The Intrinsic Ferromagnetism in a MnO2 Monolayer

Ferromagnetic Order in 2D Layers of Transition Metal Dichlorides

Magnetism in two dimensions is traditionally considered an exotic phase mediated by spin fluctuations, but far from collinearly ordered in the ground state. Recently, 2D magnetic states have been discovered in layered van der Waals compounds. Their robust and tunable magnetic state by material composition, combined with reduced dimensionality, foresee a strong potential as a key element in magnetic devices. Here, a class of 2D magnets based on metallic chlorides is presented. The magnetic order survives on top of a metallic substrate, even down to the monolayer limit, and can be switched from perpendicular to in-plane by substituting the metal ion from iron to nickel. Using functionalized STM tips as magnetic sensors, local exchange fields are identified, even in the absence of an external magnetic field. Since the compounds are processable by molecular beam epitaxy techniques, they provide a platform with large potential for incorporation into current device technologies.

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.

Intrinsic edge states and strain-tunable spin textures in the Janus 1T-VTeCl monolayer

Using first-principles calculations and micro-magnetic simulations, we investigate the electronic structures, the effect of biaxial strain on the topological characteristics, magnetic anisotropy energy (MAE), Dzyaloshinskii-Moriya interaction (DMI) and spin textures in the Janus 1T phase VTeCl (1T-VTeCl) monolayer. Our results show that 1T-VTeCl has an intrinsic edge state, and a topological phase transition with a sizeable band gap is achieved by applying biaxial strain. Interestingly, the MAE can be switched from the in-plane to the off-plane with a compressive strain of -5%. Microscopically, the origin of MAE is mainly associated with the large spin-orbit coupling (SOC) from the heavy nonmagnetic Te atoms rather than that from the V atoms. Furthermore, the induced DMI (0.09 meV) can occur stabilizing magnetic merons without applying temperatures and magnetic fields. Then, the skyrmions, frustrated antiferromagnetism and vortex are induced after applying a suitable compressive strain. Our study provides compelling evidence that the 1T-VTeCl monolayer with topological properties holds great potential for application in spintronic devices, as well as information storage devices based on different magnetic phases achievable through strain engineering.

Inducing abundant magnetic phases and enhancing magnetic stability by edge modifications and physical regulations for NiI2 nanoribbons

Recently, a magnetic semiconducting NiI2 monolayer was successfully fabricated. To obtain richer magneto-electronic properties and find new physics for NiI2, we studied the zigzag-type NiI2 nanoribbon (ZNiI2NR) with edges modified by different concentrations of H and/or O atoms. Results show that these ribbons hold a higher energy stability, thermal stability, and magnetic stability, and the Curie temperature can be increased to 143 from 15 K for the bare-edged ribbons. They feature a half-semiconductor, bipolar magnetic semiconductor, or half-metal, depending on the edge-terminated atomic species and concentrations, and are closely related to the ribbon edge states, impurity bands or hybridized bands. By applying strain or an electric field, ribbons can achieve a reversible multi-magnetic phase transition among a bipolar magnetic semiconductor, half-semiconductor, half-metal, and magnetic metal. This is because strain changes the Ni-I bond length, resulting in a variation of bond configurations (weight of ionic and covalent bonds) and the number of unpaired electrons. The compressive strain can increase the Curie temperature because it makes the edged Ni-I-Ni bond angle closer to 90°, leading to the FM d-p-d superexchange interaction being increased. The electric field varies the magnetic phase because it alters the electrostatic potential of the ribbon edges, and the Curie temperature is enhanced under the electric field because the ribbon is changed to a metallic state (half-metal or magnetic metal), in which the magnetic Ni atoms satisfy the Stoner criterion and hold a large magnetic exchange coefficient and electron state density at the Fermi surface.

Charge doping and electric field tunable ferromagnetism and Curie temperature of the MnS2 monolayer

Two-dimensional ferromagnets with a long-range ferromagnetic ordering at finite temperature present a bright prospect for their potential applications in nanoscale spintronic devices. The tuning of their intrinsic ferromagnetism and Curie temperature is essential for the development of next-generation data storage and spintronic devices. In this work, the electronic structures, ferromagnetism and Curie temperature of two-dimensional MnS2 monolayer are controlled by charge doping and electric field using first principles calculations. The results show that the dynamic and thermal stability of monolayer MnS2 for all of the cases can be still maintained. Moreover, there is no existence of phase transition and all MnS2 monolayers at any charge doping concentrations and electric field intensities favor ferromagnetic coupling. For the manipulation of electron doping, the calculated total magnetic moment Mtot of the MnS2 monolayer exhibits an increase from 3.112 to 3.491μB per unit cell. Further analysis indicates that a transition from half-metal to metal occurs by introducing the charge doping and vertical electric field, and the Mn 3d electronic states are the major determinants of ferromagnetism. Additionally, the charge doping enables the magnetic anisotropy energy to transform from an in-plane easy axis to the magnetization direction out of the plane. The Curie temperature Tc of the MnS2 monolayer can be moderately enhanced above room temperature by hole doping and application of a vertical electric field. Remarkably, Tc reaches its peak at 767 K at a hole doping concentration of -0.8e. This work enriches the microscopic understanding of the tuning mechanism of ferromagnetism and supplies a sound theoretical basis for subsequent experimental studies.

