Introduction

Multiferroic materials, which exhibit at least two types of ferroic order—ferroelectricity1,2, ferromagnetism3,4, ferroelasticity5,6 and so on—have attracted significant attention due to their promising applications in high-density multifunctional devices7, such as transducers8, actuators9, and field-effect transistors10. Recently, two-dimensional (2D) materials have emerged as a promising class, drawing considerable interest for their atomically thin properties and potential applications in nanoelectronics11,12,13. In particular, 2D multiferroics, driven by magnetoelectric14,15,16, piezoelectric17,18,19, and magnetoelastic20,21 coupling effects, have demonstrated significant potential for applications in non-volatile memory22, sensors23, and energy harvesting systems24.

With the rapid growth in the discovery of multiferroic materials, the study of ferroelasticity – ferromagnetism (FE-FM) multiferroics has gained significant attention6,20,21. Recent theoretical advancements have identified several candidate materials, such as VSSe25, t-VP26, and MnPS327, where magnetic anisotropy can be modulated by ferroelastic strain, contributing to this burgeoning field. These systems typically exhibit two equivalent orientation variants, which can be reversibly switched by applying opposite in-plane strains. However, in most cases, the ferroelastic and magnetic orders are only weakly coupled. For instance, Seixas et al. investigated the prototype monolayer α-SnO and found that the coupling between FM and FE depends on the density of holes present in the material28. Similarly, Xu et al. proposed AgF2, an antiferromagnetic (AFM) ferroelastic semiconductor with high spin polarization29, as a promising material for further exploring spin-dependent phenomena30,31, yet the coupling between structural and magnetic transitions remains indirect. Therefore, it is highly desirable to explore 2D FE-FM multiferroic materials with intrinsic and robust magnetoelastic coupling.

In this work, we reveal that Co2Cl2 monolayers exhibit intrinsic 2D multiferroic behavior, where FM and FE are strongly coupled through an anisotropic lattice distortion—characterized by in-plane expansion and out-of-plane contraction—enabling reversible control of magnetic and electronic states via in-plane strain. Specifically, the Co2Cl2 monolayers undergo a metal-insulator transition during structural changes, with the FE-I phase characterized by a lattice constant of 3.24 Å displaying metallic properties, while the FE-II phase, with a lattice constant of 3.76 Å, is insulating. This transition is governed by the Jahn-Teller effect, which distorts the tetrahedral crystal field around Co2+ ions under FE strain. Additionally, Co2Cl2 exhibits FM behavior in the FE-I phase (Curie temperature TC = 394 K) and Néel-AFM behavior in the FE-II phase (Néel temperatures TN = 214 K), with a FM-AFM transition observed at the critical point. These findings not only deepen our understanding of multiferroic phenomena but also highlight the potential for 2D multiferroics in advanced spintronic applications.

