Introduction

A magnetic skyrmion, usually a few nanometers in diameter, is a topologically protected magnetic quasi-particle with a whirling spin texture in real space1. Stable magnetic skyrmions, emerging in various magnetic materials1,2,3,4,5,6 as a result of competing Heisenberg exchange and Dzyaloshinskii–Moriya interaction (DMI)7, can be driven by low current density8,9,10,11,12,13. The creation and annihilation of magnetic skyrmions in thin films have been demonstrated by current14,15, marking a significant step toward low-dimensional skyrmion systems. In recent experiments skyrmion and its motion under electric current have been observed in Fe3GeTe216,17, proving 2D magnetic materials a new category of skyrmion medium. In addition, another study showed that ferroelectric (FE) polarization can be integrated into the magnetic skyrmion systems to realize nonvolatile control via the magnetoelectric coupling effect in BaTiO3/SrRuO3 perovskite heterostructure (HS)18. It suggests that skyrmions can be controlled directly by electric fields—instead of electric current—via polarization switching. This significantly reduces energy consumption. However, whether this type of control can be extended to atom-thick van der Waals (vdW) HS remains largely elusive. Once achieved, it delivers great application potential for high-performance spintronic devices based on 2D skyrmions.

Since the discovery of graphene, extensive research on two-dimensional ferromagnetic (FM)19,20,21,22,23,24,25 and FE26,27,28,29,30,31,32 materials has been carried out rapidly. The magnetic anisotropy in 2D materials induced by spin–orbit coupling enables the long-range magnetic ordering, forming easy-axis or easy-plane 2D magnets. In the easy-axis 2D magnets, skyrmions are usually of the Néel-type, whereas in the easy plane 2D magnet, skyrmions usually exist in bimerons form33,34,35. When 2D FE and FM materials are combined to form atomic layer-thick multiferrous vdW HSs, such 2D system endows nonvolatile coupling between two ferroic orderings36,37,38, compensating the scarcity of the single-phase multiferroic material. Furthermore, nonvolatile FE polarization controlled magnetic skyrmions through the magnetoelectric coupling effect is highly anticipated in such systems. In contrast to the traditional perovskite-based multiferroic HSs, 2D multiferroic HSs have an inherent advantage in achieving strong magnetoelectric coupling, that is, all atoms are exposed to the surface, which makes magnetism more sensitive to FE polarization. Recent reports have demonstrated that the interlayer magnetoelectric coupling in a 2D vdW HSs survives the large space between two different ferroic layers. For example, polarization can manipulate a variety of properties including the conductivity of the CrI3 in the CrI3/Sc2Co2 HS36, the magnetic anisotropy of the CrGeTe3 in CrGeTe3/In2Se3 HS37, and magnetic ordering of the FeI2 in the FeI2/In2Se3 HS38. All these works indicate the possibility of electric control of the magnetism and even skyrmions in 2D vdW HSs.

Although the existence of magnetoelectric coupling effect has been confirmed in the 2D vdW HSs, the influence of the polarization on the magnetism still lacks systematic investigation. Besides, the usual low Curie temperature of the 2D magnetic monolayer limits the study in terms of practical applications. In this work, we propose a LaCl/In2Se3 multiferroic HS, where In2Se3 is an ideal 2D FE material with controllable out-of-plane spontaneous polarization24,39,40,41, while LaCl was synthesized decades ago and proved to be a vdW layer compound42,43,44,45. Furthermore, LaCl monolayer as an easy-plane FM metal has been confirmed in many works46,47,48,49. In addition, La-5d orbital has a strong spin–orbit coupling, which satisfies the requirement of producing strong Dzyaloshinskii–Moriya interaction, i.e., a necessary condition for the generation of magnetic chiral skyrmions. The nearly perfect lattice matching (lattice mismatching rate <0.1%) between the two vdW compounds makes them ideal model systems to construct HS for theoretical studies.

