2Se3 from upward to downward would convert the bi-NiI2 from half-metal to semiconductor. Meanwhile, the easy magnetization axis of bi-NiI2 also undergoes a transition from the in-plane to the out-of-plane direction. It shows that the cooperation between the band shift induced by the polarization field and selective charge transfer at the interface is responsible for achieving the nonvolatile half-metallicity. The half-metallic behavior and the MAE in the heterostructure can be further adjusted by introducing strain. The prototypes of a FE memory device and SFET are designed using the vdW heterostructure. This work offers a possible scheme to achieve and control the half-metallicity in 2D A-type antiferromagnet. It opens opportunities for spintronic devices.

Methods

First principles calculations were performed within the framework of density functional theory (DFT) by the projector-augmented wave (PAW) method40, as implemented in the Vienna ab initio simulation package (VASP)41,42. The Perdew–Burke–Ernzerhof generalized gradient approximation (GGA) was adopted to describe the exchange and correlation functional43,44. The kinetic energy cutoff of 500 eV for the plane-wave basis set was used throughout the calculation. Structural relaxations were carried out until the residual force on each atom was <0.005 eV/Å, and the energy convergence criteria of 10−6 eV was employed. The Brillouin zone was sampled using a Γ-centered Monkhorst–Pack scheme with 17 × 17 × 1. A vacuum layer with a thickness larger than 30 Å was set to eliminate interactions between periodic images. The interlayer vdW interaction is described by the DFT-D3 method45,46. The GGA + U method was employed to treat the strongly correlated Ni-3d electrons47. To determine the appropriate effective Hubbard U (Ueff) for the bi-NiI2, the band structures with Ueff varying from 0.0 to 8.0 eV were calculated, as illustrated in Supplementary Fig. 13. By comparing the bandgap obtained from the GGA + U method with that from the experiment25, we found that the result of Ueff = 5.0 eV is more reliable, and thus the Ueff = 5.0 eV was adopted in our calculation.