Nonvolatile electrical control of spin polarization in the 2D bipolar magnetic semiconductor VSeF

Abstract

Nonvolatile electrical control of spin polarization in two-dimensional (2D) magnetic semiconductors is greatly appealing toward future low-dissipation spintronic nanodevices. Here, we report a 2D material VSeF, which is an intrinsic bipolar magnetic semiconductor (BMS) featured with opposite spin-polarized valence and conduction band edges. We then propose a general nonvolatile strategy to manipulate both spin-polarized orientations in BMS materials by introducing a ferroelectric gate with proper band alignment. The spin-up/spin-down polarization of VSeF is successfully controlled by the electric dipole of ferroelectric bilayer Al₂Se₃, verifying the feasibility of the design strategy. The interfacial doping effect from ferroelectric gate also plays a role in enhancing the Curie temperature of the VSeF layer. Two types of spin field effect transistors, namely multiferroic memory and spin filter, are further achieved in VSeF/Al₂Se₃ and VSeF/Al₂Se₃/Al₂Se₃ multiferroic heterostructures, respectively. This work will stimulate the application of 2D BMS materials in future spintronic nanodevices.

Introduction

Two-dimensional (2D) magnetic materials, showing great potential in information storage, transmission and processing by utilizing the spin degree of freedom^1,2,3, have attracted extensive interests since the experimental discovery of atom-thick magnetic materials CrI₃⁴, Cr₂Ge₂Te₆⁵, and Fe₃GeTe₂⁶. Meanwhile, the sheer openness of 2D magnetic materials makes them possess gate tunability and integrated flexibility^6,7, which is appealing for next-generation nanoscale spintronic devices. In order to develop high-performance 2D spintronic nanodevices, the flexible manipulation of carriers’ spin polarization is highly desirable. As compared with the traditional external magnetic field control of spin orientation in materials, electric field control is an extremely exciting research area, both in fundamental science and technology application^8,9,10, such as exploring multiferroic physics and exploiting the magnetoelectric coupling in ultrafast magnetic memories^11,12,13,14. Recently, magnetic anisotropy^15,16,17, magnetic conductivity^18,19,20, magnetic configuration^21,22,23 and magnetic moment²⁴ have been reported to be tuned by the ferroelectric polarization via interfacial magnetoelectric effects.

Bipolar magnetic semiconductors (BMSs), whose valence band maximum (VBM) and conduction band minimum (CBM) are derived from opposite spin channels, offer an ideal platform to achieve the electrical manipulation of both spin orientation around Fermi energy^25,26. Till now, only a few intrinsic 2D BMSs have been theoretically predicted^{27,28,29,30,31,32}, where the origins of bipolar semiconducting character are complicated and remain to be further explored. On the other hand, the state-of-the-art proposed way to manipulate carriers’ spin-polarized orientation in BMS materials requires persistent electrical control which is volatile and achieved by applying a gate voltage^19,26,33. Thus, designing 2D BMSs, exploring the formation mechanism of the bipolar semiconducting properties, and realizing nonvolatile control of the carriers’ spin polarization are crucial for 2D BMSs’ application. That will stimulate and accelerate the future development of 2D BMS materials in 2D spintronics.

In this work, we first report an intrinsic 2D BMS VSeF with a strongly correlated charge-transfer-type electronic band structure, where the hole effective mass is far less than the electron effective mass. Inspired by the ferroelectric (FE) materials with spontaneous electric polarization, we propose a general strategy to achieve nonvolatile manipulation of the carriers’ spin polarization in BMSs by introducing a FE gate with proper band alignment. Using first-principles calculation, our proposal has been achieved in the BMS VSeF monolayer by putting it on 2D FE Al₂Se₃ layer, considering the lattice mismatch. As stacked on a single-layer FE Al₂Se₃, monolayer VSeF preserves its BMS character when Al₂Se₃ (↓) is downward electric polarized, while it transforms into a half-metal upon reversing the electric polarized orientation of Al₂Se₃ (↑). To induce a larger built-in electric field, we increase the thickness of the FE layer to bilayer Al₂Se₃. It is found that the VSeF is n-doped with spin-up carriers by the upward electric polarization of bilayer Al₂Se₃ (↑), while it’s p-doped with spin-down carriers by the downward electric polarization of bilayer Al₂Se₃ (↓). Due to the interfacial doping effect, the Curie temperature of VSeF can be enhanced from 66 K to 71 K, 76 K and 81 K in VSeF/Al₂Se₃ (↑), VSeF/biAl₂Se₃ (↓) (bilayer Al₂Se₃) and VSeF/biAl₂Se₃ (↑), respectively. Based on these multiferroic van der Waals (vdW) heterostructures, we further design two types of spin field effect transistors (FETs), namely few-layer multiferroic memory and spin filter, using VSeF/Al₂Se₃ bilayer heterostructure and VSeF/biAl₂Se₃ trilayer heterostructure, respectively. We find that the choices of FE gates are abundant. Different FE gates would lead to different carriers’ doping concentrations. Our results pave the way for the realization and application of 2D BMS in future spintronic nanodevices.