Bilayer hexagonal structure MnN2 nanosheets with room-temperature ferromagnetic half-metal behavior and a tunable electronic structure

Two-dimensional (2D) layered materials have atomically thin thickness and outstanding physical properties, attracting intensive research in the past year. As one of these materials, a 2D magnet is an ideal platform for fundamental physics research and magnetic device development. Recently, a non-MoS2-type geometry was found to be more favorable in 2D transition-metal dinitrides. In this work, driven by this new configuration, we perform a comprehensive first-principles study on the bilayer hexagonal structure of 2D manganese dinitrides. Our results show that 2D MnN2 is a ferromagnetic half-metal at its ground state with 100% spin-polarization ratio at the Fermi energy level. The phonon spectrum calculation and ab initio molecular dynamics simulation show that the 2D MnN2 crystal has a high thermodynamic stability and its 2D lattice can be retained at room-temperature. Monte Carlo simulations based on the Heisenberg model predict a Curie temperature of over 563 K and its electronic properties can be regulated by biaxial strain. The half-metallic states are mainly contributed by Mn d orbitals, and the magnetic exchange of the system mainly comes from the Mn-N-Mn super-exchange. The p-d orbital hybridization will provide a small antiparallel magnetic moment of N atoms, and the p-orbital dangling bond can be eliminated by oxidation to enhance the total magnetic moment of the system. The study of magnetic anisotropy energy indicates that the easy magnetization axis is in-plane and hybridization between Mn dyz and dz2 orbitals gives the largest magnetic anisotropy contribution. In view of these results, we consider that novel 2D MnN2 is one of the most promising two-dimensional materials for nano-spintronic applications.

A facile and green synthesis of Mn and P functionalized graphitic carbon nitride nanosheets for spintronics devices and enhanced photocatalytic performance under visible-light

Manganese and phosphorus co-doped, graphitic carbon nitride (g-C₃N₄) nanosheet (Mn/P-g-C₃N₄) is prepared by facile and green calcination process of melamine (C₃H₆N₆), manganese chloride tetrahydrate (MnCl₂·4H₂O), and ammonium dihydrogen phosphate ((NH₄)H₂PO₄). The Mn/P co-doping significantly enhances magnetic values compared to pristine-g-C₃N₄, phosphorus-doped g-C₃N₄ (P-g-C₃N₄), and manganese-doped g-C₃N₄ (Mn-g-C₃N₄). We find that Mn/P-g-C₃N₄ is a half-metallic ferromagnetic material having a magnetic moment and Curie temperature of 4.51 μ_B and ∼ 800 K, respectively. The ultraviolet-visible (UV-vis) absorption spectrum of Mn/P-g-C₃N₄ reveals superior absorption in broader wavelength compared to pristine-g-C₃N₄, P-g-C₃N₄, and Mn-g-C₃N₄. The methyl orange degradation efficiency of Mn/P-g-C₃N₄ photocatalyst is 94 %, which is three times more than that of pristine-g-C₃N₄ (29 %) and more significant than the P-g-C₃N₄ (46 %) and Mn-g-C₃N₄ (58 %). Furthermore, density functional theory (DFT) calculation explains the origin of high magnetic behavior, the boosted photocatalytic efficiency of Mn/P-g-C₃N₄, and the essential material properties like structure, bandgap, the density of states (DOS), and atomic level interaction. This work may be helpful for reasonably designing ferromagnetic material for spintronics devices and boosting visible-light (VL) photocatalytic performance for environmental remediation.

Systematic DFT+U and Quantum Monte Carlo Benchmark of Magnetic Two-Dimensional (2D) CrX3 (X = I, Br, Cl, F)

The search for two-dimensional (2D) magnetic materials has attracted a great deal of attention because of the experimental synthesis of 2D CrI₃, which has a measured Curie temperature of 45 K. Often times, these monolayers have a higher degree of electron correlation and require more sophisticated methods beyond density functional theory (DFT). Diffusion Monte Carlo (DMC) is a correlated electronic structure method that has been demonstrated to be successful for calculating the electronic and magnetic properties of a wide variety of 2D and bulk systems, since it has a weaker dependence on the Hubbard parameter (U) and density functional. In this study, we designed a workflow that combines DFT +U and DMC in order to treat 2D correlated magnetic systems. We chose monolayer CrX₃ (X = I, Br, Cl, F), with a stronger focus on CrI₃ and CrBr₃, as a case study due to the fact that they have been experimentally realized and have a finite critical temperature. With this DFT+U and DMC workflow and the analytical method of Torelli and Olsen, we estimated a maximum value of 43.56 K for the T_c of CrI₃ and 20.78 K for the T_c of CrBr₃, in addition to analyzing the spin densities and magnetic properties with DMC and DFT+U. We expect that running this workflow for a well-known material class will aid in the future discovery and characterization of lesser known and more complex correlated 2D magnetic materials.

Electrical and magnetic properties of antiferromagnetic semiconductor MnSi2N4 monolayer

Two-dimensional antiferromagnetic semiconductors have triggered significant attention due to their unique physical properties and broad application. Based on first-principles calculations, a novel two-dimensional (2D) antiferromagnetic material MnSi₂N₄ monolayer is predicted. The calculation results show that the two-dimensional MnSi₂N₄ prefers an antiferromagnetic state with a small band gap of 0.26 eV. MnSi₂N₄ has strong antiferromagnetic coupling which can be effectively tuned under strain. Interestingly, the MnSi₂N₄ monolayer exhibits a half-metallic ferromagnetic properties under an external magnetic field, in which the spin-up electronic state displays a metallic property, while the spin-down electronic state exhibits a semiconducting characteristic. Therefore, 100% spin polarization can be achieved. Two-dimensional MnSi₂N₄ monolayer has potential application in the field of high-density information storage and spintronic devices.