Results and Discussion

The calculation method and the geometric structure of Co2Cl2

In our study, we sought to identify materials with specific magnetic properties using data from the Computational 2D Materials Database (C2DB)32. To achieve this, we employed the SISSO (sure independence screening and sparsifying operator) algorithm, a cutting-edge machine learning tool designed for high-dimensional feature selection and model construction33. We began by extracting structures from the C2DB that contain Co and Cl elements, generating a set of potential new structural units from these elements. Next, we calculated the geometric distances between these newly generated structures and a Si-based double-nested graphene-like structure, which served as our target. By ranking these distances, we were able to identify the structures most closely resembling the target, highlighting promising candidates for further investigation. Through this method, we identified the Co2Cl2 monolayer, which closely resembles the Si-based double-nested graphene-like structure due to its minimal geometric distance. As shown in Fig. 1a, the Co2Cl2 monolayer exhibits a hexagonal-like structure composed of four atomic layers, with Co atoms in the middle and Cl atoms forming tetrahedra above and below the Co layers. We investigated the energy of the Co2Cl2 monolayer under various biaxial strains and observed a double-well potential energy plot, illustrated in Fig. 1b. This indicates a spontaneous FE phase transition occurs within the Co2Cl2 monolayer, leading to a transformation from the transition structure to the FE phase with two variants (denoted as FE-I and FE-II). These variants are non-equivalent due to opposing lattice distortions: in the FE-I phase, the in-plane lattice constant decreases while the out-of-plane Co–Co distance increases; in contrast, the FE-II phase exhibits in-plane lattice expansion accompanied by a reduction in the out-of-plane Co–Co distance. Notably, spontaneous 2D ferroelasticity only occurs on the Co2Cl2 monolayer, but is absent in Co2F2 and Co2Br2 monolayer. The lattice constant of FE-I is 3.24 Å, which is smaller than that of FE-II (3.76 Å), while the critical point has a lattice constant of 3.41 Å. Upon imposition of biaxial strain and full lattice relaxation, the Co2Cl2 monolayer transforms into the FE-II configuration, which exhibits global energetic stability. Moreover, the magnitudes of the FE transition energy barrier and the reversible FE strain are closely associated with practical applications34,35. As shown in Fig. 1b, the switching between the two FE variants in the Co2Cl2 monolayer can be achieved by passing through the transition structure, accompanied by an energy barrier that differs from the energy difference between the transition structure and FE phases. Specifically, the kinetic energy barrier from FE-I to FE-II is estimated to be around 0.12 eV, while the reverse transition from FE-II to FE-I requires a barrier of approximately 0.24 eV. This asymmetry suggests potential differences in coercive fields, resulting in asymmetric hysteresis behavior. Such characteristics could be advantageous for designing non-volatile memory devices with tailored switching properties. The similarity in kinetic energy barrier to that of other 2D multiferroic materials25,36,37 further supports the possibility of strain-induced variant switching occurring under laboratory conditions in the Co2Cl2 monolayer. The energy difference between the two phases with their stable magnetic orders is 0.12 eV, while the phases with FM states show a difference of 0.06 eV (more details in Supplemental Fig. 1). These results demonstrate significant ferroelastic anisotropy. On the other hand, we also investigated the magnetic properties of the Co2Cl2 monolayer under biaxial strains. Our calculations indicate that the Néel-AFM order is the ground state within the FE-II phase region. Conversely, with decreasing lattice constants, the FM order becomes energetically more favorable within the FE-I phase region. Moreover, a magnetic transition occurs at the critical point: the FM state is energetically favored below this point, while the Néel-AFM order becomes the ground state above it.

Fig. 1: Crystal Structure of Co2Cl2 monolayer and Its Total Energy and Magnetization as Functions of Strain.
Fig. 1: Crystal Structure of Co2Cl2 monolayer and Its Total Energy and Magnetization as Functions of Strain.The alternative text for this image may have been generated using AI.
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a Top (left panel) and side (right panel) views of the crystal structure of the Co2Cl2 monolayer, where the solid black rhombus in the top view represents the primitive cell. The right panel shows FE-I and FE-II of the Co2Cl2 monolayer. b Simulated strain-energy double well curve, illustrating the structural transition between two ferroelastic phase variants through the transition state of the Co2Cl2 monolayer. Red arrows illustrate the orientations of spins. c Calculated energy contour plot for Co2Cl2 monolayer versus the planar lattice parameters. The energy zero corresponds to the transition state. d Variation of magnetization of a Co atom with lattice constant in the unit cell. The spin exchange energy as function of the lattice constant.

To check the ground state magnetic configurations of Co2Cl2, we systematically evaluated four possible magnetic orders—FM, Néel-AFM, Zigzag-AFM, and Stripy-AFM—using a \(3\times 2\sqrt{3}\) supercell (details in Supplemental Fig. 2). The results (Supplemental Table 1) show that the FE-I and FE-II phases have FM and Néel-AFM ground states, respectively. In addition, our global magnetic structure searches38 also confirmed that conclusion. To further investigate the effect of uniaxial strain on the FE properties, we examined the spontaneous FE phase transition in the Co2Cl2 monolayer. This transition transforms the monolayer from the parent regular tetragonal FE-I phase to a tetragonal FE-II phase with two distinct orientation variants, as shown in Fig. 1b. The energy landscape relative to the transition structure configuration was analyzed across the entire 2D plane of lattice constant strain. The transition structure of the Co2Cl2 monolayer corresponds to the saddle point in the energy landscape. From Fig. 1c, it is shown that the energy of the FE-II phase represents the global minimum. Additionally, two low-energy regions tangent to the transition structure were identified at the FE-I and FE-II configurations, forming two intersecting disk-like areas. This suggests that the Co2Cl2 monolayer structure has a strong tendency to undergo lattice deformation along the planar a and b axes, allowing it to stabilize in a more energetically favorable phase with tetrahedral symmetry (a = b).