Results

Structure and magnetic properties of VSeF monolayer

The crystal structure of the VSeF monolayer, as depicted in Fig. 1a, consists of buckled double VSe layers sandwiched by two F atomic layers. The VSeF monolayer crystallizes in the orthorhombic symmetry group (space group Pmmn), which takes the same structure as the experimentally synthesized 2D magnetic semiconductor CrSBr³⁴. VSeF monolayer is screened from MXY compounds (M = Ti, V, Cr, Mn, Fe, Co, Ni, X = O, S, Se, Te, Y = F, Cl, Br, I), taking CrSBr as prototype structure. The calculated results are summarized in Supplementary Table 1, containing stable nonmagnetic metals, nonmagnetic semiconductors, magnetic metals and magnetic semiconductors. Among them, only VSF and VSeF are dynamically stable 2D bipolar magnetic semiconductors (BMS). Supplementary Fig. 1 presents the electronic band structure and phonon spectrum of VSF, which is similar with that of VSeF. The calculated lattice parameters of VSeF monolayer are listed in Supplementary Table 2. Phonon spectrum calculation was performed. As shown in Fig. 1b, no imaginary frequency is observed in the phonon spectrum, indicating that VSeF monolayer is dynamically stable. The thermal stability of VSeF monolayer is evaluated by performing ab initio molecular dynamical (AIMD) simulations at 300 K and 500 K. The geometric structure of the VSeF monolayer at different temperatures keeps intact (Supplementary Fig. 2), which indicates that VSeF monolayer is thermally stable. The thermodynamical stability of VSeF monolayer is evaluated by performing a global structure optimization for 2D V-Se-F crystal via CALYPSO code^35,36, and investigating its energy above convex hull. We didn’t find other structures which have lower formation energies than that of our studied structure after 15-generation optimizations. In addition, the energy above convex hull obtained from the Computational 2D Materials Database (C2DB) is only 0.14 eV/atom, lower than the thermodynamical stability criteria of 0.2 eV/atom in previous literatures^37,38. These results thus indicate that VSeF monolayer is thermodynamically stable.

Fig. 1: Structure and magnetic properties of VSeF monolayer.

a Top and side views of VSeF monolayer, and a local distorted VSe₄F₂ octahedron. Red, yellow, and gray balls represent V, Se, and F atoms, respectively. b Phonon spectrum of VSeF monolayer. c The 3d orbital splitting from an ideal octahedron with O_h symmetry to a distorted octahedron with C_2v symmetry, and further splitting with a larger energy gap between occupied states and unoccupied states in V³⁺ 3d² due to the electronic correlation. d Simulated magnetic moment (black data) and magnetic susceptibility (red data) as functions of temperature for 2D VSeF.

The magnetic property of VSeF monolayer is largely dependent on the local environment of V³⁺. Each V³⁺ is surrounded by four Se^2- and two F^- forming a distorted octahedron VSe₄F₂ with C_2v symmetry. As illustrated in Fig. 1c, under an ideal octahedral crystal field with O_h symmetry, the fivefold degenerate d orbitals split into double degenerate e_g orbitals and threefold degenerate t_2g orbitals. In VSeF, the distorted octahedral crystal field further lifts double degenerate e_g orbitals into two a₁ orbitals, and threefold degenerate t_2g orbitals into b₁, b₂, and a₂ orbitals. The two V³⁺ d² electrons occupy two of three nearly degenerate orbitals (b₂ and a₂ orbitals), which is different from the situation in CrSBr³⁹. In the case of Cr³⁺ d³ orbitals, the three nearly degenerate orbitals (b₁, b₂, and a₂ orbitals) are half-filled, which can be described by the nondegenerate single-band Hubbard model. However, the physical picture of the partial occupation of degenerate orbitals needs to be described by a multiband Hubbard model.

The multi-orbital Hamiltonian is given as

$$H = - t\mathop {\sum}\nolimits_{ < ij > ,m\sigma } {\left( {d_{im\sigma }^{\dagger} d_{jm\sigma } + h.c.} \right)} + \mathop {\sum}\nolimits_{i,m\sigma } {\varepsilon _md_{im\sigma }^{\dagger} d_{im\sigma }} + U\mathop {\sum}\nolimits_{i,m} {n_{im \uparrow }n_{im \downarrow } + \left( {U^\prime - \frac{J}{2}} \right)} \mathop {\sum}\nolimits_{i,m > m^\prime } {n_{im}n_{im^\prime }} - J\mathop {\sum}\nolimits_{i,m > m^\prime } {2{{{\mathbf{S}}}}_{im} \cdot {{{\mathbf{S}}}}_{im^\prime }}$$

(1)

where i and j represent the two neighboring magnetic sites, m and m’ are the orbital indexes. The first term describes the nearest-neighbor hopping, the second term describes the on-site orbital energies, the third to fifth terms are the intra- (U) and interorbital (U’) Coulomb interactions and the Hund’s coupling (J), where U’ = U – 2 J^40,41. Single-band Hubbard model only contains the first three items of Eq. (1), completely neglecting the interorbital Coulomb interactions. However, when the strongly correlated degenerate orbitals are partially filled, the interorbital repulsion between occupied orbitals and unoccupied orbitals (U’ – J) cannot be neglected, which is crucial to decide the electronic structure (Fig. 1c). Similar cases have been reported in VS₂⁴², VI₃⁴³, VOCl⁴⁴, TiOCl⁴¹, etc. In VI₃ (V³⁺ with d² electronic configuration), the Hubbard U value shifts up (down) the unoccupied (occupied) orbital levels producing a semiconducting character⁴³.

