Two-Dimensional Ferroics and Multiferroics: Platforms for New Physics and Applications

Room-temperature multiferroicity in sliding van der Waals semiconductors with sub-0.3 V switching

The search for van der Waals (vdW) multiferroic materials has been challenging but also holds great potential for the next-generation multifunctional nanoelectronics. The group-IV monochalcogenide, with an anisotropic puckered structure and an intrinsic in-plane polarization at room temperature, manifests itself as a promising candidate with coupled ferroelectric and ferroelastic order as the basis for multiferroic behavior. Unlike the intrinsic centrosymmetric AB stacking, we demonstrate a multiferroic phase of tin selenide (SnSe), where the inversion symmetry breaking is maintained in AA-stacked multilayers over a wide range of thicknesses. We observe that an interlayer-sliding-induced out-of-plane (OOP) ferroelectric polarization couples with the in-plane (IP) one, making it possible to control out-of-plane polarization via in-plane electric field and vice versa. Notably, thickness scaling yields a sub-0.3 V ferroelectric switching, which promises future low-power-consumption applications. Furthermore, coexisting armchair- and zigzag-like structural domains are imaged under electron microscopy, providing experimental evidence for the degenerate ferroelastic ground states theoretically predicted. Non-centrosymmetric SnSe, as the first layered multiferroic at room temperature, provides a novel platform not only to explore the interactions between elementary excitations with controlled symmetries, but also to efficiently tune the device performance via external electric and mechanical stress.

Magnetodielectric properties in two dimensional magnetic insulators

Magnetodielectric (MD) materials are important for their ability to spin-charge conversion, magnetic field control of electric polarization and vice versa. Among these, two-dimensional (2D) van der Waals (vdW) magnetic materials are of particular interest due to the presence of magnetic anisotropy (MA) originating from the interaction between the magnetic moments and the crystal field. Also, these materials indicate a high degree of stability in the long-range spin order and may be described using suitable spin Hamiltonians of the Heisenberg, XY, or Ising type. Recent reports have suggested effective interactions between magnetization and electric polarization in 2D magnets. However, MD coupling studies on layered magnetic materials are still few. This review covers the fundamentals of MD coupling by explaining related key terms. It includes the necessary conditions for having this coupling and sheds light on the possible microscopic mechanisms behind this coupling starting from phenomenological descriptions. Apart from that, this review classifies 2D magnetic materials into several categories for reaching out each and every class of materials. Additionally, this review summarizes recent advancements of some pioneer 2D MD materials. Last but not the least, the current review provides possible research directions for enhancing MD coupling in those and mentions the possibilities for future developments.

Robust Ferroelectricity in Nonstoichiometric 2D AgCr1-xS2 via Chemical Vapor Deposition

Ferroelectricity in two-dimensional (2D) materials at room temperature has attracted significant interest due to their substantial potential for applications in non-volatile memory, nanoelectronics, and optoelectronics. The intrinsic tendency of 2D materials toward nonstoichiometry results in atomic configurations that differ from those of their stoichiometric counterparts, thereby giving rise to potential ferroelectric polarization properties. However, reports on the emergence of room temperature ferroelectric effects in nonstoichiometric 2D materials remain limited. This study reports the observation of room temperature ferroelectricity in nonstoichiometric AgCr1-xS2 ternary 2D transition metal dichalcogenides synthesized via chemical vapor deposition. The noncentrosymmetric crystal structure and switchable ferroelectric polarization are confirmed through second harmonic generation (SHG) and piezoresponse force microscopy (PFM) measurements. It is determined that the primary cause of ferroelectric polarization is the interlayer movement of ordered asymmetric Ag atoms under the influence of numerous chromium (Cr) vacancies along with interlayer atom displacement. Furthermore, two types of electrical devices based on in-plane (IP) and out-of-plane (OOP) polarization are demonstrated. This work offers a new perspective for fabricating ternary ultrathin 2D transition metal dichalcogenides ferroelectric materials and presents a potential pathway for creating exceptional multifunctional materials.

Recent progresses in transmission electron microscopy studies of two-dimensional ferroelectrics

The rich potential of two-dimensional materials endows them with superior properties suitable for a wide range of applications, thereby attracting substantial interest across various fields. The ongoing trend towards device miniaturization aligns with the development of materials at progressively smaller scales, aiming to achieve higher integration density in electronics. In the realm of nano-scaling ferroelectric phenomena, numerous new two-dimensional ferroelectric materials have been predicted theoretically and subsequently validated through experimental confirmation. However, the capabilities of conventional tools, such as electrical measurements, are limited in providing a comprehensive investigation into the intrinsic origins of ferroelectricity and its interactions with structural factors. These factors include stacking, doping, functionalization, and defects. Consequently, the progress of potential applications, such as high-density memory devices, energy conversion systems, sensing technologies, catalysis, and more, is impeded. In this paper, we present a review of recent research that employs advanced transmission electron microscopy (TEM) techniques for the direct visualization and analysis of ferroelectric domains, domain walls, and other crucial features at the atomic level within two-dimensional materials. We discuss the essential interplay between structural characteristics and ferroelectric properties on the nanoscale, which facilitates understanding of the complex relationships governing their behavior. By doing so, we aim to pave the way for future innovative applications in this field.

The electronic and magnetic properties modulated by ferroelectric polarization switching in two-dimensional VSeTe/Sc2CO2 van der Waals heterostructures

Exploring multiferroic materials that combine magnetic and ferroelectric properties is scientifically interesting and has important technical implications for many functions of nanoscale devices. In this work, spintronics and magnetoelectric coupling devices are proposed in two-dimensional (2D) layered ferromagnetic (FM)/ferroelectric (FE) van de Waals (vdW) heterostructures, VSeTe/Sc2CO2, employing density functional theory (DFT) calculations. The results indicate that the VSeTe/Sc2CO2 vdW heterostructure changes from a metal to a semiconductor in Sc2CO2-P↑ and Sc2CO2-P↓ polarization states. At the same time, the charge at the interface of the VSeTe/Sc2CO2 heterostructure will also be redistributed with the transformation of the ferroelectric polarization state, resulting in the change of the distribution of the electronic states near the Fermi level, and thus the change in the magnetic anisotropy energy (EMAE) of the heterostructure. Interestingly, biaxial strain brings reversibility and non-volatile regulation to the heterostructure of semiconductors and metals. The results provide an effective way to fabricate magnetoelectric coupling devices with 2D multiferroic heterostructures.