Two-dimensional heterotriangulene-based manganese organic frameworks: bipolar magnetic and half semiconductors with perpendicular magnetocrystalline anisotropy

Two-dimensional (2D) organic intrinsic magnetic semiconductors have potential applications in low-dimensional organic spintronic devices due to their remarkable physical properties. However, 2D metal-organic frameworks with magnetic and semiconducting properties are rare. In this work, the electronic and magnetic properties of 2D heterotriangulene-based manganese organic frameworks including triphenylamine (TPA) and triphenylborane (TPB) organic ligands with methylene (M), carbonyl (C) or oxygen (O) coordination groups were studied by first-principles calculations. XTPA-Mn (X = M and O) is a bipolar magnetic semiconductor with a large spin-flip band gap. CTPA-Mn and XTPB-Mn (X = M, C and O) are half semiconductors with perpendicular magnetocrystalline anisotropy. The electronic properties of materials ranging from half semiconductors to bipolar magnetic semiconductors appear in CTPA-Mn and XTPB-Mn (X = M and C) at biaxial strains. XTPA-Mn and XTPB-Mn with a frustrated antiferromagnetic configuration are semiconductors with good ductility and stability. These results enrich the diversity of 2D organic intrinsic magnetic semiconductors, which have potential applications in spintronic devices.

Topological band transition between hexagonal and triangular lattices with (px,py) orbitals

By combining tight-binding modelling with density functional theory based first-principles calculations, we investigate the band evolution of two-dimensional (2D) hexagonal lattices with (p_x,p_y) orbitals, focusing on the electronic structures and topological phase transitions. The (p_x,p_y)-orbital hexagonal lattice model possesses two flat bands encompassing two linearly dispersive Dirac bands. Breaking the A/B sublattice symmetry could transform the model into two triangular lattices, each featuring a flat band and a dispersive band. Inclusion of the spin-orbit coupling and magnetization may give rise to quantum spin Hall and quantum anomalous Hall (QAH) states. As a proof of concept, we demonstrate that half-hydrogenated stanene is encoded by a triangular lattice with (p_x,p_y) orbitals, which exhibits ferromagnetism and QAH effect with a topological gap of ∼0.15 eV, feasible for experimental observation. These results provide insights into the structure-property relationships involving the orbital degree of freedom, which may shed light on future design and preparation of 2D topological materials for novel electronic/spintronic and quantum computing devices.

Effects of Mono-Vacancies of Oxygen and Manganese on the Properties of the MnO2/Graphene Heterostructure

The effects of the monovacancies of oxygen (VO) and manganese (VMn) on the structural and electronic properties of the 1T−MnO2/graphene heterostructure are investigated, within the framework of density functional theory (DFT). We found that the values of the formation energy for the heterostructure without and with vacancies of VO and VMn were −20.99 meVÅ2 , −32.11meVÅ2, and −20.81 meVÅ2, respectively. The negative values of the formation energy indicate that the three heterostructures are energetically stable and that they could be grown in the experiment (exothermic processes). Additionally, it was found that the presence of monovacancies of VO and VMn in the heterostructure induce: (a) a slight decrease in the interlayer separation distance in the 1T−MnO2/graphene heterostructure of ~0.13% and ~1.41%, respectively, and (b) a contraction of the (Mn−O) bond length of the neighboring atoms of the VO and VMn monovacancies of ~2.34% and ~6.83%, respectively. Calculations of the Bader charge for the heterostructure without and with VO and VMn monovacancies show that these monovacancies induce significant changes in the charge of the first-neighbor atoms of the VO and VMn vacancies, generating chemically active sites (locales) that could favor the adsorption of external atoms and molecules. From the analysis of the density of state and the structure of the bands, we found that the graphene conserves the Dirac cone in the heterostructure with or without vacancies, while the 1T−MnO2 monolayer in the heterostructures without and with VO monovacancies exhibits half-metallic and magnetic behavior. These properties mainly come from the hybridization of the 3d−Mn and 2p−O states. In both cases, the heterostructure possesses a magnetic moment of 3.00 μβ/Mn. From this behavior, it can be inferred the heterostructures with and without VO monovacancies could be used in spintronics.

High-Throughput Computational Screening for Bipolar Magnetic Semiconductors

Searching ferromagnetic semiconductor materials with electrically controllable spin polarization is a long-term challenge for spintronics. Bipolar magnetic semiconductors (BMS), with valence and conduction band edges fully spin polarized in different spin directions, show great promise in this aspect because the carrier spin polarization direction can be easily tuned by voltage gate. Here, we propose a standard high-throughput computational screening scheme for searching BMS materials. The application of this scheme to the Materials Project database gives 11 intrinsic BMS materials (1 experimental and 10 theoretical) from nearly ~40000 structures. Among them, a room-temperature BMS Li₂V₃TeO₈ (mp-771246) is discovered with a Curie temperature of 478 K. Moreover, the BMS feature can be maintained well when cutting the bulk Li₂V₃TeO₈ into (001) nanofilms for realistic applications. This work provides a feasible solution for discovering novel intrinsic BMS materials from various crystal structure databases, paving the way for realizing electric-field controlled spintronics devices.

Coexistence of Semiconducting Ferromagnetics and Piezoelectrics down 2D Limit from Non van der Waals Antiferromagnetic LiNbO3-Type FeTiO3

Stable two-dimensional (2D) ferromagnetic semiconductors (FMSs) with multifunctional properties have attracted extensive attention in device applications. Non van der Waals (vdW) transition-metal oxides with excellent environmental stability, if ferromagnetic (FM), may open up an unconventional and promising avenue for this subject, but they are usually antiferromagnetic or ferrimagnetic. Herein, we predict an FMS, monolayer Fe₂Ti₂O₉, which can be obtained from LiNbO₃-type FeTiO₃ antiferromagnetic bulk, has a moderate band gap of 0.87 eV, large perpendicular magnetization (6 μ_B/fu) and a Curie temperature up to 110 K. The intriguing magnetic properties are derived from the double exchange and negative charge transfer between O_p orbitals and Fe_d orbitals. In addition, a large in-plane piezoelectric (PE) coefficient d₁₁ of 5.0 pm/V is observed. This work offers a competitive candidate for multifunctional spintronics and may stimulate further experimental exploration of 2D non-vdW magnets.