The two d² electrons of V³⁺ in VSeF produce a local magnetic moment of 2 μ_B, which is in accordance with the results from DFT calculations. To determine the magnetic ground state of VSeF monolayer, we considered five possible magnetic configurations (Supplementary Fig. 3). It is found that the ferromagnetic state is the most stable configuration. And the ferromagnetic ground state of VSeF is robust against the Hubbard U (Supplementary Fig. 5) and spin-orbit coupling (SOC) effect (Supplementary Table 3). The easy axis of magnetization of VSeF monolayer is along the out-of-plane direction, whose energy is lower than that of the in-plane direction (Supplementary Table 4). Based on the classical Heisenberg Hamiltonian,

$$H = - \mathop {\sum}\nolimits_{i \ne j} {J_1{{{\mathbf{S}}}}_i \cdot {{{\mathbf{S}}}}_j} - \mathop {\sum}\nolimits_{i \ne k} {J_2{{{\mathbf{S}}}}_i \cdot {{{\mathbf{S}}}}_k} - \mathop {\sum}\nolimits_{i \ne m} {J_3{{{\mathbf{S}}}}_i \cdot {{{\mathbf{S}}}}_m} + \mathop {\sum}\nolimits_i {A_x\left( {S_i^x} \right)^2} + \mathop {\sum}\nolimits_i {A_y\left( {S_i^y} \right)^2}$$

(2)

where J₁, J₂, and J₃ are the nearest, next-nearest and third-nearest-neighbor exchange interaction parameters, respectively. A_x and A_y represent to single-ion anisotropy along the x and y direction, respectively. These parameters can be extracted by comparing the relative energies of different magnetic configurations (Supplementary Table 4). We carried out Monte Carlo simulation to estimate the Curie temperature (T_c) by using a 50 × 50 superlattice. The susceptibility is calculated according to χ = (〈E²〉 − 〈E〉²)/(k_BT). The calculated magnetization and susceptibility indicate that the Curie temperature is around 66 K (Fig. 1d), which is higher than that of the experimentally known T_c of 2D magnetic semiconductor CrI₃ (45 K).

Electronic structures and the origin of BMS

The electronic band structure of VSeF calculated by the GGA + U (U_eff = 3.25 eV) shows that the VSeF monolayer behaves as a BMS, where the VBM and CBM are derived from different spin channels (Fig. 2a). As the HSE06 functional generally gives more accurate band structures for semiconductors, we also calculated the band structure of VSeF by using an HSE06 functional (Supplementary Fig. 6), which is qualitatively consistent with the result from GGA + U calculation, indicating that the BMS character of VSeF is robust. Since the Se atom is heavy, the spin-orbit coupling (SOC) effect may affect the electronic structure of VSeF, we further calculated the electronic band structure including the SOC effect. The calculated band structure (Supplementary Fig. 7) exhibits bipolar character, which is consistent with that obtained without considering SOC effect. The spin-resolved projected density of states (PDOS) shows that the VBMs of both spin channels are mainly contributed by Se-p orbitals, and the CBMs are mainly contributed by V-d orbitals (Fig. 2a). That is in accordance with the partial charge densities of VBMs and CBMs of both spin channels (Fig. 2b). The charge densities of VBMs of both spin channels (①: spin up channel; ②: spin down channel) are similar, showing the main Se-p_x orbital feature and partial Se-p_x and V-d_xz bonding feature. The charge densities of CBMs of both spin channels (③: spin up channel; ④: spin down channel) which are mainly localized in V atoms are also similar.

Fig. 2: Electronic structures and the origin of BMS.

a Spin-resolved band structure where red lines and blue dashed lines represent spin-up and spin-down channels, respectively, element-resolved PDOS of VSeF monolayer and zoom-in PDOS near the Fermi level where blue, magenta, and gray regions represent the PDOS contributed by V, Se, and F atoms, respectively. Fermi level is set to 0 eV, as labeled by horizontal black dashed line. b Partial charge densities of VBMs and CBMs of both spin channels. The marked numbers correspond to band decomposed locations in panel a. The magenta and blue isosurfaces represent the electron densities of VBMs and CBMs, respectively, where the isosurface value is 4 × 10^–3 e·bohr^-3. c Schematic spin-resolved DOS of VSeF monolayer with the BMS behavior where the red and blue colors represent spin-up and spin-down channel, respectively, and the BMS feature can be described by three energy parameters (Δ₁, Δ₂, and Δ₃). Δ₂ is the bipolar bandgap. d The variations of three energy parameters (Δ₁, Δ₂, and Δ₃) as the U_eff = U – J parameter. When U_eff is less than 1.25 eV, VSeF is a metal (Δ₂ = 0; the pink region). Once U_eff is larger than 1.25 eV, VSeF is a BMS (the gray region).