Defect effects on the electronic, valley, and magnetic properties of the two-dimensional ferrovalley material VSi2N4

Due to their novel spin and valley properties, two-dimensional (2D) ferrovalley materials are expected to be promising candidates for next-generation spintronic and valleytronic devices. However, they are subject to various defects in practical applications. Therefore, the electronic, valley, and magnetic properties may be modified in the presence of the defects. In this work, utilizing first-principles calculations, we systematically studied the effects of defects on the electronic, valley, and magnetic properties of the 2D ferrovalley material VSi2N4. It has been found that C doping, O doping, and N vacancies result in the half-metallic feature, Si vacancies result in the metallic feature, and V vacancies result in a bipolar gapless semiconductor. These defect-induced electronic properties can be effectively tuned by changing defect concentration and layer thickness. Since the impurity bands do not affect the K and K' valleys, valley polarization is well maintained in O-doped and N-defective systems. Importantly, these defects play a crucial role in modifying the magnetic properties of the pristine VSi2N4, especially the magnitude of local magnetic moments and the magnetic anisotropy energy. Detailed analysis of the density of states demonstrates that the variations of the total magnetic moment and magnetic anisotropy energy with biaxial strain are determined by the electronic states near the Fermi level rather than the type of defect, which provides a new understanding of the effects of defects on the magnetic properties of 2D materials. Moreover, the layer thickness can affect the magnetic coupling between defects and surrounding V atoms. Our results offer insight into the electronic, valley, and magnetic properties of VSi2N4 in the presence of various point defects.

Multiferroicity driven by single-atom adsorption on the two-dimensional semiconductor ScCl3

In recent years, two-dimensional (2D) transition metal halides (such as CrI3) have received more and more attention for the practical applications of spintronic devices due to their unique electronic and magnetic properties. However, most 2D transition metal halides are centrosymmetric and are non-polar, which hinders their applications on nonvolatile memories. Here, on the basis of first-principles calculations, we predict that the adsorption of K single-atoms on the ScCl3 monolayer (denoted as K@ScCl3) could break the structural centrosymmetry and induce a reversible large out-of-plane electric polarization. Simultaneously, the adsorption of K single-atoms induces a magnetic moment localized on Sc ions, which forms a ferromagnetic order with an estimated Curie temperature of ∼37 K. These make the K@ScCl3 monolayer a ferromagnetic ferroelectric semiconductor. These findings propose a new route to realize 2D multiferroic materials, which is of great significance for the research and development of spintronics.

First-principles predictions of room-temperature ferromagnetism in orthorhombic MnX2 (X = O, S) monolayers

Two-dimensional ferromagnets with high spin-polarization at ambient temperature are of considerable interest because they might be useful for making nanoscale spintronic devices. We report that even though bulk phases of MnO2 are generally antiferromagnetic with low ordering temperatures, the corresponding MnO2 and MnS2 monolayers are ferromagnetic, and MnS2 is a high temperature half metallic ferromagnet. Based on first-principles calculations, we find that the MnO2 monolayer is an intrinsic ferromagnetic semiconductor with a Curie temperature TC of ∼300 K, while the half-metallic MnS2 monolayer has a remarkably high TC of ∼1150 K. Both compounds have substantial magnetocrystalline anisotropy, out of plane in the case of MnO2 monolayers, and in plane along the b-axis of orthorhombic MnS2 monolayer. Interestingly, a metal-insulator phase transition occurs in the MnS2 monolayer when the applied biaxial strain is beyond -2%. Tuning near this metal-insulator transition offers additional possibilities for devices. The present work shows that MnX2 (X = O, S) monolayers have the properties required for ultrathin nano-spintronic devices.

Robust Magnetoelectric Coupling in FeTiO3/Ga2O3 Non-van der Waals Heterostructures

Magnetoelectric coupling represents a significant breakthrough for next-generation electronics, offering the ability to achieve nonvolatile magnetic control via electrical means. In this comprehensive investigation, leveraging first-principles calculations, we unveil a robust magnetoelectric coupling within multiferroic heterostructures (HSs) by ingeniously integrating a non-van der Waals (non-vdW) magnetic FeTiO3 monolayer with the ferroelectric (FE) Ga2O3. Diverging from conventional van der Waals (vdW) multiferroic HSs, the magnetic states of the FeTiO3 monolayer can be efficiently toggled between ferromagnetic (FM) and antiferromagnetic (AFM) configurations by reversing the polarization of the Ga2O3 monolayer. This intriguing phenomenon arises from polarization-dependent substantial interlayer electron transfers and the interplay between superexchange and direct-exchange magnetic couplings of the iron atoms. The carrier-mediated interfacial interactions induce crucial shifts in Fermi level positions, decisively imparting distinct electronic characteristics near the Fermi level of composite systems. These novel findings offer exciting prospects for the future of magnetoelectric technology.

Spin-Driven Ferroelectricity in Two-Dimensional Magnetic Heterostructures

Achieving magnetic control of ferroelectricity or electric control of magnetism is usually challenging in material systems as their magnetism and ferroelectricity have distinct fundamental origins and are subject to different symmetry constraints. However, such control has significant promise for a wide range of device applications. In this work, we employ first-principles density functional theory calculations to demonstrate the emergence of spin-driven ferroelectricity in a vertically stacked two-dimensional (2D) van der Waals magnetic heterostructure, formed by two ferromagnetic (FM) CrBr3 layers separated by an antiferromagnetic (AFM) MnPSe3 layer, delicately designed to be structurally inversion symmetric but magnetically asymmetric. The spin-induced out-of-plane electric polarization of the entire heterostructure can be reversibly controlled by an external magnetic field. We further validate the effectiveness of this design strategy in several other lattice-matched FM/AFM/FM heterostructures, thereby providing a novel family of multiferroic systems based on 2D materials.