Machine Learning Study of the Magnetic Ordering in 2D Materials

Magnetic materials have been applied in a large variety of technologies, from data storage to quantum devices. The development of two-dimensional (2D) materials has opened new arenas for magnetic compounds, even when classical theories discourage their examination. Here we propose a machine-learning-based strategy to predict and understand magnetic ordering in 2D materials. This strategy couples the prediction of the existence of magnetism in 2D materials using a random forest and the Shapley additive explanations method with material maps defined by atomic features predicting the magnetic ordering (ferromagnetic or antiferromagnetic). While the random forest model predicts magnetism with an accuracy of 86%, the material maps obtained by the sure independence screening and sparsifying method have an accuracy of ∼90% in predicting the magnetic ordering. Our model indicates that 3d transition metals, halides, and structural clusters with regular transition-metal sublattices have a positive contribution in the total weight deciding the existence of magnetism in 2D compounds. This behavior is associated with the competition between crystal field and exchange splitting. The machine learning model also indicates that the atomic spin orbit coupling (SOC) is a determinant feature for the identification of the patterns separating ferro- from antiferromagnetic order. The proposed strategy is used to identify novel 2D magnetic compounds that, together with the fundamental trends in the chemical and structural space, pave novel routes for experimental exploration.

FeSi2: a two-dimensional ferromagnet containing planar hexacoordinate Fe atoms

As an unconventional bonding pattern different from conventional chemistry, the concept of planar hypercoordinate atoms was first proposed in the molecular system, and it has been recently extended to 2D periodic systems. Using first-principles calculations, herein we predict a stable FeSi₂ monolayer with planar hexacoordinate Fe atoms. Due to its abundant multicenter bonds, the FeSi₂ monolayer shows excellent thermal and kinetic stability, anisotropic mechanical properties and room-temperature ferromagnetism (T _C ∼360 K). Furthermore, we have demonstrated the feasibility of directly growing an FeSi₂ monolayer on a Si (110) substrate while maintaining the novel electronic and magnetic properties of the freestanding monolayer. The FeSi₂ monolayer synthesized in this way would be compatible with the mature silicon semiconductor technology and could be utilized for spintronic devices.

Large perpendicular magnetic anisotropy of transition metal dimers driven by polarization switching of two-dimensional ferroelectric In2Se3 substrate

Large perpendicular magnetic anisotropy (MA) is highly desirable for realizing atomic-scale magnetic data storage which represents the ultimate limit of the density of magnetic recording. In this work, we study...

Ferroelectric and Room-Temperature Ferromagnetic Semiconductors in the 2D MIMIIGe2X6 Family: First-Principles and Machine Learning Investigations

Inspired by experimentally discovering ferromagnetism and ferroelectricity in two-dimensional (2D) CrGeTe₃ and CuInP₂S₆ with similar geometric structures, respectively, we systematically investigated ferroic properties in a large family of 2D M_IM_IIGe₂X₆ (M_I and M_II = metal elements, X = S/Se/Te) by combining high-throughput first-principles calculations and the machine learning method. We identified 12 stable 2D multiferroics containing simultaneously ferromagnetic (FM) and ferroelectric (FE) properties and 35 2D ferromagnets without FE polarization. Particularly, the predicted FM Curie temperatures (T_C) of eight 2D FM+FE semiconductors are close to or above room temperature. The ferroelectricity originates from the spontaneous geometric symmetry breaking induced by the unexpected shift of Ge-Ge atomic pairs and the emergence of Ge lone pair electrons, which also strengthens the p-d orbital hybridization between X atoms and metal atoms, leading to enhanced super-super-exchange interactions and raising the FM T_C. Our findings not only enrich the family of 2D ferroic materials and present room-temperature FM semiconductors but also disclose the mechanism of the emerging ferroelectricity and enhanced ferromagnetism, which sheds light on the realization of high temperature multiferroics as well as FM semiconductors.

2D auxetic material with intrinsic ferromagnetism: a copper halide (CuCl2) monolayer

The discovery of ferromagnetism in monolayer transition metal halides exemplified by CrI₃ has opened a new avenue in the field of two-dimensional (2D) magnetic materials, and more such 2D materials are waiting to be explored. Herein, using an unbiased structure search combined with first-principles calculations, we have identified a novel CuCl₂ monolayer, which exhibits not only intrinsic ferromagnetism but also auxetic mechanical properties originating from the interplay of lattice and Cu-Cl tetrahedron symmetries. The predicted Curie temperature of CuCl₂ reaches ∼47 K, and its ferromagnetism is associated with the strong hybridization between the Cu 3d and Cl 3p states in the configuration. Moreover, upon biaxial tensile strain or carrier doping, the CuCl₂ monolayer can be converted from ferromagnetic to non-magnetic and from half-metal to metal. These properties endow this CuCl₂ monolayer with great potential for applications in auxetic/spintronic nanodevices.

Noncollinear Magnetic Order in Two-Dimensional NiBr2 Films Grown on Au(111)

Metal halides are a class of layered materials with promising electronic and magnetic properties persisting down to the two-dimensional limit. While most recent studies focused on the trihalide components of this family, the rather unexplored metal dihalides are also van der Waals layered systems with distinctive magnetic properties. Here we show that the dihalide NiBr2 grows epitaxially on a Au(111) substrate and exhibits semiconducting and magnetic behavior starting from a single layer. Through a combination of a low-temperature scanning-tunneling microscopy, low-energy electron diffraction, X-ray photoelectron spectroscopy, and photoemission electron microscopy, we identify two competing layer structures of NiBr2 coexisting at the interface and a stoichiometrically pure layer-by-layer growth beyond. Interestingly, X-ray absorption spectroscopy measurements revealed a magnetically ordered state below 27 K with in-plane magnetic anisotropy and zero-remanence in the single layer of NiBr2/Au(111), which we attribute to a noncollinear magnetic structure. The combination of such two-dimensional magnetic order with the semiconducting behavior down to the 2D limit offers the attractive perspective of using these films as ultrathin crystalline barriers in tunneling junctions and low-dimensional devices.