The spin exchange energy, defined as the energy difference between FM and Néel-AFM configurations, is plotted as a function of lattice constant in Fig. 1d. Our investigation reveals that the FE-II variant exhibits a strong preference for Néel-AFM ordering, with an exchange energy of approximately −0.34 eV. Conversely, the FE-I structure favors FM ordering, with an associated energy value as high as 0.08 eV. Notably, the critical point structure between these two variants demonstrates a neutral exchange energy of 0 eV. Furthermore, our findings demonstrate that when the lattice constant is smaller than that of the critical point, the system’s exchange energy remains negative and exhibits a significant magnitude. However, a sign change occurs in the exchange energy when the lattice constant exceeds that of the critical point. This observation indicates a shift in magnetic behavior and highlights the sensitivity of exchange interactions to changes in lattice parameters. Additionally, the relationship between the magnetic moment and lattice constant is illustrated in Fig. 1d. The magnetic moment on each Co atom changes significantly during the FM-to-AFM transition as the lattice constant increases. Specifically, when the lattice constant is below the critical point, the magnetic moment remains constant at 2.42 μB. However, upon reaching the critical point, the magnetic moment of a Co atom sharply decreases to 1.94 μB, accompanied by a metal-insulator transition. As the lattice constant continues to increase beyond the critical point, the magnetic moment of Co atom gradually increases again.

Analysis of Stability and Electronic Structure

The stability of Co2Cl2 monolayers was investigated through phonon spectra analysis. As shown in Fig. 2a, b, we find that there is no obvious imaginary mode in the whole Brillouin zone, which confirms the dynamic stability of the FE-I and FE-II phase. First-principles molecular dynamics simulations also confirm that the Co2Cl2 monolayer is stable at room temperature in Fig. 2c, d. These results indicate that both FE-I and FE-II Co2Cl2 monolayers are experimentally feasible. To explore the electronic properties of the Co2Cl2 monolayers, the calculated spin-polarized band structures are shown in Fig. 2e, f for the FE-I and FE-II phase respectively. Interestingly, the electronic structures differ significantly between the FE-I and FE-II phases. The FE-I phase exhibits metallic behavior, while the FE-II phase of the Co2Cl2 monolayer is characterized as insulator with a direct band gap of 1.25 eV. Such phenomenon indicates that as the FE switches between the FE-I and FE-II phases, there will be a metal-insulator transition at the critical point. It is noteworthy that in the FE-I phase, the spin-up band exhibits high electron mobility, characterized by a steep band crossing the Fermi level, while the spin-down channel displays reduced conductivity, evidenced by the presence of two nearly flat bands. The steep spin-up bands indicate high conductivity, while the flat spin-down bands suggest reduced conductivity. In addition, we also use the hybrid HSE06 functional, which is more accurate in describing the electronic behavior, to investigate the electronic properties of the Co2Cl2 monolayer. The FE-I phase remains metallic, while the FE-II phase is insulating, with a direct band gap as large as 1.97 eV.

Fig. 2: Phonon and electronic structures.
Fig. 2: Phonon and electronic structures.The alternative text for this image may have been generated using AI.
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Phonon dispersion spectra for the relaxed FE-I (a) and FE-II (b). Evolution of the total free energies of Co2Cl2 monolayer at 300 K calculated by first-principles molecular dynamics for the FE-I (c) and FE-II (d). Spin-polarized electronic band structures and orbital-projected partial density of states (PDOS) for FE-I phase (e) and FE-II phase (f) of Co2Cl2 monolayer. Black and red curves denote the spin-up and spin-down bands, respectively. The Fermi level is set to zero.