Ferroic Phases in Two-Dimensional Materials

Two-dimensional (2D) ferroics, namely ferroelectric, ferromagnetic, and ferroelastic materials, are attracting rising interest due to their fascinating physical properties and promising functional applications. A variety of 2D ferroic phases, as well as 2D multiferroics and the novel 2D ferrovalleytronics/ferrotoroidics, have been recently predicted by theory, even down to the single atomic layers. Meanwhile, some of them have already been experimentally verified. In addition to the intrinsic 2D ferroics, appropriate stacking, doping, and defects can also artificially regulate the ferroic phases of 2D materials. Correspondingly, ferroic ordering in 2D materials exhibits enormous potential for future high density memory devices, energy conversion devices, and sensing devices, among other applications. In this paper, the recent research progresses on 2D ferroic phases are comprehensively reviewed, with emphasis on chemistry and structural origin of the ferroic properties. In addition, the promising applications of the 2D ferroics for information storage, optoelectronics, and sensing are also briefly discussed. Finally, we envisioned a few possible pathways for the future 2D ferroics research and development. This comprehensive overview on the 2D ferroic phases can provide an atlas for this field and facilitate further exploration of the intriguing new materials and physical phenomena, which will generate tremendous impact on future functional materials and devices.

Charge disproportionation-induced multiferroics and electric field control of magnetism in a 2D MXene - Mo2NCl2

Two-dimensional (2D) magnetoelectric multiferroic materials with the coexistence of magnetization and ferroelectric polarization hold potential for application for the development of next-generation nano-memory devices. However, intrinsic 2D multiferroics with a high critical temperature and strong magnetoelectric coupling are still rare to date. Here, we propose a novel mechanism of 2D monolayer multiferroicity. Based on density functional theory (DFT), we predicted that in a Mo2NCl2 monolayer, the non-equilibrium charge disproportionation of Mo ions will induce an out-of-plane electric polarization, making this material a 2D monolayer multiferroic material. More importantly, the magnetic critical temperature is calculated to be ∼168 K, which is larger than those of the recently reported 2D multiferroic and ferromagnetic systems. Our findings also provide a promising platform to control the magnetic properties and electric behavior in 2D multiferroics using an external electric field.

Spontaneous valley polarization and valley-nonequilibrium quantum anomalous Hall effect in Janus monolayer ScBrI

Topology and ferrovalley (FV) are two essential concepts in emerging device applications and the fundamental research field. To date, relevant reports are extremely rare about the coupling of FV and topology in a single system. By Monte Carlo (MC) simulations and first-principles calculations, a stable intrinsic FV ScBrI semiconductor with high Curie temperature (T_C) is predicted. Because of the combination of spin-orbital coupling (SOC) and exchange interaction, the Janus monolayer ScBrI shows a spontaneous valley polarization of 90 meV, which is located in the top valence band. For the magnetization direction perpendicular to the plane, the changes from FV to half-valley-metal (HVM), to valley-nonequilibrium quantum anomalous Hall effect (VQAHE), to HVM, and to FV can be induced by strain engineering. It is worth noting that there are no particular valley polarization and VQAHE states for in-plane (IP) magnetic anisotropy. By obtaining the real magnetic anisotropy energy (MAE) under different strains, due to spontaneous valley polarization, intrinsic out-of-plane (OOP) magnetic anisotropy, a chiral edge state, and a unit Chern number, the VQAHE can reliably appear between two HVM states. The increasing strains can induce VQAHE, which can be clarified by a band inversion between d_x²-y²/d_xy and d_z² orbitals, and a sign-reversible Berry curvature. Once synthesized, the Janus monolayer ScBrI would find more significant applications in topological electronic, valleytronic, and spintronic nanodevices.

A first-principles study on the multiferroicity of semi-modified X2M (X = C, Si; M = F, Cl) monolayers

The research of two-dimensional multiferroic materials has attracted extensive attention in recent years. In this work, we systematically investigated the multiferroic properties of semi-fluorinated and semi-chlorinated graphene and silylene X₂M (X = C, Si; M = F, Cl) monolayers under strain using first principles calculations based on density functional theory. We find that the X₂M monolayer has a frustrated antiferromagnetic order, and a large polarization with a high reversal potential barrier. When increasing the applied biaxial tensile strain, the magnetic order remains unchanged, but the polarization flipping potential barrier of X₂M gradually decreases. When the strain increases to 35%, although the energy required to flip the fluorine and chlorine atoms is still very high in the C₂F and C₂Cl monolayers, it goes down to 312.5 meV and 260 meV in unit cells of the Si₂F and Si₂Cl monolayers, respectively. At the same time, both semi-modified silylenes exhibit metallic ferroelectricity with a band gap of at least 0.275 eV in the direction perpendicular to the plane. The results of these studies show that Si₂F and Si₂Cl monolayers may become a new generation of information storage materials with magnetoelectric multifunctional properties.

Tuning of the electronic and photocatalytic properties of Janus WSiGeZ4 (Z = N, P, and As) monolayers via strain engineering

Recently, MA₂Z₄ materials have received tremendous attention due to their amazing electronic, spintronic, and optoelectronic properties. In this work, we propose a class of 2D Janus materials WSiGeZ₄ (Z = N, P, and As). It was found that their electronic and photocatalytic properties are sensitive to the change of the Z element. Biaxial strain results in an indirect-direct band gap transition in WSiGeN₄ and a semiconductor-metal transition in WSiGeP₄ and WSiGeAs₄. Comprehensive studies demonstrate that these transitions as well as valley-contrasting physics are closely related to the crystal field induced orbital distribution. By taking into account several features of the excellent photocatalysts reported for water splitting, we predict three promising photocatalytic materials WSi₂N₄, WGe₂N₄, and WSiGeN₄. Their optical and photocatalytic properties can be well modulated by applying biaxial strain. Our work not only provides a class of potential electronic and optoelectronic materials but also enriches the study of Janus MA₂Z₄ materials.