CrSbS3 monolayer: a potential phase transition ferromagnetic semiconductor

Two dimensional intrinsic ferromagnetic semiconductors with controllable magnetic phase transition are highly desirable for spintronics. Nevertheless, reports on their successful experimental realization are still rare. Herein, based on first principles calculations, we propose to achieve such a functional material, namely CrSbS₃ monolayer by exfoliating from its bulk crystal. Intrinsic CrSbS₃ monolayer is a ferromagnetic half semiconductor with a moderate bandgap of 1.90 eV. It features an intriguing magnetic phase transition from ferromagnetic to antiferromagnetic when applying a small compressive strain (∼2%), making it ideal for fabricating strain-controlled magnetic switches or memories. In addition, the predicted strong anisotropic absorption of visible light and small effective masses make the CrSbS₃ monolayer promising for optoelectronic applications.

Recent progress on emergent two-dimensional magnets and heterostructures

Intrinsic two-dimensional (2D) magnetic materials own strong long-range magnetism while their characteristics of the ultrathin thickness and smooth surface provide an ideal platform for manipulating the magnetic properties at 2D limit. This makes them to be potential candidates in various spintronic applications compared to their corresponding bulk counterparts. The discovery of magnetic ordering in 2D CrI₃and Gr₂Ge₂Te₆nanostructures stimulated tremendous research interest in both experimental and theoretical studies on various intrinsic magnets at 2D limit. This review gives a comprehensive overview of the recent progress on the emergent 2D magnets and heterostructures. Firstly, several kinds of typical 2D magnetic materials discovered in the last few years and their fabrication methods are summarized in detail. Secondly, the current strategies for manipulating magnetic properties in 2D materials are further discussed. Then, the recent advances on the construction of representative van der Waals magnetic heterostructures and their respective performance are provided. With the hope of motivating the researchers in this area, we finally offered the challenges and outlook on 2D magnetism.

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.

Thickness Dependent Magnetic Transition in Few Layer 1T Phase CrTe2

Room temperature two-dimensional (2D) ferromagnetism is highly desired in practical spintronics applications. Recently, 1T phase CrTe₂ (1T-CrTe₂) nanosheets with 5 and thicker layers have been successfully synthesized, which all exhibit the properties of ferromagnetic (FM) metals with Curie temperatures around 305 K. However, whether the ferromagnetism therein can be maintained when continuously reducing the nanosheet's thickness to monolayer limit remains unknown. Here, through first-principles calculations, we explore the evolution of magnetic properties of 1 to 6 layer CrTe₂ nanosheets and several interesting points are found: First, unexpectedly, monolayer CrTe₂ prefers a zigzag antiferromagnetic (AFM) state with its energy much lower than that of FM state. Second, in 2 to 4 layer CrTe₂, both the intralayer and interlayer magnetic coupling are AFM. Last, when the number of layers is equal to or greater than 5, the intralayer and interlayer magnetic coupling become FM. Such highly thickness dependent magnetism provides a new perspective to control the magnetic properties of 2D materials.

An exploration into two-dimensional metal oxides, and other 2D materials, synthesised via liquid metal printing and transfer techniques

Two-dimensional (2D) metal oxides can be difficult to synthesise, and scaling up production using traditional methods is challenging. However, a new liquid metal-based technique, that utilises both "top-down" and "bottom-up" processes, has recently been introduced. These liquids oxidise to form an oxide surface "skin" which may be exfoliated as a 2D flake and subsequently used in various electronic devices and chemical reactions.

1T-CrO2 monolayer: a high-temperature Dirac half-metal for high-speed spintronics

Two-dimensional (2D) materials with complete spin-polarization, high-speed conduction electrons, large Curie temperatures and robust ferromagnetic ground states are desirable for spintronic applications. Based on first-principles calculations, we demonstrate that the 1T-CrO₂ monolayer is an intrinsic 3d ferromagnetic Dirac half metal (DHM) with two symmetry protected Dirac cones near the Fermi level. The Fermi velocities (3.21 × 10⁵ m s^-1 and 4.85 × 10⁵ m s^-1) of the Dirac cones are in the same order as that of graphene, indicating its excellent transport properties. Its 2.48 eV half-metallic gap is large enough to prevent the spin-flip transition. Moreover, the two Dirac cones are robust against biaxial strain of up to ±4%. The robust ferromagnetism is mainly contributed by the 3d states of Cr and its Curie temperature is up to 507 K. Our results indicate that the ferromagnetic 1T-CrO₂ monolayer is a promising candidate for high temperature, high efficiency spintronics applications.

Boosting oxygen reduction activity and enhancing stability through structural transformation of layered lithium manganese oxide

Structural degradation in manganese oxides leads to unstable electrocatalytic activity during long-term cycles. Herein, we overcome this obstacle by using proton exchange on well-defined layered Li2MnO3 with an O3-type structure to construct protonated Li2-xHxMnO3-n with a P3-type structure. The protonated catalyst exhibits high oxygen reduction reaction activity and excellent stability compared to previously reported cost-effective Mn-based oxides. Configuration interaction and density functional theory calculations indicate that Li2-xHxMnO3-n has fewer unstable O 2p holes with a Mn3.7+ valence state and a reduced interlayer distance, originating from the replacement of Li by H. The former is responsible for the structural stability, while the latter is responsible for the high transport property favorable for boosting activity. The optimization of both charge states to reduce unstable O 2p holes and crystalline structure to reduce the reaction pathway is an effective strategy for the rational design of electrocatalysts, with a likely extension to a broad variety of layered alkali-containing metal oxides.