A detailed analysis of the spin density and projected density of states (PDOS) for the FE-I and FE-II phases (in Fig. 2) reveals that the spin charges primarily localize around the Co ions. Furthermore, it is observed that the spin polarization near the Fermi level is predominantly contributed by the Co-3d and Cl-p orbitals. The presence of a tetrahedral crystal field, induced by the four surrounding Cl− ions, causes the five degenerate Co-d orbitals to undergo a splitting into three t2 and two e orbitals. In the FE-I phase, the majority-spin t2 orbitals are positioned near the Fermi level, while a minor fraction of the minority-spin t2 orbitals remain unoccupied. This orbital configuration reduces the magnetic moment of each Co atom to 2.42 μB. Conversely, in the FE-II phase, both t2 and e orbitals lie below the Fermi level, collectively generating a magnetic moment of 2 μB on each Co atom.

Co-Cl Bonding Mechanisms

Our DFT calculations show that the Young’s modulus of monolayer Co2Cl2 is only 16 N/m, which is significantly lower than those of graphene (340 N/m39), MoS2 (180 N/m40), and even monolayer CrI3 (28 N/m41,42). This significantly low mechanical stiffness suggests that Co2Cl2 can be easily stretched or compressed in experimental conditions, such as through substrate-induced lattice mismatch. Although Co2Cl2 is a typical van der Waals structure, significant intralayer quasicovalent Co-Cl bonds can form, influencing its electronic and magnetic properties. To gain a comprehensive understanding of the Co-Cl bond properties in Co2Cl2 monolayers, we employed crystal orbital Hamilton population (COHP) analysis43,44 to investigate the bonding and antibonding contributions in both FE-I and FE-II phases, in Fig. 3a, b. Negative values of the -COHP indicate the antibonding character of orbitals at a given energy, while positive values correspond to bonding character43. In the FE-I phase, low-level electronic states overlap by Co-3d orbitals and Cl-p orbital, resulting in the occupation of antibonding states far below the Fermi level, which weakens the Co-Cl bonds. Conversely, in the FE-II phase, it was observed that all electron-occupied states originated from bonding states located below the Fermi level, which indicates the robust stability of the structure.

Fig. 3: Bonding, structural and magnetic properties.
Fig. 3: Bonding, structural and magnetic properties.The alternative text for this image may have been generated using AI.
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a -COHP plot for FE-I. b -COHP plot for FE-II. Insets show the Electron localization function (ELF) of Co-Cl bond for each corresponding phase. ELF for the Co2Cl2 monolayers in the (c) FE-I and (d) FE-II, respectively. e Co-Cl bond lengths and -ICOHP values for Co2Cl2 at different lattice constant. f Magnetic moments in the monolayers as functions of temperature, derived from Monte Carlo simulations based on the Heisenberg model.

Besides, in order to study the bonding characteristics of Co2Cl2 monolayer, we calculated the electron localization function (ELF). The ELF rearranging the jellium-like homogeneous electron gas value, normalizing it between 0 and 1.0. As shown in Fig. 3c, a few localized electron distributions around the Co and Cl atoms indicate the weak Co-Cl bonding for FE-I phase. However, there are apparent localized electron distributions around the adjacent Co and Cl atoms on the [101] plane in Fig. 3d, denoting strong covalent characteristics for FE-II phase. Meanwhile, we specifically calculated the ELF value along the Cl-Co bond direction, as shown in the insets of Fig. 3a, b. Our results indicate that in the FE-II phase, there is a significant increase in the ELF value near the Co atom, which facilitates the formation of Co-Cl bonds. This is consistent with the integrated -COHP (-ICOHP) analysis, which provides a quantitative measure of bond strength. This is consistent with the integrated -COHP (-ICOHP) analysis, which provides a quantitative measure of bond strength. Specifically, the -ICOHP value in the FE-II phase reaches –1.07 eV, in contrast to only –0.12 eV in the FE-I phase, indicating much stronger bonding in FE-II. This difference is primarily attributed to the longer Co–Cl bond length in the FE-I phase (3.33 Å), compared to the shorter bond length in the FE-II phase (2.45 Å).