Doping-induced magnetism and magnetoelectric coupling in one-dimensional NbOCl3 and NbOBr3

Low-dimensional multiferroic systems with magnetoelectric coupling have attracted considerable attention due to their important applications in high-density low-power storage. Based on the first-principles calculations, we demonstrated that the recently proposed one-dimensional (1D) ferroelectric materials NbOCl₃ and NbOBr₃ have good stabilities, and found that they can be easily separated from the bulk phase. Due to the flat band near the Fermi level, the itinerant ferromagnetism can be induced over a wide range of electron-doping concentrations, and it leads to the coexistence of ferroelectricity and ferromagnetism in 1D NbOX₃ (X = Cl, Br) and finite-length nanochains. More interestingly, there is strong magnetoelectric coupling on finite-length nanochains, which is caused by the spontaneous electrical polarization and redistribution of magnetic carriers. In addition, magnetism also can be introduced by oxygen vacancies. We also analyzed the effects of doping concentration, strain, and length on ferroelectric polarization and magnetism. Our findings provide a way to design and search low-dimensional multiferroics.

Two-Dimensional Ferroelasticity and Domain-Wall Flexoelectricity in HgX2 (X = Br or I) Monolayers

Electromechanical phenomena in two-dimensional (2D) materials can be related to sizable electric polarizations and switchable spontaneous ferroelasticity, allowing them to be used as miniaturized electronic and memory devices. Even in a parent centrosymmetric (nonpolar) ferroelastic (FE) material, non-zero polarization can be produced around the FE domain wall, owing to the strain-gradient-induced flexoelectricity. Compared with the negligibly weak flexoelectric effect in bulk compounds, significant electric polarizations can be expected in 2D FE materials that sustain a large elastic strain and a strain gradient. Using first-principles calculations, we predict that spontaneous 2D ferroelasticity and domain-wall flexoelectricity can be simultaneously realized in synthetic HgX₂ (X = Br or I) monolayers. The FE phase renders three oriented variants, which form FE domain walls with a large strain gradient and the associated domain-wall flexoelectric polarizations. Our thermodynamic stability analysis and kinetic barrier simulations allow us to manipulate the domain-wall flexoelectricity via applied mechanical stress, thereby enabling future electromechanical applications in nanoelectronics.

Multiferroicity in a Two-Dimensional Non-van der Waals Crystal of AgCr2X4 (X = S or Se)

Two-dimensional (2D) intrinsic multiferroics have long been pursued not only for their potential technological applications but also as model systems for studying emergent quantum phenomena and coupling mechanisms between various order parameters in low-dimensional space. However, the realization of 2D multiferroics is still a challenge. In this paper, we reveal that 2D AgCr₂X₄ (X = S or Se) crystals, which have been synthesized from the non-van der Waals (non-vdW) AgCrX₂ bulk phase, are type I half-metallic/metallic multiferroics in which ferroelectricity and ferromagnetism coexist. The off-centering displacement of the Ag ion introduces out-of-plane polarization, and the magnetism originates from the interactions between Cr atoms. Remarkably, AgCr₂Se₄ shows topologically nontrivial spin textures, such as Meron pairs and Néel-type skyrmions, under suitable temperatures and magnetic fields. Our findings demonstrate that 2D multiferroics can be achieved from non-vdW materials and in turn open a new avenue for 2D multiferroics.

Monolayer H-MoS2 with high ion mobility as a promising anode for rubidium (cesium)-ion batteries

Secondary ion batteries rely on two-dimensional (2D) electrode materials with high energy density and outstanding rate capability. Rb- and Cs-ion batteries (RIBs and CIBs) are late-model batteries. Herein, using first-principles calculations, the potential performance of H-MoS2 as a 2D electrode candidate in RIBs and CIBs has been investigated. The M-top site on 2D H-MoS2 possesses the most stable metal atom binding sites, and after adsorbing Rb and Cs atoms, its Fermi level goes up to the conduction band, indicating a semiconductor-to-metal transition. The maximal theoretical capacities of RIBs and CIBs are 372.05 (comparable to those of commercial graphite-based LIBs) and 223.23 mA h g-1, respectively, due to the strong adsorption capability of H-MoS2 for Rb and Cs ions. Noticeably, the diffusion barriers of Rb and Cs on H-MoS2 are 0.037 and 0.036 eV, respectively. Such a low diffusion barrier gives MoS2-based RIBs and CIBs high rate capability. In addition, H-MoS2 also has the characteristics of suitable open-circuit voltage, low expansion, good cycle stability, low cost, and easy experimental realization. These results indicate that MoS2-based RIBs and CIBs are innovative batteries with great potential, and may provide opportunities for cross-application of energy storage and multiple disciplines.

Toward Room-Temperature Electrical Control of Magnetic Order in Multiferroic van der Waals Materials

Electrical control of magnetic order in van der Waals (vdW) two-dimensional (2D) systems is appealing for high-efficiency and low-dissipation nanospintronic devices. For realistic applications, a vdW 2D material with ferromagnetic (FM) and ferroelectric (FE) orders coexisting and strongly coupling at room temperature is urgently needed. Here we present a potential candidate for nonvolatile electric-field control of magnetic orders at room temperature. Using first-principles calculations, we predict the coexistence of room-temperature FM and FE orders in a 2D transition metal carbide, where the spatial distribution of magnetic moments strongly couples with the orientation of out-of-plane electric polarization. Furthermore, an electric-field switching between interfacial FM and ferrimagnetic orders is realizable through constructing a multiferroic vdW heterostructure based on this material. These findings make a significant step toward realizing room-temperature multiferroicity and strong magnetoelectric coupling in 2D materials.

Excited-State Properties of CuInP2S6 Monolayer as Photocatalyst for Water Splitting

In recent years, two-dimensional (2D) materials of ferroelectricity have been illustrated to have great potential in solar energy conversion processes such as photocatalytic water splitting, although the optical properties of such materials are rarely discussed. In combination with the first-principles calculations, many-body Green's function method was used to obtain the excited-state properties of the representative CuInP₂S₆ to unravel the ingredients affecting the photocatalytic behavior. In particular, quasiparticle (QP) band gap correction and bound exciton binding energy are 1.25/1.38 and 0.93/0.87 eV for paraelectric/ferroelectric CuInP₂S₆, respectively. In addition to facilitating the charge carrier recombination, here we emphasize that the large exciton binding energy reduces the reduction potential of the photoexcited electrons. In bilayer structures, the improved photocatalytic performance should be ascribed to the type-II band alignment and large band edge offsets (0.44 and 0.33 eV for CuInP₂S₆), rather than the increased light absorption due to the reduced band gap.