The BMS feature of VSeF can be described by three energy gaps (Δ₁, Δ₂, and Δ₃), as shown in Fig. 2c. The Δ₂ gap is defined as the spin-flip gap between the VBM and CBM from different spin channels. Δ₁ + Δ₂ and Δ₂ + Δ₃ represent the spin-conserved gaps for two spin channels, respectively. Fig 2c depicts the schematic density of states (DOS) of VSeF, where the Se-p orbital bands with broad bandwidth are full-occupied, while the V-d orbital bands are partially occupied and localized. According to the aforementioned multiband Hubbard model, the orbital repulsion between the occupied states and unoccupied states with the same spin orientation is U’ – J, while the orbital repulsion between the occupied states and unoccupied states from different orbitals with different spin orientation is U’. Therefore, we investigated the influence of the effective Hubbard U parameter U_eff on the band structure of VSeF. As shown in Supplementary Fig. 8, the splitting between occupied V-d orbitals and unoccupied V-d orbitals gradually increases with U_eff value, and a transition from metal to BMS happens when U_eff equals 1.25 eV, indicating the strongly correlated characteristic of VSeF. When U_eff equals 0, VSeF is a metal where the d-orbital splitting originated from the distorted crystal field is small. Increasing the U_eff value gradually enhances the interorbital splitting between occupied and unoccupied orbitals, inducing a semiconducting bandgap. The magnitude of the three energy gaps (Δ₁, Δ₂, and Δ₃) as a function of U_eff are summarized in Fig. 2d. In the BMS region, Δ₁ and Δ₂ gradually increase with U_eff value, while Δ₃ is less affected. That’s in accordance with the depicted picture in Fig. 2c.

It is worth noting that VSeF is a charge-transfer semiconductor, where the hole effective mass is smaller than the electron-effective mass⁴⁵. Therefore, the carrier mobility of VSeF is largely dependent on the carrier type. Here, due to the broken time-reversal symmetry in ferromagnetism, the spin-up channels of valence band (VB) and conduction band (CB) together downward shift, while the spin-down channels upward shift, lifting Kramer’s degeneracy. Therefore, the VBM and CBM of VSeF are derived from the opposite spin channel. Δ₁ and Δ₃ are the spin exchange splitting gaps of VB and CB, respectively. Due to the partial hybridization between Se-p_x orbitals and V-d_xz orbitals in VBMs, the spin splitting gap Δ₁ is moderate. The origin of BMS in VSeF is different from the BMS formation mechanism of other transition metal compounds proposed by Deng et al., where the bipolar bandgap Δ₂ is derived from the spin exchange splitting of the same d orbital^28,46.

Monolayer Al₂Se₃ ferroelectric gate

The electronic structure of BMS enables electrical fields to control the carriers’ spin-polarization directions. It’s common to manipulate the spin polarization of BMS materials by applying a gate voltage (Supplementary Fig. 9). The 100% spin-polarized channel currents can be realized by changing the sign of the applied gate voltage. Supplementary Fig. 10 shows the variation of band structure of VSeF with the carrier concentrations. Upon hole (electron) doping, the spin-down (spin-up) carriers dominate the Fermi level. Besides, VSeF monolayer always keeps the ferromagnetic magnetic ground state under different carrier doping concentrations (Supplementary Fig. 11). However, the realization of electrical control of spin polarization by applying a gate voltage in BMS materials remains to be explored in the experiment. And this way to control carriers’ spin polarization is volatile, requiring a persistent external electrical field.

To solve these problems, we proposed that it’s possible to manipulate the spin polarization of BMS materials by applying a ferroelectric gate, as shown in Fig. 3a. Ferroelectric materials exhibit spontaneous polarization which can be maintained even if removing the external electric field. And the ferroelectric polarization can be switched by applying a short-term pulse voltage. Due to the built-in electric field induced by the ferroelectric polarization, the energy band alignment between ferroelectric dielectric layer and BMS channel layer can be altered by switching the direction of ferroelectric polarization. Consequently, the charge transfer between ferroelectric layer and BMS layer is also tunable (Fig. 3a). When the VBM of FE locates within the CBMs of spin-up and spin-down channel of BMS, n-type doping occurs in BMS, and electron carriers possess spin-up orientation. When the CBM of FE locates within the VBMs of spin-up and spin-down channel of BMS, p-type doping occurs in BMS, and hole carriers possess spin-down orientation. Therefore, nonvolatile electrical control of spin polarization is expected to be realized by constructing multiferroic BMS/FE heterostructures. This way can overcome the volatility in traditional electrical control approaches, which is more energy-efficiency.