As shown by the PDOS plot in Fig. 2, the FE-I phase exhibits unoccupied Cl-p electronic states, resulting in increase in antibonding contributions. In contrast, FE-II phase strong p-d electronic states overlap in the below the Fermi level (−1.5 eV to 0 eV), which makes the bonding contributions increase. To further explore how strain affects Co–Cl bonding, we analyzed the evolution of –ICOHP and bond length as functions of lattice constant, as shown in Fig. 3e. At smaller lattice constants, both the –ICOHP and bond strength gradually increase due to the decreasing Co–Cl bond length. Notably, at the critical point, a sharp rise in –ICOHP is observed, accompanied by a sudden drop in bond length. This phenomenon is likely induced by a significant narrowing of the structure’s c-axis and is accompanied by a metal-insulator transition. As the lattice constant continues to increase, the strength of the Co-Cl bond remains high, driven by the increasing -ICOHP and the shorter bond length.

Model Hamiltonian

High-performance magnetic materials that remain stable at room temperature are rare. Next, we turn our attention to the magnetic phase transition temperature for the Co2Cl2 monolayer, which is key to exploring its potential application in spintronic devices. We further performed the MC simulations based on the Heisenberg model to estimate critical temperature, which is widely used in previous studies45. The spin Hamiltonian of the Heisenberg model can be expressed as:

$$H=-{J}_{1}\sum\limits_{i,j}{S}_{i}\cdot {S}_{j}-{J}_{2}\sum\limits_{i,k}{S}_{i}\cdot {S}_{k}-{J}_{3}\sum\limits_{i,l}{S}_{i}\cdot {S}_{l}$$

where Si and Sj represent the spin moment of the Co atom at i and j sites, respectively. We consider the first (J1), second (J2), and third (J3) nearest neighboring exchange interactions as shown in Fig. 4e and neglect all the other weaker interactions. The exchange parameters were extracted using the perturbation method46. For the FE-I phase (FM), the calculated values of J1, J2, and J3 are 42.5, 7.7, and 3.7 meV, respectively. In contrast, for the FE-II phase (Néel-AFM), the corresponding values are −20.6, 4.5, and −1.2 meV. As shown in Fig. 3f, the Curie temperature (TC) of the FM FE-I phase is approximately 394 K, while the Néel temperature (TN) of the AFM FE-II phase is about 214 K. These critical values are higher than most reported 2D magnetic materials, such as CrI3 (40 K)3 and Cr2Ge2Te6 (61 K)4.

Fig. 4: Spin exchange interactions.
Fig. 4: Spin exchange interactions.The alternative text for this image may have been generated using AI.
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Total and orbital-decomposed Heisenberg exchange interactions (J) values as a function of neighboring distance for FE-I (a) and FE-II (b). Positive and negative values correspond to FM and Néel-AFM interactions, respectively. Schematic diagram illustrating the tetrahedral crystal-field orbital splittings and occupations for Co-3d orbitals in the Co2Cl2 monolayer for FE-I (c) and FE-II (d). e Detail of the three effective exchange interactions considered in this work. f Illustration of the direct exchange and superexchange mechanisms.

To elucidate the spin exchange mechanism in the Co2Cl2 monolayer, we first analyze the orbital occupations of the Co atoms. We decompose the Heisenberg magnetic interactions into three distinct channels: e-e, t2-t2, and e-t2, with these orbitals defined within local coordinate systems. The computed results for the FE-I and FE-II phases are summarized in Fig. 4a, b, respectively. Our analysis reveals that the t2-t2 interactions predominantly contribute to the overall magnetic exchange. Additionally, we find that the interactions involving third-nearest neighbors are notably weak. Consequently, the e-e interactions exhibit magnitudes that are substantially smaller than those of the e-t2, and t2-e channels, indicating that the e-e interactions play a negligible role in the magnetic behavior of the system. Secondly, each Co atom is surrounded by four Cl atoms, forming a tetrahedral crystal field. This tetrahedral environment induces the splitting of the five d-orbitals into double-degenerate e (\({\rm{d}}_{{\rm{x}}^{2}{\mbox{-}{\rm{y}}^{2}}}\), \({\rm{d}}_{{\rm{z}}^{2}}\)) states and triple-degenerate t2 (dxy, dyz, dxz) orbitals. Additionally, differences in electronegativity and bond length of the Co-Cl bonds cause significant distortion in the Co-centered tetrahedron. This distortion induces the Jahn-Teller effect, leading to further splitting of the degenerate orbitals and resulting in substantial spin splitting between the spin-up and spin-down states (in Fig. 4).