Carrier doping-induced strong magnetoelastic coupling in 2D lattice

The realization of intertwined ferroelasticity and ferromagnetism in two-dimensional (2D) lattices is of great interest for broad nanoscale applications but still remains a remarkable challenge. Here, we propose an alternative approach to realize the strongly coupled ferromagnetism and ferroelasticity by carrier doping. We demonstrate that prototypical 2D β-PbO is dynamically, thermally and mechanically stable. Under hole doping, 2D β-PbO possesses ferromagnetism and ferroelasticity simultaneously. Moreover, the robustness of ferromagnetic and ferroelastic orders is doping tunable. In particular, 2D β-PbO features an in-plane easy magnetization axis that is coupled with the lattice direction, enabling the ferroelastic manipulation of the spin direction. Furthermore, the efficient ferroelastic control of the anisotropic optical property and spin splitting in 2D β-PbO are also clarified. Our study highlights a new direction for 2D magnetoelastic research and enables the possibility for multifunctional devices.

Two-dimensional ferroelasticity and negative Poisson's ratios in monolayer YbX (X = S, Se, Te)

Two-dimensional ferroelastic materials and two-dimensional materials with negative Poisson's ratios have attracted great interest. Here, using first-principles calculations, we reveal monolayer YbX (X = S, Se, Te) materials that harbor both ferroelasticity and negative Poisson's ratios. Indirect wide band gaps of about 3 eV have been found in these three materials. Mechanical analysis reveals that the three materials are flexible and they possess large in-plane negative Poisson's ratios from -0.114 to -0.366. Meanwhile, the ferroelasticity in the monolayer YbX shows moderate energy barriers and strong ferroelastic signals, beneficial for applications in shape memory devices. These intriguing properties make monolayer YbX promising candidate materials for applications in nanoelectronics and nanomechanics.

Hydrogen-Intercalated 2D Magnetic Bilayer: Controlled Magnetic Phase Transition and Half-Metallicity via Ferroelectric Switching

Electrically controlled magnetism in two-dimensional (2D) multiferroics is highly desirable for both fundamental research and the future development of low-power nanodevices. Herein, inspired by the recently experimentally realized 2D antiferromagnetic MnPSe₃ [ Nat. Nanotechnol. 2021, 16 (7), 782] and guided by a heteromagnetic structural design, we engineer strong magnetoelectric coupling in a hydrogen-intercalated 2D MnPSe₃ bilayer. Hydrogen functionalization breaks the centrosymmetry of bilayer MnPSe₃, leading to out-of-plane ferroelectricity. Moreover, there is a phase transition from antiferromagnetic semiconductor to ferromagnetic half-metal in the H-bonded MnPSe₃ layer, while the other remains antiferromagnetic and semiconducting. When reversing the electrical polarization, the intercalated H atom can flip between the top and bottom layers with an ultralow switching barrier, which allows one to tune the magnetic order and conductivity of the individual layers via an external electric field. Our results pave a new avenue to realize strong magnetoelectric coupling in single-phase multiferroic material. The ferroelectricity-controlled magnetic phase transition and half-metallicity offer promising applications in nanoscale spintronics such as electrically written and magnetically read memories.

A study on the multiferroic properties of semi-hydrogenated X2H (X = C, Si, and Ge) monolayer films

In recent years, the research on the physical properties of two-dimensional (2D) materials has attracted much attention. In this paper, the magnetic and ferroelectric (FE) properties of semi-hydrogenated graphene, silylene and germanene X₂H (X = C, Si, and Ge) under strain are systematically investigated. The results have shown that X₂H is a magnetic FE semiconductor with ferromagnetic (FM) and FE structures, both perpendicular to the plane, a large energy gap, and a high polarization reversal barrier. It is found that both the polarization reversal barrier and the magnitude of FE polarization gradually decrease, but the FM state remains the same, upon gradually increasing the tensile strain. As the tensile strain is increased to 19%, the barriers of the Si₂H and Ge₂H monolayer films to flip a single valence bond are decreased to 1.123 eV and 0.768 eV, respectively, and the systems still maintain semiconductor characteristics. When the strain is increased to 20%, the films begin to show metallicity in the plane of films, but still have the polarity perpendicular to the plane because of the anisotropy of the band structure. These research results suggest that the magnetoelectric properties of Si₂H and Ge₂H monolayer films provide the possibility for achieving a new generation of information storage materials.

Mechano-ferroelectric coupling: stabilization enhancement and polarization switching in bent AgBiP2Se6 monolayers

Two-dimensional (2D) van der Waals (vdW) ferroelectrics are core candidates for the development of next-generation non-volatile storage devices, which rely highly on ferroelectric stability and feasible approaches to manipulate the ferroelectric polarization and domain. Here, based on density functional theory calculations, we demonstrate that the bending deformation can not only manipulate the polarization direction and domain size of AgBiP₂Se₆ monolayers but also significantly improve the ferroelectric stability. The ordered polarization in the bent AgBiP₂Se₆ monolayers can be well maintained at a temperature of 200 K in molecular dynamics simulations; by contrast, it is broken at only 100 K for their freestanding counterparts. These phenomena can be attributed to synergic effects from the asymmetric strain energy induced by a strain gradient and a reduced migration barrier of Ag ions from convex to concave surfaces. More interestingly, a ferroelectric bubble can be induced in the monolayer under biaxial compression strain. This mechano-ferroelectric coupling represents a new mechanism and feasible route towards stabilization and polarization flip in 2D ferroelectrics.