Fig. 3: Manipulation of BMS by the ferroelectric gate and VSeF/Al₂Se₃ bilayer heterostructures.

a Schematic diagram of spin FET based on BMS, the spin orientations in the conducting channel (BMS region, marked in blue) can be controlled by switching the electric polarization of ferroelectric dielectric (FE region, marked in yellow). The bottom panel depicts the desired band alignments between BMS and FE under different ferroelectric polarized states, and associated charge transfers. Here, the solid and dashed lines represent VBM and CBM, respectively. Black arrows denote the electron spin, where electrons fill to the VBMs. The spin-up and spin-down bands of BMS are split, due to the intrinsic magnetism of BMS. b Top and side views of VSeF/Al₂Se₃ bilayer heterostructures. The red arrow represents the polarization direction of Al₂Se₃. c Band alignments of VSeF/Al₂Se₃ (↑) and VSeF/Al₂Se₃ (↓) with respect to the vacuum level of VSeF. The red and blue bars show the band edges of spin-up and spin-down channels of BMS, respectively, the purple bars show the band edges of FE. d Layer-resolved PDOS of VSeF/Al₂Se₃ (↑) and VSeF/Al₂Se₃ (↓), where the orange and purple lines represent the PDOS contributed by VSeF and Al₂Se₃, respectively. The potential energy decreases along the direction of black dashed line.

To verify the proposal, we first constructed a multiferroic vdW heterostructure for the predicted 2D BMS VSeF by combining a 2D ferroelectric Al₂Se₃, as shown in Fig. 3b. Single-layer Al₂Se₃ possesses the same structure as α-In₂Se₃ monolayer with hexagonal symmetry group⁴⁷, which is screened from the family of 2D ferroelectric III₂-VI₃ materials by considering the band alignments and lattice mismatch between VSeF monolayer and 2D III₂-VI₃ ferroelectrics (Supplementary Fig. 12). The ferroelectric polarization state depends on the movement of the middle Se layer. When the middle Se atom is close to the bottom (upper) Al atom, it’s upward (downward) polarization P ↑ (P ↓ ). Considering the lattice mismatch, the relaxed $\sqrt 3 \times 3$ -Al₂Se₃ supercell with orthorhombic lattice is strained by 2.3% (x direction) and -6.8% (y direction) to match the 2 × 2-VSeF. To evaluate the stability of Al₂Se₃ ferroelectric state under strained, we calculated the entire ferroelectric polarization reversal path of strained Al₂Se₃ to compare the energy difference between the centrosymmetric phase and ferroelectric phase. As shown in Supplementary Fig. 13, the ferroelectric state of strained Al₂Se₃ is still more stable than the paraelectric phase. We considered 24 possible stacking mode between VSeF and Al₂Se₃ by shifting their relative positions in the in-plane direction. As shown in Supplementary Fig. 14, by comparing the total energies of these 24 configurations, the most stable structures are obtained, which are the same for both P ↑ and P ↓ .

In our calculations, we fixed the lattice constant of VSeF and only relaxed the atomic positions in heterostructures for eliminating the strain influences on the BMS properties of VSeF. Due to the built-in electric field, there is a potential drop of 1.73 eV across the two sides of Al₂Se₃ (Supplementary Fig. 15), which produces different band alignments when VSeF contacts with P ↑ and P ↓ Al₂Se₃. As illustrated in Fig. 3c, the different band alignments lead to different interfacial charge transfer. When combined with P ↑ Al₂Se₃, the potential energy of VSeF is lower than that of Al₂Se₃ (Supplementary Fig. 16a), which makes that the spin-up CBM of VSeF is lower than the VBM of Al₂Se₃, suggesting that electrons can transfer from Al₂Se₃ to spin-up channel of VSeF. In contrast, for VSeF/Al₂Se₃ (↓), the potential energy of Al₂Se₃ is lower (Supplementary Fig. 16b), but the CBM of Al₂Se₃ is still slightly higher than the spin-down VBM of VSeF. Therefore, the electrons transfer from VSeF to Al₂Se₃ is blocked.

The calculated layer-resolved PDOS are consistent with the analysis of band alignments. As indicated in Fig. 3d, in VSeF/Al₂Se₃ heterostructure, the potential energy decreases along the direction of black dashed arrow, leading to the band relative shift between VSeF and Al₂Se₃. We found that the half-metallicity with spin-up polarization appears in the VSeF part of VSeF/Al₂Se₃ (↑) heterostructure, showing n-type doping feature. In contrast, VSeF remains as a semiconductor, when combined with P ↓ Al₂Se₃. Therefore, the ferromagnetic half-metal/semiconductor switching in VSeF can be controlled by the polarized states of the Al₂Se₃ monolayer.