Our results show that the magnetic skyrmions in bimerons form is generated in the atom-thick vdW LaCl/In2Se3 multiferrous HS, see Fig. 1a, due to the broken inversion symmetry of LaCl by the In2Se3 FE polarization. The bimerons can be driven by current and generated or annihilated by FE switching. The diameter of bimeron is only about 23 nm, which enhances the controllability and integrability of the bimerons-based functional devices. In addition, we have systematically investigated the effect of the polarization orientation and magnitude on magnetism and realized the tuning of the Curie temperature and the magnetic easy axis. The strong magnetoelectric coupling effect observed in the 2D HS is unprecedented. Our results pave a new avenue for future devices based on vdW structures.

Fig. 1: Crystal structure diagram of LaCl/In2Se3 HS.
figure 1

a Illustrations of a magnetic bimeron. b, c show the top and side views of the HS, respectively. The gray arrow represents the polarization direction of In2Se3. d Magnetic structure of LaCl for calculating the exchange coupling parameter (DMI vector).

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Results

Material model and computational details

We combined first-principles density functional theory (DFT) and micromagnetic simulation to investigate the magnetism of LaCl monolayer and LaCl/In2Se3. Monte Carlo simulation was performed to locate the FM Curie temperature. The electronic properties and basic magnetic parameters of the LaCl monolayer and the LaCl/In2Se3 were calculated using the VASP package50,51 based on the projected augmented wave (PAW) pseudopotentials. We constructed the HS along the [001] direction, see Fig. 1b, c, fully releasing the xy-plane lattice constant and spatial ion coordinates. The lattice constants of the free-standing LaCl and In2Se3 monolayer are, respectively, 4.033 Å and 4.035 Å—only 0.1% lattice mismatch rate, and we can thus safely neglect the influence of strain. The Heisenberg type spin Hamiltonian of LaCl can be expressed as,

$$H = - J_1\mathop {\sum }\limits_{i,j} {\mathbf{M}}_i \cdot {\mathbf{M}}_j - J_2\mathop {\sum }\limits_{i,k} {\mathbf{M}}_i \cdot {\mathbf{M}}_k - J_3\mathop {\sum }\limits_{j,l} {\mathbf{M}}_j \cdot {\mathbf{M}}_l - {\mathbf{D}}_1\mathop {\sum }\limits_{i,j} {\mathbf{M}}_i \times {\mathbf{M}}_j \\ - \, {\mathbf{D}}_2\mathop {\sum }\limits_{i,k} {\mathbf{M}}_i \times {\mathbf{M}}_k - {\mathbf{D}}_3\mathop {\sum }\limits_{j,l} {\mathbf{M}}_j \times {\mathbf{M}}_l - K\mathop {\sum }\limits_i \left( {M_i^z} \right)^2,$$
(1)

where J1, J2, and J3 are the exchange coupling parameters; and similar notation applies to the DM vectors (D1, D2, and D3), as shown in Fig. 1d. M denotes the magnetic moment of each atom, and K is the perpendicular magnetic anisotropy constant. The calculation method of the exchange coupling parameter, perpendicular magnetic anisotropy constant, and DM vectors are summarized in the Supplementary Information part1 and part2. Subsequently, the parameters extracted from DFT calculation were used subsequently as the input to the micromagnetic simulation using OOMMF software52. The boundary effect was taken into account by imposing the interfacial DMI in micromagnetic simulations53.

The skyrmion is defined in terms of the nonzero integer topological charge defined as12,54,

$$Q = \frac{1}{{4\pi }}{\int} {\mathbf{m}} \cdot \left( {\frac{{\partial {\mathbf{m}}}}{{\partial x}} \times \frac{{\partial {\mathbf{m}}}}{{\partial y}}} \right)dxdy,$$
(2)

where m is the normalized magnetization. When Q is quantized at the value ±1, we may refer this state to a skyrmion.

In addition, we performed Monte Carlo simulations with a 50 × 50 × 1 supercell based on the Heisenberg model to find the FM Curie temperature (Tc) of the LaCl monolayer and LaCl/In2Se3. For each temperature, 105 Monte Carlo updates were employed. The FM Curie temperature Tc is estimated by the peak position of the magnetic susceptibility (see Supplementary Information, Part 3).