Transition of CrI2 from a two-dimensional network to one-dimensional chain at the monolayer limit

Two-dimensional (2D) magnets show promising applications in spintronic devices and appeal increasing attention. CrI₂, a counterpart of CrI₃, is a magnetic van der Waals crystal. However, the structure of CrI₂ at the monolayer limit is not well studied. Here, based on the density functional theory, we revealed the relationship between different phases of CrI₂ monolayer and proposed a novel and stable chain structure. The one-dimensional (1D) CrI₂ chain is a ferromagnetic semiconductor with robust electronic properties against twisting and tensile strain. Interestingly, the CrI₂ chain exhibits superelasticity with a failure strain as large as 39%. In addition, both the magnetic moments on Cr atoms and the exchange energy increase with an increase in the tensile strain. Our results push magnetic ordering from 2D to 1D, which shows possible application prospects in magnetoelectric and spintronic devices.

Robust Intrinsic Multiferroicity in a FeHfSe3 Layer

As a consequence of the mutually exclusive origins of ferroelectricity and magnetism, multiferroic materials with electromagnetic coupling are rare. In this work, stable two-dimensional FeHfSe₃ with experimental accessibility is however demonstrated to harbor robust electromagnetic coupling. FeHfSe₃ illustrates spontaneous in-plane polarization of 1.29 × 10^-10 C/m, and the energy barrier of 116.54 meV ensures easy switching and a high Curie temperature. In addition, semiconducting FeHfSe₃ possesses a stable antiferromagnetic ground state with a Néel temperature of approximately 300 K. In the case of applying strain, ferroelectricity and magnetism coexist stably, and uniaxial tensile strain can effectively enhance the ferroelectricity.

Single-Layer Zirconium Dihalides ZrX2 (X = Cl, Br, and I) with Abnormal Ferroelastic Behavior and Strong Anisotropic Light Absorption Ability

Recently, two-dimensional (2D) metal halides have brought out an intensive interest for their unique mechanical, electronic, magnetic, and topological properties. Here, we theoretically report the existence of the single-layer (SL) zirconium dihalide materials ZrX₂ (X = Cl, Br, and I) using first-principles calculations. SL ZrX₂, which can be obtained from its bulk phase through simple mechanical exfoliation, shows the dynamic, thermodynamic, and mechanical stability. Halogen atoms can effectively tune the electronic structure, dipole moment transition, band alignment, and light absorption. Specifically, ZrX₂ monolayers intrinsically exhibit a ferroelasticity with an abnormal 120° orientation rotation, possessing a moderate switching barrier of 24-39 meV/atom. Importantly, we observe superior anisotropic light absorption responses on SL ZrX₂ in the visible region. Besides, a series of ZrX₂-based excitonic solar cells have been proposed, which hold a large power conversion efficiency limit of 12.4-18.7%.

Unconventional distortion induced two-dimensional multiferroicity in a CrO3 monolayer

Two-dimensional (2D) multiferroic materials with the coexistence of electric and spin polarization offer a tantalizing potential for high-density multistate data storage. However, intrinsic 2D multiferroic semiconductors with high thermal stability are still rare to date. Here, we propose a new mechanism of single-phase multiferroicity. Based on first-principles calculations, we predicted that in a CrO₃ monolayer, the unconventional distortion of the square antiprismatic crystal field on Cr-d orbitals will induce an in-plane electric polarization, making this material a single-phase multiferroic semiconductor. Importantly, the magnetic Curie temperature is estimated to be ∼220 K, which is quite high as compared to those of the recently reported 2D ferromagnetic and multiferroic semiconductors. Moreover, both ferroelectric and antiferroelectric phases are observed, providing opportunities for electrical control of magnetism and energy storage and conversion applications. These findings provide a comprehensive understanding of the magnetic and electric behavior in 2D multiferroics and will motivate further research on the application of related 2D electromagnetics and spintronics.

Two-dimensional ferroelasticity in van der Waals β'-In2Se3

Two-dimensional (2D) materials exhibit remarkable mechanical properties, enabling their applications as flexible and stretchable ultrathin devices. As the origin of several extraordinary mechanical behaviors, ferroelasticity has also been predicted theoretically in 2D materials, but so far lacks experimental validation and investigation. Here, we present the experimental demonstration of 2D ferroelasticity in both exfoliated and chemical-vapor-deposited β'-In₂Se₃ down to few-layer thickness. We identify quantitatively 2D spontaneous strain originating from in-plane antiferroelectric distortion, using both atomic-resolution electron microscopy and in situ X-ray diffraction. The symmetry-equivalent strain orientations give rise to three domain variants separated by 60° and 120° domain walls (DWs). Mechanical switching between these ferroelastic domains is achieved under ≤0.5% external strain, demonstrating the feasibility to tailor the antiferroelectric polar structure as well as DW patterns through mechanical stimuli. The detailed domain switching mechanism through both DW propagation and domain nucleation is unraveled, and the effects of 3D stacking on such 2D ferroelasticity are also discussed. The observed 2D ferroelasticity here should be widely available in 2D materials with anisotropic lattice distortion, including the 1T' transition metal dichalcogenides with Peierls distortion and 2D ferroelectrics such as the SnTe family, rendering tantalizing potential to tune 2D functionalities through strain or DW engineering.

Catalysis based on ferroelectrics: controllable chemical reaction with boosted efficiency

Catalysts, which can accelerate chemical reactions, show promising potential to alleviate environmental pollution and the energy crisis. However, their wide application is severely limited by their low efficiency and poor selectivity due to the recombination of photogenerated electron-hole pairs, the back-reaction of interactants. Accordingly, ferroelectrics have emerged as promising catalysts to address these issues with the advantages of promoted light adsorption, boosted catalytic efficiency as a result of their intrinsic polarization, suppressed electron-hole pair recombination, and superior selectivity via the ferroelectric switch. This review summarizes the recent research progress of catalytic studies based on ferroelectric materials and highlights the controllability of catalytic activity by the ferroelectric switch. More importantly, we also comprehensively highlight the underlying working mechanism of ferroelectric-controlled catalysis to facilitate a deep understanding of this novel chemical reaction and guide future experiments. Finally, the perspectives of catalysis based on ferroelectrics and possible research opportunities are discussed. This review is expected to inspire wide research interests and push ferroelectric catalysis to practical applications.