The Co atoms in the Co2Cl2 monolayer are in a 3d74s2 electronic configuration. To enhance our comprehension of the d-orbital valence electron arrangement of the magnetic atom Co, we utilize the MLWFs derived from the on-site d levels, taking into account the spin occupancy. We observe that in the FE-I phase, as shown in Fig. 4c, the energy levels of the dxy orbitals are higher than those of the dxz and dyz orbitals. This electronic configuration, with the e orbitals fully occupied and the t2 orbital partially occupied, leads to metallic behavior. Conversely, in the FE-II phase of the Co2Cl2 monolayer, we find that the dxy orbitals are higher in energy than dxz and dyz orbital as shown in Fig. 4d. Based on the arrangement of spin occupancies, we observe that the dxz and dyz orbitals exhibit a semi-filled state, while the remaining orbitals are fully occupied. This electronic configuration leads to insulating behavior with a 2 μB magnetic moment. Consequently, we can infer that the valence state of Co in the Co2Cl2 monolayer is Co-3d84s2.

The underlying magnetic coupling in the Co2Cl2 monolayer can be understood from the competition between direct exchange and superexchange interactions. It is well known that the direct exchange interaction favors Néel-AFM ordering and that the distance between Co-Co magnetic ions significantly influences the electron hopping ability. On the other hand, the superexchange interaction, which usually involves one or more Cl ligands acting as mediators, facilitates electron hopping between two magnetic ions. As shown in Supplementary Fig. 3, in the FE-I phase, the Co–Cl–Co bond angle between unit cells (θ1) is 85.7°, which is close to 90°. This angle favors FM ordering via the Co(d)–Cl(p)–Co(d) superexchange mechanism according to the Goodenough–Kanamori–Anderson rules47,48,49. Within the unit cell, the Co–Cl–Co bond angle (θ2) is 51.8°, and the Co–Co distance is 3.33 Å, indicating relatively weak direct exchange. In contrast, for the FE-II phase, the θ1 becomes 101.6°, still favoring FM superexchange between unit cells. However, within the unit cell, the Co–Cl–Co angle increases to 63.4°, and the Co–Co distance shortens to 2.45 Å, greatly enhancing direct exchange interactions between adjacent Co atoms. Therefore, as shown in Fig. 4f, the FE-I phase exhibits FM behavior due to the Co(d)-Cl(p)-Co(d) superexchange interaction. In contrast, the FE-II phase displays Néel-AFM behavior, driven by the direct Co(d)-Co(d) exchange interaction. The magnetism of the Co2Cl2 monolayer with varying lattice constants arises from the competition between the Co-Co bond and the Co-Cl bond interactions. This competition influences the orbital hybridizations, which in turn determine the overall magnetic properties of the monolayer.