Bilayer Al₂Se₃ ferroelectric gate

To realize nonvolatile electrical control of spin polarization in VSeF, we further tried to stack VSeF on the bilayer Al₂Se₃ forming a trilayer vdW heterostructure (Fig. 4a), where the bilayer Al₂Se₃ possesses enhanced ferroelectric polarization^47,48. Similar to VSeF/Al₂Se₃ bilayer heterostructure, we first calculated the band alignments for VSeF/biAl₂Se₃ (↑) and VSeF/biAl₂Se₃ (↓). As shown in Fig. 4b, the band alignments between VSeF and neighbor Al₂Se₃ (FE1) are less affected by the added bottom Al₂Se₃ (FE2), which are similar to that of VSeF/Al₂Se₃ bilayer heterostructure. Particularly, due to the built-in electric field, there also exists charge transfer between bilayer Al₂Se₃. To visualize the charge redistribution in VSeF/biAl₂Se₃ heterostructure, the charge density difference, plane-averaged charge density difference (Δρ) and the z-direction integral of plane-averaged charge density difference (n) are shown in Fig. 4c, d for VSeF/biAl₂Se₃ (↑) and VSeF/biAl₂Se₃ (↓), respectively. The negative Δρ represents the charge depletion and the positive Δρ represents the charge accumulation.

Fig. 4: VSeF/biAl₂Se₃ trilayer heterostructures.

a Side views of VSeF/biAl₂Se₃ trilayer heterostructures. The red arrow represents the polarization direction of Al₂Se₃. b Band alignments of VSeF/biAl₂Se₃ (↑) and VSeF/biAl₂Se₃ (↓) with respect to the vacuum level of VSeF. The red and blue bars depict the band edges of spin-up and spin-down channel of VSeF, respectively. The purple bars depict the band edges of two layers of FE Al₂Se₃. c, d Charge density difference, planar-averaged density difference (black line) and the integral (red lines) of planar-averaged density difference along z-direction for VSeF/biAl₂Se₃ (↑) and VSeF/biAl₂Se₃ (↓), respectively, where the blue dashed lines indicate the atomic boundary of each layer, and the cyan and magenta isosurfaces represent electronic accumulation and depletion with isovalue of 2.03 × 10^–3 e Å⁻³, respectively. e, f Layer-resolved PDOS of VSeF/biAl₂Se₃ (↑) and VSeF/biAl₂Se₃ (↓). The potential energy decreases along the direction of black dashed line. FE1 and FE2 denote the upper Al₂Se₃ layer and the bottom Al₂Se₃ layer, respectively. The orange, purple, and pink lines represent the PDOS contributed by VSeF, FE1, and FE2, respectively.

Clearly, the charge transfer not only occurs between VSeF and FE1, but also between FE1 and FE2. The z-direction integral of plane-averaged charge density difference indicates that the total charge depletion and accumulation of each layer mainly occur within VSeF and FE2, and the variation of total charge of FE1 is small. Therefore, it can be equivalently viewed that the charge transfer mainly happens between VSeF and FE2, where the FE1 acts as a bridge. As reflected in the layer-resolved PDOS (Fig. 4e, f), because the effective charge transfer occurs within VSeF and FE2, both VSeF and FE2 exhibit metallicity, while FE1 always remains as a semiconductor. Interestingly, n-doped VSeF with spin-up carriers appears in VSeF/biAl₂Se₃ (↑) heterostructure, and p-doped VSeF with spin-down carriers appears when reversing the ferroelectric polarization of bilayer Al₂Se₃. Therefore, nonvolatile electric control of spin polarization is achieved in VSeF/biAl₂Se₃ trilayer heterostructure. Different spin-orientation channel current in VSeF can be switched by the polarized states of bilayer Al₂Se₃.

Doping effect on VSeF from FE substrates

It’s worth noting that the VSeF layer always maintains the ferromagnetic ground state and out-of-plane easy magnetization axis in all heterostructures, as shown in Supplementary Table 4, the energies of out-of-plane ferromagnetic configuration are lowest for whichever heterostructure. Due to the interfacial engineering on magnetism^49,50, we further explored the influence of FE substrates on the Curie temperature of VSeF. As shown in Figs. 5a, b, the T_c value of VSeF is enhanced to 71 K, 76 K and 81 K in VSeF/Al₂Se₃ (↑), VSeF/biAl₂Se₃ (↓) and VSeF/biAl₂Se₃ (↑) heterostructures, respectively. While for the VSeF/Al₂Se₃ (↓) heterostructure, the T_c value is slightly decreased to 61 K. Since the lattice constants of VSeF layer are fixed in all heterostructures and the structure variations of VSeF layer are minor (Supplementary Table 5 and Supplementary Fig. 4), the change of T_c value can be primarily attributed to the interfacial charge transfer between VSeF and FE substrates. VSeF layer is n-type doped in VSeF/Al₂Se₃ (↑) and VSeF/biAl₂Se₃ (↑) heterostructures, and p-type doped in VSeF/biAl₂Se₃ (↓) heterostructure, exhibiting ferromagnetic half-metallic property. However, VSeF layer keeps its ferromagnetic semiconducting property in VSeF/Al₂Se₃ (↓) heterostructure. Generally, due to the existence of itinerant carriers, ferromagnetic metals possess higher Curie temperatures than that of ferromagnetic semiconductors^4,5,6.