Review on Recent Developments in 2D Ferroelectrics: Theories and Applications

Although only a few 2D materials have been predicted to possess ferroelectricity, 2D ferroelectrics are expected to play a dominant role in the upcoming nano era as important functional materials. The ferroelectric properties of 2D ferroelectrics are significantly different than those of traditional bulk ferroelectrics owing to their intrinsic size and surface effects. To date, 2D ferroelectrics have been reported to exhibit diverse properties ranging from bulk photovoltaic and piezoelectric/pyroelectric effects to the spontaneous valley and spin polarization. These properties are either dependent on ferroelectric polarization or coupled with it for easy electric control, thus making 2D ferroelectrics applicable to multifunctional nanodevices. At present, cumulative efforts are being made to explore 2D ferroelectrics in theories, experiments, and applications. Herein, such theories and methods are briefly introduced. Subsequently, intrinsic and extrinsic origins of 2D ferroelectricity are separately summarized. In addition, invented or laboratory-validated 2D ferroelectric-based applications are listed. Finally, the existing challenges and prospects of 2D ferroelectrics are discussed.

Single-Entity Approach to Investigate Surface Charge Enhancement in Magnetoelectric Nanoparticles Induced by AC Magnetic Field Stimulation

Magneto-electric nanoparticles (MENPs), composed of a piezoelectric shell and a ferromagnetic core, exhibited enhanced cell uptake and controlled drug release due to the enhanced localized electric field (surface charge/potential) and the generation of acoustics, respectively, upon applying alternating current (AC) magnetic (B)-field stimulation. This research, for the first time, implements an electrochemical single-entity approach to probe AC B-field induced strain mediated surface potential enhancement on MENP surface. The surface potential changes at the single-NP level can be probed by the open circuit potential changes of the floating carbon nanoelectrode (CNE) during the MENP-CNE collision events. The results confirmed that the AC B-field (60 Oe) stimulation caused localized surface potential enhancement of MENP. This observation is associated with the presence of a piezoelectric shell, whereas magnetic nanoparticles were found unaffected under identical stimulation.

Intrinsic Valley Polarization and High-Temperature Ferroelectricity in Two-Dimensional Orthorhombic Lead Oxide

Recent years have witnessed a surge of research in two-dimensional (2D) ferroelectric structures that may circumvent the depolarization effect in conventional perovskite oxide films. Herein, by first-principles calculations, we predict that an orthorhombic phase of lead(II) oxide, PbO, serves as a promising candidate for 2D ferroelectrics with good stability. With a semiconducting nature, 2D ferroelectric PbO exhibits intrinsic valley polarization, which leads to robust ferroelectricity with an in-plane spontaneous polarization of 2.4 × 10^-10 C/m and a Curie temperature of 455 K. Remarkably, we reveal that the ferroelectricity is strain-tunable, and ferroelasticity coexists in the PbO film, implying the realization of 2D multiferroics. The underlying physical mechanism is generally applicable and can be extended to other oxide films such as ferroelectric SnO and GeO, thus paving an avenue for future design and fabrication of functional ultrathin devices that are compatible with Si-based technology.

Polymorphism in Post-Dichalcogenide Two-Dimensional Materials

Two-dimensional (2D) materials exhibit a wide range of atomic structures, compositions, and associated versatility of properties. Furthermore, for a given composition, a variety of different crystal structures (i.e., polymorphs) can be observed. Polymorphism in 2D materials presents a fertile landscape for designing novel architectures and imparting new functionalities. The objective of this Review is to identify the polymorphs of emerging 2D materials, describe their polymorph-dependent properties, and outline methods used for polymorph control. Since traditional 2D materials (e.g., graphene, hexagonal boron nitride, and transition metal dichalcogenides) have already been studied extensively, the focus here is on polymorphism in post-dichalcogenide 2D materials including group III, IV, and V elemental 2D materials, layered group III, IV, and V metal chalcogenides, and 2D transition metal halides. In addition to providing a comprehensive survey of recent experimental and theoretical literature, this Review identifies the most promising opportunities for future research including how 2D polymorph engineering can provide a pathway to materials by design.

Robust Magnetoelectric Effect in the Decorated Graphene/In2Se3 Heterostructure

The magnetoelectric effect is a fundamental physical phenomenon that synergizes electric and magnetic degrees of freedom to generate distinct material responses like electrically tuned magnetism, which serves as a key foundation of the emerging field of spintronics. Here, we show by first-principles studies that ferroelectric (FE) polarization of an In₂Se₃ monolayer can modulate the magnetism of an adjacent transition-metal (TM)-decorated graphene layer via a ferroelectrically induced electronic transition. The TM nonbonding d-orbital shifts downward and hybridizes with carbon-p states near the Fermi level, suppressing the magnetic moment, under one FE polarization, but on reversed FE polarization this TM d-orbital moves upward, restoring the original magnetic moment. This finding of robust magnetoelectric effect in the TM-decorated graphene/In₂Se₃ heterostructure offers powerful insights and a promising avenue for experimental exploration of ferroelectrically controlled magnetism in two-dimensional (2D) materials.

Prediction of two-dimensional ferromagnetic ferroelectric VOF2 monolayer

Nowadays, designing and searching for materials with multiple functional characteristics are the keys to achieving high-performance electronic devices. Among many candidates, two-dimensional multiferroic materials have great potential to be applied in highly integrated magnetoelectric devices, such as high-density non-volatile memories. Here, we predict a two-dimensional material, VOF₂ monolayer, to possess intrinsic ferroelectric and ferromagnetic properties. The VOF₂ monolayer owns the largest in-plane ferroelectric polarization (332 pC m^-1) in the family of VOX₂ (X: halogen) oxyhalides. Different from other VOX₂ monolayers whose magnetic ground states are antiferromagnetic or noncollinear spiral textures, the VOF₂ monolayer owns a robust ferromagnetic ground state, which is rare but highly desirable. Our theoretical prediction provides a good candidate and starting point for the further pursuit of more two-dimensional multiferroic materials with high-performance magnetoelectricity.