Reconfigurable Switch Matrix

Field-programmable gate arrays (FPGAs) are integral components in modern electronics, offering reconfigurability and versatility for a wide range of applications, from telecommunications to consumer electronics50,51. A critical component of FPGAs is the switch matrix, which facilitates the routing of signals between logic blocks52. Traditional switch matrices mainly utilize fuse-based and anti-fuse technologies, which render them typically irreversible after configuration53. While this irreversible characteristic enhances the stability of the circuits to some extent, it also limits flexibility and adaptability for later adjustments, especially in scenarios that require frequent changes or reconfigurations. As illustrated in Fig. 5a, we propose a design scheme for a switch matrix based on Co2Cl2 monolayers multiferroic properties. The Co2Cl2 monolayer leverages ferroelastic phase transitions to modulate its conductive properties, providing a dynamic approach to signal routing within FPGAs. As depicted in Fig. 5b, the FE-I phase of Co2Cl2 exhibits metallic characteristics, allowing for high conductivity essential for efficient signal transmission. Conversely, the FE-II phase acts as an insulator, effectively preventing electrical flow. This dual-phase capability is crucial for implementing a switch matrix that can dynamically respond to varying operational requirements. By employing the ferroelastic phase transition properties of Co2Cl2, as shown in Fig. 5c, we can precisely control the conductivity of the interconnects. This feature enables the matrix to “open” or “close” connections on demand, improving flexibility and applicability.

Fig. 5: FPGA device based on Co2Cl2 monolayer.
Fig. 5: FPGA device based on Co2Cl2 monolayer.The alternative text for this image may have been generated using AI.
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a Schematic of FPGAs device based on Co2Cl2 monolayers. b Simplified depiction of the band structures for FE-I and FE-II. c Ferroelastic hysteresis loop of the Co2Cl2 monolayer.

Conclusions

In summary, our study unveils that the Co2Cl2 monolayer exhibits unconventional multiferroic behavior, distinct from typical 2D FM–FE materials. Specifically, it hosts two structurally and magnetically non-equivalent FE variants—FE-I and FE-II—that can be switched under biaxial strain. Compared to FE-II, the in-plane Co–Co distance of FE-I is shortened, while the out-of-plane Co–Co distance is increased. Notable findings include spontaneous ferroelastic phase transition FE-I and FE-II variants under biaxial strain, with distinct magnetic orders influenced by lattice parameters—FE-I favoring FM and FE-II exhibiting AFM behavior. FE-II displays semiconductor characteristics with a 1.22 eV direct band gap, in stark contrast to the metallic nature of FE-I. The calculated Tc of 394 K for FE-I and TN of 214 K FE-II, respectively, highlight potential spintronic applications. We also evaluated the dynamical and thermal stability of both phases and discussed their potential applications in devices, such as an FPGA. This study sheds light on 2D multiferroics, opening pathways for advanced nanoelectronics and spintronic devices, leveraging magnetoelastic coupling and strain-engineered magnetic behaviors of Co2Cl2 monolayers.

Methods

In this work, the first-principles calculations are performed based on the density functional theory (DFT)54,55 as implemented in the Vienna Ab initio Simulation Package (VASP)56 code. The projector augmented wave (PAW)57,58 method is adopted to treat the ionic potential. The generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE)59 functional is used for the exchange correction interactions. The energy cutoff for the plane wave basis expansion is set to be 350 eV. A vacuum space of 15 Å along z-direction is adopted. The convergence criteria of the force and the energy are 0.001 eV/ Å and 1 × 10−8 eV, respectively. The Monkhorst-Pack k-point mesh of 12 × 12 × 1 is used for sampling 2D Brillouin zone. DFT + U60 method is adopted with U = 4 eV for d electrons of Co atom, as employed in previous works61. To accurately describe the van der Waals interactions in Co2Cl2 monolayer, the Grimme’s empirical DFT-D3 method with Becke-Johnson damping was incorporated62. The magnetic interactions were obtained by using the magnetic force theory (MFT) with the code TB2J46.

The on-site energetic between orbitals were obtained by calculating maximally localized Wannier functions63 (MLWF) using Wannier90 package64. We assessed the stability of the Co2Cl2 monolayer by calculating the phonon spectrum with PHONOPY65. The bond strength within the Co2Cl2 monolayer structures was analyzed using the LOBSTER program43. To investigate this phenomenon further, we employed the climbing image nudged elastic band method66, to calculate the transition barrier between the FE-I and FE-II phases. Using the magnetic interaction parameters determined by the first-principles calculations, we apply Monte Carlo (MC) simulations with the heat bath method67,68 to investigate the ground state spin configuration at zero temperatures. The spin textures are derived from a 60 × 60 supercell, with 1 × 105 MC steps executed for random spin configurations.