Room-temperature ferromagnetism in two-dimensional transition metal borides: a first-principles investigation

It is currently technologically important to predict new two-dimensional (2D) ferromagnetic materials for next-generation information storage media. However, discovered 2D ferromagnetic materials are still rare. Here, we explored the fact that 2D transition metal borides are potential room-temperature 2D ferromagnetic materials. By performing first-principles calculations, we found that the CrB monolayer is a ferromagnetic (FM) metal, while the FeB monolayer is a typically antiferromagnetic (AFM) semiconductor. Interestingly, both CrB and FeB monolayers are FM metals with a moderate magnetic anisotropy energy by saturating with functional groups. Monte Carlo simulations show that the Curie temperature (Tc) of the CrB monolayer is about 520 K, which is further increased to 580 K and 570 K through -F and -OH chemical modification, while Tc is about 250 K, 275 K and 300 K for the FeBF, FeBO and FeBOH monolayer, respectively. Thus, the 2D transition metal borides have great potential applications in information storage devices.

Theoretical study of tunable magnetism of two-dimensional MnSe2through strain, charge, and defect

Two-dimensional transition metal dichalcogenide MnSe₂(2D-MnSe₂) with Curie temperature approximate to 300 K has a significant spintronic application on thin-film devices. We demonstrate theoretically a tunable magnetic transition of 2D-MnSe₂between anti-ferromagnetic (AFM) metal and ferromagnetic (FM) half metal as strain increasing. Mechanism of that transition involves a competition betweend-p-dthrough-bond andd-ddirect interaction in 2D-MnSe₂. Hole doping is an alternative way to enhance the stability of FM coupling. Adsorption (including Li, Na, Cl and F) and vacancy (Mn and Se) studies confirm that the controllable magnetism of 2D-MnSe₂is related to both interaction competition and charge doping. Tensile strains can greatly amplify through-bond interaction and exchange parameters, resulting in a sharp increase of Curie temperature.

Functionalization induced quantum spin Hall to quantum anomalous Hall phase transition in monolayer jacutingaite

As novel states of quantum matter, quantum spin Hall (QSH) and quantum anomalous Hall (QAH) states have attracted considerable interest in condensed matter and materials science communities. Recently, a monolayer of the naturally occurring mineral jacutingaite (Pt2HgSe3), was theoretically proposed to be a large-gap QSH insulator and experimentally confirmed. Here, based on first-principles calculations and tight-binding modeling, we demonstrate QSH to QAH phase transition in jacutingaite by chemical functionalization with chalogen. We show that two-dimensional (2D) chalogenated jacutingaite, Pt2HgSe3-X (X = S, Se, Te), is ferromagnetic with Curie temperature up to 316 K, and it exhibits QAH effect with chiral edge states inside a sizeable topological gap. The physical mechanism lies in the adsorption induced transformation of the original Kane-Mele model into an effective four-band model involving (px, py) orbitals on a hexagonal lattice, so that the topological gap size can be controlled by spin-orbit coupling strength of the chalogen (0.28 eV for Pt2HgSe3-Te). These results not only show the promise of functionalization in orbital-engineering of 2D functional structures, but also provide an ideal and practical platform for achieving exotic topological phases for dissipationless transport and quantum computing.

A Symmetry-Breaking Phase in Two-Dimensional FeTe2 with Ferromagnetism above Room Temperature

Recently, ferromagnetism observed in monolayer two-dimensional (2D) materials has attracted attention due to the promise of its application in next-generation spintronics. Here, we predict a symmetry-breaking phase in 2D FeTe₂ that differs from conventional transition metal ditellurides shows superior stability and room-temperature ferromagnetism. Through density functional theory calculations, we find the exchange interactions in FeTe₂ consist of short-range superexchange and long-range oscillatory exchanges mediated by itinerant electrons. For six nearest neighbors, the exchange constants are calculated to be 50.95, 33.41, 2.70, 11.02, 14.46, and -4.12 meV. Furthermore, the strong relativistic effects on Te²⁺ induce giant out-of-plane exchange anisotropy and open up a significantly large spin wave gap (Δ^SW) of 1.22 meV. All of this leads to robust ferromagnetism with the T_c surpassing 423 K, which is predicted by the renormalization group Monte Carlo method, sufficiently higher than room temperature. Our findings shed light on the promising future of FeTe₂ in 2D magnetic research and spintronic applications.

First-principles investigation of a new 2D magnetic crystal: Ferromagnetic ordering and intrinsic half-metallicity

The development of two-dimensional (2D) magnetic materials with half-metallic characteristics is of great interest because of their promising applications in spintronic devices with high circuit integration density and low energy consumption. Here, by using density functional theory calculations, ab initio molecular dynamics, and Monte Carlo simulation, we study the stability, electronic structure, and magnetic properties of a OsI₃ monolayer, of which crystalline bulk is predicted to be a van der Waals layered ferromagnetic (FM) semiconductor. Our results reveal that the OsI₃ monolayer can be easily exfoliated from the bulk phase with small cleavage energy and is energetically and thermodynamically stable at room temperature. Intrinsic half-metallicity with a wide bandgap and FM ordering with an estimated T_C = 35 K are found for the OsI₃ monolayer. Specifically, the FM ordering can be maintained under external biaxial strain from -2% to 5%. The in-plane magnetocrystalline anisotropy energy of the 2D OsI₃ monolayer reaches up to 3.89 meV/OsI₃, which is an order larger than that of most magnetic 2D materials such as the representative monolayer CrI₃. The excellent magnetic features of the OsI₃ monolayer therefore render it a promising 2D candidate for spintronic applications.