Pressure Effect on Electronic and Excitonic Properties of Purely J-Aggregated Monolayer Organic Semiconductor

Different from monolayer inorganic semiconductors, such as transition metal dichalcogenides, monolayer organic semiconductors derived from perylene have attracted much attention because of their strong absorption and bright photoluminescence (PL). Pressure has proved to be an effective tool in probing the exciton behavior in monolayer semiconductors. Here, by studying the high-pressure behavior of purely J-aggregated monolayer organic semiconductors experimentally and theoretically, we find a red shift of PL spectra due to a decrease of band gap, which is consistent with fluorescent images taken under pressure. The PL center dominates the perylene group and the band edges are flat, indicating Frenkel exciton in the monolayer organic semiconductor under ambient conditions. With increasing pressure, the band edges become more dispersive, suggesting the exciton transform to Wannier-Mott exciton, which is commonly observed in inorganic semiconductors.

Multiferroic decorated Fe2O3 monolayer predicted from first principles

Two-dimensional (2D) multiferroics exhibit cross-control capacity between magnetic and electric responses in a reduced spatial domain, making them well suited for next-generation nanoscale devices; however, progress has been slow in developing materials with required characteristic properties. Here we identify by first-principles calculations robust 2D multiferroic behaviors in decorated Fe2O3 monolayers, showcasing Li@Fe2O3 as a prototypical case, where ferroelectricity and ferromagnetism stem from the same origin, namely Fe d-orbital splitting induced by the Jahn-Teller distortion and associated crystal field changes. These findings establish strong material phenomena and elucidate the underlying physics mechanism in a family of truly 2D multiferroics that are highly promising for advanced device applications.

A new family of two-dimensional ferroelastic semiconductors with negative Poisson's ratios

Two-dimensional (2D) materials with both ferroelasticity and negative Poisson's ratios have attracted intensive interest, but it is very rare to have both ferroelasticity and negative Poisson's ratios in a single material. Directional positive and negative Poisson's ratios in a switchable ferroelastic dielectric may enable non-destructive readout in ferroelastic data storage. Herein, we propose 14 kinds of stable 2D semiconductors: AB monolayers (A = Sc, Y, La; B = N, P, As, Sb, Bi) based on first-principles calculations. The band gaps of AB monolayers cover a wide range from 0.69 eV to 2.15 eV. Mechanical analysis reveals that these materials are flexible and 12 of 14 are predicted to possess an in-plane negative Poisson's ratio (NPR). Moreover, 10 of these 14 systems possess an out-of-plane NPR. More encouragingly, all AB monolayers are identified as 2D ferroelastic materials with reversible strains of around 5.94% to 20.30%. The ferroelastic switching barriers, mechanical properties and electronic structures of these materials are discussed in detail. Such outstanding properties make the AB monolayers very promising as switchable anisotropic 2D materials for nanoelectronics and micromechanical applications.

Two-Dimensional Multifunctional Metal-Organic Frameworks with Simultaneous Ferro-/Ferrimagnetism and Vertical Ferroelectricity

Exploring 2D multifunctional materials with intrinsic ferro-/ferrimagnetism and vertical ferroelectricity is a highly desirable but challenging task. Here, motivated by the recently synthesized organometallic frameworks K₃Fe₂[PcFeO₈], we propose to realize such materials in a series of 2D K₃M₂[PcMO₈] (M = Cr-Co) nanosheets. First-principles calculations suggest 2D K₃Cr₂[PcCrO₈] as a ferromagnetic half metal with a Curie temperature of 140 K, whereas others (M = Mn, Fe, and Co) are all ferrimagnetic semiconductors with the Curie temperatures between 66 and 150 K. Moreover, the structural distortion due to the out-of-plane K⁺ counterions leads to a significant vertical electric polarization. The estimated intensity of polarization for K₃Fe₂[PcFeO₈] is 143 pC/m, with the ferroelectric phase-transition barrier being 0.38 eV per formula. This work highlights the potential of 2D organometallic frameworks such as K₃M₂[PcMO₈] as a versatile platform for designing multifunctional materials with simultaneous ferro-/ferrimagnetism and vertical ferroelectricity.

Intrinsic ferromagnetism with high temperature, strong anisotropy and controllable magnetization in the CrX (X = P, As) monolayer

2D ferromagnetic (FM) materials with high temperature, large magnetocrystalline anisotropic energy (MAE), and controllable magnetization are highly desirable for novel nanoscale spintronic applications. Herein by using DFT and Monte Carlo simulations, we demonstrate the possibility of realizing intrinsic ferromagnetism in 2D monolayer CrX (X = P, As), which are stable and can be exfoliated from their bulk phase with a van der Waals layered structure. Following the Goodenough-Kanamori-Anderson (GKA) rule, the long-range ferromagnetism of CrX is caused via a 90° superexchange interaction along Cr-P(As)-Cr bonds. The Curie temperature of CrP is predicted to be 232 K based on a Heisenberg Hamiltonian model, while the Berezinskii-Kosterlitz-Thouless transition temperature of CrAs is as high as 855 K. In contrast to other 2D magnetic materials, the CrP monolayer exhibits a significant uniaxial MAE of 217 μeV per Cr atom originating from spin-orbit coupling. Analysis of MAE reveals that CrP favors easy out-of-plane magnetization, while CrAs prefers easy in-plane magnetization. Remarkably, hole and electron doping can switch the magnetization axis in between the in-plane and out-of-plane direction, allowing for the effective control of spin injection/detection in 2D structures. Our results offer an ideal platform for realizing 2D magnetoelectric devices such as spin-FETs in spintronics.

Janus TiXY Monolayers with Tunable Berry Curvature

Up to now, two-dimensional (2D) materials with both valley polarization and the Rashba effect are still rare. In this work, a new kind of Janus monolayers TiXY (X ≠ Y, X/Y = Cl, Br, I) is demonstrated to have physical properties of benefit for spintronics and valleytronics. In particular, Janus TiBrI shows Zeeman-type spin splitting of 70 meV, large Berry curvature of 106.22 bohr², and, at the same time, a large Rashba parameter of 147.95 meV Å. On the basis of k·p perturbation theory, we proposed that the Berry curvature can be adjusted by changing the lattice parameter, which will greatly improve the transverse velocities of carriers and promote the efficiency of the valley Hall device. Biaxial strain from -2.5 to 2.5% was applied on Janus TiBrI to verify the theory mentioned above, and a general relationship between the Berry curvature and lattice constant was obtained.