Micromagnetic simulation of bimeron

Here we use P + (P−) to represent the polarization direction of the In2Se3 that is along the +z (−z) axis. The result shows that the free-standing LaCl monolayer is metallic with in-plane magnetization, consistent with previous reports55,56,57. In the HS, the interlayer spacing d between LaCl and In2Se3 is 3.58 and 3.17 Å in LaCl/P+ and LaCl/P−, respectively, indicating the non-bonded nature. Moreover, both LaCl/P + and LaCl/P− structures remain in the metallic FM state, the same as that in the monolayer LaCl, showing that the switching of the In2Se3 polarization does not directly affect the magnetic ordering in LaCl. However, the exchange interaction parameters are more sensitive to the polarization. We summarize in Table 1 the calculated exchange interaction parameters. In the P+ state, J2 and J3 are enhanced compared to that of the free-standing LaCl monolayer, whereas the magnitude of J1 sees no evident change. Upon polarization reversal to the P− state, J1 undergoes larger enhancement than J2 and J3. In addition, the FE polarization that originates from the In2Se3 layer breaks the spatial inversion symmetry in the adjacent LaCl, which gives rise to a DMI in HS7,58. We present in Table 1 the calculated in-plane D vector of the HS. The results show that the magnitude of D vector is different in two polarization states, indicating nonvolatile control of the exchange effect and DMI by the FE polarization. The DMI induced in our 2D HS by ferroelectric polarization is superior to the DMI induced in the CrI3 monolayer by an electric field that breaks its spatial inversion symmetry59: In In2Se3 the nonvolatile nature of FE polarization persists into the magnetic switching in the LaCl/P ± structure with a significant reduction of energy consumption in the proposed device.

Table 1 Magnetic parameters of LaCl/In2Se3 HS.
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We used OOMMF software to perform micromagnetic simulations of the LaCl monolayer and LaCl/P ± HSs in a nanodisk geometry with a diameter of 200 nm. The varied parameters including J, D, K, and Ms for P+ and P− states are listed in Table 1, respectively. The initial spin state was set to paramagnetic (random) states. In the LaCl/P+ configuration, bimerons spin texture emerges, as shown in Fig. 2a. The calculation shows the topological charge of the bimeron Q = 1.0, consisting of a vortex (Q = 0.5) and an anti-vortex (Q = 0.5). The extracted bimeron texture map is depicted in Fig. 2d, e. Due to the presence of in-plane anisotropy, bimeron’s outer magnetization is along the in-plane direction rather than the out-of-plane one, which consequently allows two bimerons with opposite topological numbers (Q = 1 and Q = −1) to coexist in the same magnetic domain (see Supplementary Fig. 4)60. This is significantly different from other types of skyrmions. This spin texture disappears, accompanied by a vanishing Q to zero when the polarization is reversed to the P− state, shown in Fig. 2b. Subsequently, we found that bimeron can appear when the K value ranges from −0.04 to −0.13 meV (other parameters remain unchanged). Figure 2c represents the bimeron texture when the K = −0.1 meV, showing a smaller bimeron size compared to the P+ state and this phenomenon is explained in part 5 of the Supplementary Information. In the P− state, the enhanced K value caused by the polarization completely exceeds the range that allows bimeron to exist, leading to bimeron’s annihilation in this polarized state. Furthermore, Fig. 2c verifies the above conclusion that bimerons can appear in the same magnetic domain. Therefore, by simply switching the FE polarization, two distinct magnetic states—referred to in the binary code as “0” and “1”—can be realized and could be used as building blocks for information storage. The diameter of bimeron in LaCl/P + HS is only about 23 nm, which enhances the controllability and integratability of the bimerons-based functional devices.