2D CrCl2(pyrazine)2 monolayer: high-temperature ferromagnetism and half-metallicity

The ferromagnetism in Cr-based monolayers is of current interest (2019 Nat. Nanotechnol. 14 408), however, the Curie temperature is low. How can we enhance the thermal stability of ferromagnetism? Motivated by the recent synthesis of the layered conductive magnet CrCl₂(pyrazine)₂ (2018 Nat. Chem. 10 1056), we perform first-principles calculations and Monte Carlo simulations to demonstrate that the exfoliated 2D CrCl₂(pyrazine)₂ monolayer is stable dynamically and thermally, and it is a ferromagnetic half-metal with a sizeable band gap of 2.8 eV in the semiconducting channel, and the strong in-plane Cr-Cr interaction results in a large magnetic anisotropy energy. Moreover, the sheet exhibits a high Curie temperature of 350 K due to the enhanced magnetic exchange interaction resulting from the aromatic property of pyrazine. All of these intriguing features endow 2D CrCl₂(pyrazine)₂ sheet with good potentials for applications in nanoscale spintronics devices.

Strain modulated ferromagnetic phase transitions in monolayer FeCl2 through exchange competitions: the first-principle and Monte Carlo simulations

Strain drives the magnetic phase transition of 1T-FeCl₂ through exchange competitions.

Dependence of the magnetic interactions in MoS2 monolayer on Mn-doping configurations

Understanding the magnetic properties of the various Mn doping configurations that can be encountered in 2H-MoS₂ monolayer could be beneficial for its use in spintronics. Using density functional theory plus Hubbard term (DFT  +  U) approach, we study how a single isolated, double- and triple-substitution configurations of Mn atoms within a MoS₂ monolayer could contribute to its total magnetization. We find that the doping-configuration plays a critical role in stabilizing a ferromagnetic state in a Mn-doped MoS₂ monolayer. Indeed, the Mn-Mn magnetic interaction is found to be ferromagnetic and strong for Mn in equidistant substitution positions where the separation average range of 6-11 [Formula: see text]. The strongest ferromagnetic interaction is found when substitutions are in second nearest neighbor Mo-sites of the armchair chain. Clustering is energetically favorable but it strongly reduces the ferromagnetic exchange energies. Furthermore, in term of electronic properties, we show that the Mn-doped MoS₂ monolayer can change its electronic behavior from semiconductor to half-metallic depending on the doping configuration. Our results suggest that ordering the Mn dopants on MoS₂ monolayer is needed to increase its potential ferromagnetism.

Strain-induced N-N bonding and magnetic changes in monolayer intrinsic ferromagnetic TmN2 (Tm = Tc and Nb)

The modulation of magnetic property in two-dimensional (2D) intrinsic ferromagnets is important for their future application in spintronic devices at the nanoscale. In this work, using first-principles calculation, we investigate the effects of strain on the structures, electronic structures and magnetic properties of monolayer 1H-NbN₂ and 1H-TcN₂. The results show that both the unstrained monolayer 1H-NbN₂ and 1H-TcN₂ are 2D intrinsically ferromagnetic (FM) metal, in which the magnetic moment of the 1H-NbN₂ and 1H-TcN₂ comes mainly from the d orbitals of Nb atom and the p orbitals of N atom, respectively. Remarkably, two neighboring N atoms in the unstrained 1H-NbN₂ form N-N bond, while those in the 1H-TcN₂ do not. When lattice constant a increases to 3.17 Å, monolayer 1H-TcN₂ undergoes N-N nonbonding-bonding transition at which the distance between the N atoms d _N-N suddenly drops by almost 25%. In particular, due to the bonding between two neighboring N atoms, the magnetic moment of N atoms in 1H-TcN₂ are quenched and the ground state transfers to non-magnetic. In contrast, when a decreases to 3.18 Å, monolayer 1H-NbN₂ undergoes N  -  N bonding-nonbonding transition at which the d _N-N suddenly increases from 1.79 Å to 1.97 Å. The N-N bonding-nonbonding transition induces the magnetic moments to transfer from the d orbitals of Nb atom to the p orbitals of N atom, while ground state of monolayer 1H-NbN₂ remains FM metal.

Tunable valley splitting and an anomalous valley Hall effect in hole-doped WS2 by proximity coupling with a ferromagnetic MnO2 monolayer

Two-dimensional (2D) valleytronic systems can provide information storage and processing advantages that complement or surpass those of conventional charge and spin-based semiconductor technologies. For efficient use of the valley degree of freedom, the major challenge currently is to lift the valley degeneracy to achieve valley splitting for further valleytronic operations. In this work, we demonstrate that valley splitting and efficient hole-doping in monolayer WS₂ can be achieved by the proximity coupling effect of 2D ferromagnetic MnO₂ using density functional theory and Berry curvature calculations. A valley splitting of 43 meV is induced in the valence band of WS₂. The efficient hole-doping moves the Fermi level just located between the valence band maxima of the K and K' valleys, which is suitable for the valley-polarized transport. The magnitude of valley splitting relies on the strength of interfacial orbital hybridization and can be tuned continually by applying interfacial compression or an electric field. Owing to the sizable Berry curvature and time-reversal symmetry breaking of WS₂, a spin- and valley-polarized anomalous Hall current can be generated. Then, we proposed a valleytronic device that can be used as a filter for both the spin and valley based on this WS₂/MnO₂ van der Waals heterostructure.