Fig. 5: Doping effect on VSeF layer from FE gates.

a, b The variations of magnetic moment and susceptibility as functions of temperature in VSeF/Al₂Se₃ (↓) (blue line), VSeF/Al₂Se₃ (↑) (green line), VSeF/biAl₂Se₃ (↓) (orange line) and VSeF/biAl₂Se₃ (↑) (magenta line) heterostructures. The black dashed line indicates the T_c value of pristine VSeF monolayer. c The doping concentration of VSeF layer under different FE substrates (bilayer Al₂Se₃, bilayer Ga₂Se₃ and bilayer In₂Se₃) and FE polarized states (upward polarization or downward polarization). The blue and green bars depict the doping concentrations from upward and downward electric polarized FE gates, respectively. The positive and negative doping concentration indicate electron and hole doping, respectively.

By calculated the charge density difference (Fig. 4c, d and Supplementary Fig. 17a, b), we also quantitatively analyzed the doping concentrations of Al₂Se₃ gates under different layer numbers and FE polarized states. The doping concentrations on VSeF layer are 1.6 × 10¹³ cm⁻², 0 cm⁻², 3.1 × 10¹³cm⁻² and −1.5 × 10¹³cm⁻² in VSeF/Al₂Se₃ (↑), VSeF/Al₂Se₃ (↓), VSeF/biAl₂Se₃ (↑) and VSeF/biAl₂Se₃ (↓) heterostructures, respectively. Here, the positive values represent electron doping and negative values represent hole doping. We found that the Curie temperature increases with the carrier doping concentration. And the hole carriers with smaller effective mass are more beneficial for the enhancement of T_c than electron carriers. Therefore, bilayer Al₂Se₃ FE gates not only can control the carriers’ spin polarization in VSeF channel layer, but also can enhance the Curie temperature of VSeF.

Furthermore, we revealed that such nonvolatile electric control of spin polarization can be applied to other 2D BMS/FE multiferroic heterostructures, where the choices of FE gates and 2D BMS channel materials are abundant. For example, both bilayer Ga₂Se₃ and In₂Se₃ FE substrates show reversible interfacial doping effect which results in the manipulation of carriers’ type and spin-polarized direction in VSeF layer by switching the ferroelectric polarized state (Supplementary Fig. 18 and Supplementary Fig. 19). However, since the band alignment between VSeF and different FE substrates is different, the interfacial charge transfer in VSeF/FE heterostructures would be different, which is related to the FE material species and FE polarized states. By calculating the charge density difference in different VSeF/FE heterostructures (Supplementary Fig. 17), we summarized the doping concentration of different FE gates in Fig. 5c. The carrier doping concentrations from different FE gates are all on the order of 10¹³cm⁻², which is comparable with the traditional gate-voltage applied⁵¹. Besides, we verified the nonvolatile control strategy is also achieved in LaBr₂/triAl₂Te₃ (trilayer Al₂Te₃) multiferroic heterostructure (Supplementary Fig. 20), where LaBr₂ has been predicted to be a 2D BMS⁵². For the other screened BMS VSF, the reversible control of carriers’ spin polarization is also achieved in the VSF/biGa₂S₃ multiferroic heterostructure (Supplementary Fig. 21). These results indicate the feasibility and generality of our proposed nonvolatile electrical control strategy to BMS materials.

Devices based on VSeF/Al₂Se₃ and VSeF/biAl₂Se₃ heterostructures

Nanoscale devices are the inevitable trend of future technology development. Here, we suggested that the VSeF/Al₂Se₃ bilayer and VSeF/biAl₂Se₃ trilayer vdW heterostructures are promising structures for designing nanoscale spintronic devices. As shown in Fig. 6a, b, an atom-thick multiferroic memory device can be constructed based on the VSeF/Al₂Se₃ bilayer heterostructure. Since the electronic properties of the upper VSeF layer, either ferromagnetic half-metallic (100% spin-up polarization) or semiconducting, are controllable by the polarized state of Al₂Se₃, it serves as a channel material to be selectively conductive. Spin-up electrons can propagate through the VSeF (“on” state) for VSeF/Al₂Se₃ (↑) (Fig. 6a), while the electron transmission is blocked (“off” state) for VSeF/Al₂Se₃ (↓) (Fig. 6b). Here, data writing in the memory is realized by switching the ferroelectric polarized states, and data reading is realized by detecting the electrical signals.

Fig. 6: Two types of spin FETs.

a, b Atom-thick multiferroic memory based on the VSeF/Al₂Se₃ bilayer heterostructure, where the data writing and reading can be achieved by manipulating the ferroelectric polarization states of Al₂Se₃ monolayer and measuring the conductivity of VSeF channel, respectively. The red and blue arrows represent carriers’ spin-up and spin-down polarized orientations, respectively. c, d spin filter based on the VSeF/biAl₂Se₃ trilayer heterostructure, where the carriers’ spin-polarized orientation and carriers’ type (electron/hole) in the VSeF channel depend on the ferroelectric polarization states of bilayer FE Al₂Se₃.