Fig. 2: Ferroelectric regulation and current drive of bimeron.
figure 2

The top views of the micromagnetic simulation for (a) LaCl/P+ and (b) LaCl/P− HSs. c The top views of the micromagnetic simulation for LaCl/P− HS with K = −0.1 meV, the red rectangle shows two bimerons with opposite topological numbers. d–f Blue–red color represents the region of x, y, z component along the magnetic direction of a bimeron. g Snapshots of the bimeron moving under a current of j = 3 × 1010 A m−2 on nanotracks.

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Fig. 3: Evolutions of spin textures under the modulations of magnetic anisotropy.
figure 3

Relaxed magnetic configurations under various K-values.

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We show in Fig. 3 the magnetization as a function of K while keeping other parameters the same as those in the LaCl/P+ configuration. When K is positive, the perpendicular magnetic anisotropy provides an easy axis to support magnetizations pointing either up or down. In this case, the formation of Néel-type skyrmions is energetically favored. When K is negative, however, the easy axis is confined within plane by the in-plane anisotropy, forcing the Néel-type skyrmions to evolve into vortices, the FM stripes into anti-vortices, and eventually the Néel-type skyrmions transform into bimerons.

The current-driven motion of bimeron in the LaCl/P+ configuration was simulated on a 150  × 600 nm nanotrack. Prior to the injection of current, we created and relaxed the bimeron near the left end of the nanotrack. An in-plane current of j = 3 × 1010 A m−2 was later applied along the x direction to mobilize the bimeron, see Fig. 2g. The bimeron remains stable while traversing the nanotrack at the speed of 72.17 m s−1; the transverse motion along the y-axis is due to the skyrmion Hall effect11,61.

Regulation of LaCl magnetism by In2Se3 polarization

In our system, the out-of-plane polarization of the In2Se3 layer redistributes charges in the LaCl layer to screen the polarization field, resulting in a change in the magnetic properties of LaCl. The enhanced polarization is thus expected to improve the regulation for LaCl magnetism. For the ferroelectric substrate In2Se3, polarization increases as a function of the film thickness and saturates as the thickness increases to three layers26. Therefore, using a three-layered In2Se3, we simulated an enhanced polarization which is denoted as 3 P± for simplicity. Note that the method by increasing the layer thickness for better effect does not apply to all 2D HS system. For example, in the WTe2/CrI3 HS, the conductance of WTe2 depends on the nearest CrI3 layer and is not affected by the CrI3 thickness62. The impact of the polarization intensity in In2Se3 on the magnetism in LaCl is shown in Fig. 4a, b. We found that J1 and K increase significantly with the polarization intensity along the −z direction; both reach its maximum at 3 P−, 348 and 449% increase with respect to that of LaCl monolayer, respectively. When the polarization switches to the +z direction, the in-plane exchange interaction parameters J2 and J3 have enhanced in the LaCl/3 P+ configuration compared to the monolayer LaCl. K decreases gradually with a decreasing polarization, and the easy-axis switches to out-of-plane in the LaCl/3 P+ configuration. Therefore, the polarization vector offers a channel via which we may tune the exchange coupling and magnetic anisotropy. As a result of such correlation, the Curie temperature of LaCl shifts with the polarization switching, which is confirmed by the Monte Carlo simulation shown in Fig. 4c. We are thus able to tune the magnetism of the HS from FM LaCl/(3)P+ to paramagnetic LaCl/(3)P− by the polarization when the temperature is in the range between 92 K (102 K) and 99 K (110 K). They discuss the Tc in detail in part 3 of the Supplementary Information. The magnetoelectric coupling in our system is robust and the two FE polarization states are stable: One can be switched into the other by an external electric field, yet either can survive the field removal. This bistability of FE polarization of In2Se3 means that the magnetic properties of the LaCl layer can be switched steadily between the two states. This feature is highly desirable in nonvolatile information storage.

Fig. 4: The influence of polarization intensity on magnetic parameters.
figure 4

a Exchange interaction parameters in LaCl. b Perpendicular magnetic anisotropy constant in LaCl (c) Curie temperature (Tc) of LaCl. Since we only calculated the DMI of LaCl/P± , the effects of the perpendicular magnetic anisotropy and exchange interaction terms on Tc are presented by the data in black squares, and the effect of DMI on Tc in LaCl/P± is presented by the data in red spheres. d The number of electrons gained of LaCl. e The net magnetic moment of LaCl. In these figures, 3 P± represents a configuration that contains three In2Se3 layers.

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Moreover, we found that the net magnetic moment is highly correlated with the charge transfer between LaCl and In2Se3, which is shown in Fig. 4d, e. The decrease in the electron number on the LaCl side is beneficial to the increase in the net magnetic moment of the system. In the LaCl/(3)P− configuration in particular, compared to LaCl/(3)P+ , more electrons participate in charge transfer to In2Se3, resulting in a significant increase in the net magnetic moment of the system. As shown in Fig. 5a, the spin-up states in the LaCl/3 P− configuration is populated more than the spin-down state. Viewing the decrease in the electron number on the LaCl side, we are able to conclude that the charge transfer across the interface from LaCl to In2Se3 occurs mainly in the spin-down state.

Fig. 5: Charge transfer in different polarization states.
figure 5

a Spin-up (red line) and -down (blue line) contributions on the charge transfers in LaCl/3 P± HSs. b Differential charge density on the LaCl side. c Differential charge density distributions of LaCl/3 P± HSs and integrals of differential charge densities (black line). d The layer-resolved partial DOS of LaCl/3 P± HSs. The gray and green arrows represent the polarization direction of In2Se3 and the moving direction of Fermi level in HSs, respectively.

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The mechanism for interfacial multiferroicity

Change in electronic structure holds the key to understand the variation in magnetism induced by polarization switching. As the differential charge density distribution in Fig. 5c shows, the tuning of the magnetism can be interpreted by electronic reconfiguration that takes place on the LaCl side. In the LaCl/3 P+ configuration, pushed “down” by the FE polarization along +z, the electrons on the LaCl side are transferred from the top to the bottom surface of the entire HS, shown in Fig. 5b. While in the case of LaCl/3 P−, the opposite polarization brings “up” electrons in LaCl from the lower surface. However, unlike the case of LaCl/3 P+ , electrons are not directly transferred to the upper surface. Instead, it is concentrated in between La1 and La2. Different charge distribution ultimately affects the exchange coupling constant J on the LaCl side, rendering it different in the 3 P+ and 3 P− states. As per polarization switching, the electrons around the La ion are redistributed, leading to variation in the spin–orbit coupling of the La atom, too. This eventually gives rise to the variation of the DMI on the LaCl side.

We performed a layer-resolved partial density calculation on the LaCl/3 P± configurations to scrutinize the underlying mechanism. Figure 5d shows that the electronic distribution on the LaCl side, driven by the built-in electric field of In2Se3, remains largely unchanged yet the Fermi energy has been shifted, which is due to the change of electric potential caused by the polarization discontinuity. In addition, owing to the broken time-reversal symmetry in ferromagnetic (LaCl part) materials, the charge transfer between LaCl and In2Se3 is different for spin-up and spin-down states, which results in magnetic states change in the two states that are polarized oppositely. The above analysis reveals that the change in ferromagnetism in LaCl is mainly driven by two mechanisms: (i) change in potentials caused by the polarization discontinuity, and (ii) time-reversal symmetry breaking in magnetic materials leads to a difference in charge transfer for spin-up and spin-down states. These two requirements for polarization tuning of magnetism in HS are not limited to the present LaCl/In2Se3 system and we foresee that effective control of 2D ferromagnetism can be realized in other materials, too.

We must nevertheless point out that the surface layer of In2Se3 in the LaCl/3 P+ configuration exhibits metallic behavior and it falls into the category of polar metal. The screening effect in metal eliminates the possibility of FE switching in bulk materials. This screening is, however, negligible in an atomically thin film due to the strong penetration of the external electric field. The switchable behavior of 2D polar metals has been demonstrated experimentally29. Switching the polarization vector using an external electric field is therefore a viable solution.