As for VSeF/biAl₂Se₃ trilayer heterostructure, we designed a spin filter device (Fig. 6c, d). The spin polarization of the upper VSeF layer, either spin-up or spin-down, are controlled by the ferroelectric polarized state of bilayer Al₂Se₃. For VSeF/biAl₂Se₃ (↑), n-doped VSeF layer only allows spin-up electron carrier pass (Fig. 6c). When the polarization direction of bilayer Al₂Se₃ is reversed by an external electric field, the upper VSeF layer is p-type doped, only allowing spin-down hole carrier pass (Fig. 6d). Therefore, the manipulation of spin-polarized current can be achieved in this device.

Discussion

In summary, based on first-principles calculations, we reported an intrinsic 2D BMS VSeF and unveiled the microscopic origin of its BMS feature. The non-negligible interorbital Coulomb repulsion between occupied states and unoccupied states in V³⁺ ([Ar]3d²) and spin exchange splitting are both responsible for its bipolar character. Furthermore, we proposed a nonvolatile way to manipulate the spin polarization of BMS by introducing the ferroelectric gate. As embodied in the 2D BMS VSeF, the magnetic half-metal/semiconductor switching and spin-up/spin-down polarization switching in VSeF can be realized by manipulating the electric polarization of monolayer FE Al₂Se₃ and bilayer FE Al₂Se₃ in VSeF/Al₂Se₃ bilayer and VSeF/biAl₂Se₃ trilayer multiferroic heterostructures, respectively. These reversible switching endow VSeF with many promising applications in nanodevices, such as atom-thick multiferroic memory and spin filter. We find that the interfacial doping effect from FE gates also plays a role to enhance the Curie temperature of VSeF layer, which facilitates the utilization of spintronic nanodevices based on VSeF BMS. Finally, it’s worth noting that our proposed nonvolatile way to manipulate spin polarization in BMS materials by introducing FE gates was feasible and general, where the choices of BMS channel materials and FE gates are abundant. Therefore, our work not only reports an intrinsic 2D BMS, but also provides a feasible and general approach to achieve nonvolatile electrical control of 2D BMS.

Methods

All first-principles calculations were performed by using the density functional theory (DFT), as implemented in the Vienna ab initio simulation package (VASP)⁵³. The Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA)⁵⁴ was employed to deal with the electron exchange-correlation potentials. The projector-augmented-wave (PAW)⁵⁵ pseudopotentials were applied to describe the electron-ion interaction with a plane-wave cutoff of 520 eV. 3p⁶3d⁴4s¹ of V, 4s²4p⁴ of Se, 3s²3p⁴ of S, 2s²2p⁵ of F, 3s²3p¹ of Al, 4s²4p¹ of Ga, 5s²5p¹ of In, 5s²5p⁶5d¹6s² of La, 4s²4p⁵ of Br and 5s²5p⁴ of Te electronic configurations were treated as valence electrons, respectively. The strong Coulomb interaction between V-3d electrons is corrected by the DFT + U method in the Dudarev form⁵⁶, where the effective U parameter U_eff = U – J was applied to the d orbitals of V atoms. The hybrid Heyd-Scuseria-Ernzerhof functional (HSE06)⁵⁷ was also used to obtain the band structure for VSeF monolayer. A 20 Å thickness vacuum layer was introduced along the z-axis in all calculations. Ab initio molecular dynamical simulations (AIMD) were performed under an NVT ensemble. The ferroelectric reversal barrier was calculated using climbing nudged elastic band (CI-NEB) method^58,59. The interlayer van der Waals interaction was considered by using the DFT-D3 method of Grimme⁶⁰ for VSeF/Al₂Se₃, VSeF/biAl₂Se₃, VSeF/biGa₂Se₃, VSeF/biIn₂Se₃, LaBr₂/triAl₂Te₃ (trilayer Al₂Te₃) and VSF/biGa₂S₃ heterostructures. A dipole correction was applied to eliminate spurious dipole-dipole interaction between periodic images. Atomic positions and lattice parameters were fully relaxed until the force acting on each atom was less than 10^–3eV Å⁻¹ for VSeF monolayer, VSF monolayer and LaBr₂ monolayer. For VSeF/Al₂Se₃, VSeF/biAl₂Se₃, VSeF/biGa₂Se₃, VSeF/biIn₂Se₃, LaBr₂/triAl₂Te₃ and VSF/biGa₂S₃ heterostructures, due to the lattice mismatch, we fixed the lattice constant of VSeF, VSF and LaBr₂ ferromagnetic layer and only relaxed the atomic positions with the force convergence criterion of 10^–2eV Å⁻¹. The phonon spectrum was calculated using the finite-displacement method implemented in the PHONOPY code⁶¹. The dynamical Monte Carlo (MC) simulation based on the Heisenberg model was performed to estimate the magnetic transition temperature.