In summary, we designed and investigated a 2D vdW LaCl/In2Se3 HS. Magnetic skyrmions can exist in bimerons form therein with a diameter of about 23 nm. By switching the polarization in In2Se3, the anisotropy, FM Curie temperature, and the bimerons were manipulated. Such a robust magnetoelectric coupling effect that occurs in a 2D vdW HS is unprecedented. Further analysis shows that the coupling between FM and FE is attributed to the effect of the polarization discontinuity in the FE substrate and the broken time-reversal symmetry in the magnetic film. Therefore, such tunability in magnetic properties achieved in the LaCl/In2Se3 HS can be transplanted to other material systems, too. The significance of this work is twofold. It not only demonstrates the feasibility of nonvolatile control for magnetism and skyrmions in LaCl/In2Se3 HS but also puts forward a general idea to manipulate many characteristics of the 2D vdW HSs by two oppositely polarized states. Furthermore, this work highlights that an artificially designed 2D multiferroic HS is an ideal platform to realize large ME coupling and observe nontrivial physical properties.

Methods

The DFT method and parameters

First-principles calculations were performed using the VASP package based on the projected augmented wave pseudopotentials50,51. The electronic exchange-correlation potential is treated within the spin-polarized generalized gradient approximation plus U (GGA + U) of PBEsol formula50,63,64,65. Due to that, the GGA algorithm will underestimate the bandgap of the f orbitals, an effective 7 eV Hubbard Ueff parameter is applied on La’s f orbitals using the Dudarev method66 in order to correct its bandgap and prevents f orbitals from participating in orbital hybridization near the Fermi level. We take the van der Waals corrections as parameterized in the semiempirical DFT-D3 method into consideration for all the configurations67. The first Brillouin zone is sampled with the 9 × 9 × 1 k-points meshes for the DFT calculation both of the monolayer and the HSs. In order to ensure the energy convergence, denser k-points meshes up to 15 × 15 × 1 are also tested, which shows that 9 × 9 × 1 settings are enough to achieve the desired accuracy. A plane-wave basis set with a kinetic energy cutoff of 500 eV is employed. All structures are fully relaxed until the energy and force converge to 10−5 eV and 10−2 eV/Å, respectively. To eliminate the periodic boundary effect, a 15 Å thinness vacuum layer is introduced along the z direction. Using spin–orbit coupling for calculating magnetic anisotropic energy and DMI.

OOMMF simulations parameters

OOMMF software were used to simulate the magnetization dynamics52. The time evolution of the magnetization is described by the Landau–Lifshitz–Gilbert (LLG) equation68.

$$\frac{{d{\mathbf{M}}}}{{dt}} = - \gamma _0{\mathbf{M}} \times {\mathbf{h}}_{{\mathrm{eff}}} + \alpha \left( {{\mathbf{M}} \times \frac{{d{\mathbf{M}}}}{{dt}}} \right),$$
(3)

where heff = −δH/δM is the effective field, α is the Gilbert damping coefficient, and γ0 is the absolute gyromagnetic ratio. We include in the simulation a Slonczewski-like spin-transfer torque (STT) driven by the spin current that is generated by the spin-Hall effect,

$${\uptau} = - \frac{{\gamma _0\hbar jP}}{{2ae\mu M_{\mathrm{S}}}}{\mathbf{M}} \times \left( {{\mathbf{M}} \times {\mathbf{p}}} \right).$$
(4)

Parameter e is the electron charge and MS is the saturation magnetic moment. j is the electric current density. Spin-Hall angle P = 0.4. The lattice constant a = 4 Å. The polarization of spin current is p = −x. The parameters of LaCl monolayer and LaCl/In2Se3 HS are shown in Table 1. In simulations models, we keep α = 0.2 and γ0 = 2.211 × 105 m A−1 s−1. The size of the cells is chosen to be 4 Å × 4 Å × 5 Å.