Superior spin-polarized electronic structure in MoS2/MnO2 heterostructures with an efficient hole injection

Two-dimensional (2D) materials with intrinsic magnetism and low hole injection barriers to transition metal dichalcogenides are crucial to develop dopant-free all-2D p-type spin field effect transistors for CMOS logic and spintronic applications. Here, the electronic structures of 2D MoS₂/MnO₂ heterostructures are investigated by first-principles calculations, where the monolayered MnO₂ has two polymorphs including magnetic metal h-MnO₂ and magnetic semiconductor t-MnO₂. Both the MoS₂/h-MnO₂ and MoS₂/t-MnO₂ heterostructures show p-type doping for MoS₂. In the MoS₂/h-MnO₂ model with a semiconductor/metal contact, the charge transfer can affect the occupation of Mn 3d and O 2p orbitals, which results in a half-metallic characteristic of the heterostructure with a Schottky barrier height of only 0.15 eV. However, the MoS₂/t-MnO₂ model with a semiconductor/semiconductor contact shows a spin-gapless electronic structure. Moreover, the type-II band alignment of the MoS₂/t-MnO₂ heterostructure can facilitate the effective separation of electrons and holes, which can enhance the lifetime of interlayer excitons. The long interlayer exciton lifetime makes it a good candidate for electron-hole separators and related optoelectronic devices. By applying vertical compression, the spin channel of the half-metallic MoS₂/h-MnO₂ heterostructure can be reversed and the spin-gapless band structure of the MoS₂/t-MnO₂ heterostructure becomes half-metallic. Furthermore, by applying a gate voltage, the Schottky barrier height and the spin-gapless gap can be tailored. The tunable spin polarization, spin-polarized direction and exciton recombination rate provide a feasible way toward spintronics and optoelectronics.

Toward Room-Temperature Magnetic Semiconductors in Two-Dimensional Ferrimagnetic Organometallic Lattices

Obtaining room-temperature magnetically ordered two-dimensional (2D) semiconductors is urgently needed for high-speed nanospintronic devices but remains a big challenge. Here, we propose a potential route to solve this issue by constructing ferrimagnetic semiconductors in 2D metal organic frameworks, taking advantage of the high Curie temperature of ferrimagnetic semiconductors and easy tunability of metal organic frameworks. The proposal is confirmed by first-principles design of 2D metal organic frameworks with conjugated electron acceptors diketopyrrolopyrrole (DPP) as organic linkers and transition metal Cr (V) as nodes. The robust ferrimagnetic ordering comes from the strong direct exchange interaction between d-electron magnetic moments on transition metals and charge transfer-induced p-electron magnetic moments on DPPs, which can be modulated facilely by reducing the d-p orbital interaction distance via moderate compressive strain or increasing the d-p orbital charge transfer through introducing electron-withdrawing groups into the DPP moiety.

Mechanical, Electronic, and Magnetic Properties of NiX2 (X = Cl, Br, I) Layers

Since the recent experimental discovery of the CrI3 and CrGeTe3 monolayers, van der Waals (vdW) layered transition metal compounds have been recognized as promising candidates to realize 2D ferromagnetic (FM) semiconductors. However, until now, only limited compounds have been proposed to be ferromagnetic semiconductors. Here, on the basis of first-principles calculations, we report that the monolayer, Janus monolayer, and bilayer of NiX2 (X = Cl, Br, I) are intrinsic 2D FM semiconductors. Our results show that exfoliation energy of the NiX2 monolayer is smaller than that of graphene, and all studied NiX2 layers show semiconducting band gaps. The predicted Curie temperature values for NiX2 (X = Cl, Br, I) monolayers ranged from 120 to 170 K with Monte Carlo simulations. For the Janus monolayer, we found that the spin interaction shows a very strong magnetoelectric coupling under an external electric field. Furthermore, for the bilayer of NiX2, our results show that the interlayer coupling is quite weak, indicating the possibility of tuning the magnetic coupling through external manipulations.

Double-Exchange Magnetic Interactions in High-Temperature Ferromagnetic Iron Chalcogenide Monolayers

Smythite ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub><mml:mrow><mml:mi>F</mml:mi> <mml:mi>e</mml:mi></mml:mrow> <mml:mn>3</mml:mn></mml:msub> <mml:msub><mml:mi>S</mml:mi> <mml:mn>4</mml:mn></mml:msub> </mml:mrow> </mml:math> ) is an iron-based chalcogenide with a lamellar structure, different from the compositionally identical mineral greigite. Owing to their natural abundance, such transition metal chalcogenides are promising materials for low-cost spintronic-based devices. Herein, we discuss the charge transfer processes and complex magnetic ordering in a two-dimensional (2D) smythite lattice. We find that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>F</mml:mi> <mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn> <mml:mo>+</mml:mo></mml:mrow> </mml:msup> <mml:mo>/</mml:mo> <mml:mi>F</mml:mi> <mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow> <mml:mrow><mml:mn>3</mml:mn> <mml:mo>+</mml:mo></mml:mrow> </mml:msup> </mml:mrow> </mml:math> redox couple and complex magnetic ordering are governing factors in the charge transfer processes. A very strong ferromagnetic in-lattice coupling is also observed, which is attributed to the presence of three Fe-centres. To describe the magnetic behaviour molecular and periodic approaches have been considered. We found a substantial increase in Curie temperature with applied mechanical stress due to opening of the double exchange interaction angle. We also observe an in-plane Jahn-Teller distortion, which is further confirmed by the spin-orbit counter plot. Our study thus provides an insight into the double exchange mechanism favoured by the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>F</mml:mi> <mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn> <mml:mo>+</mml:mo></mml:mrow> </mml:msup> <mml:mo>/</mml:mo> <mml:mi>F</mml:mi> <mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow> <mml:mrow><mml:mn>3</mml:mn> <mml:mo>+</mml:mo></mml:mrow> </mml:msup> </mml:mrow> </mml:math> redox couple and results in a strong ferromagnetic ordering.

Recent Progress in the Fabrication, Properties, and Devices of Heterostructures Based on 2D Materials

With a large number of researches being conducted on two-dimensional (2D) materials, their unique properties in optics, electrics, mechanics, and magnetics have attracted increasing attention. Accordingly, the idea of combining distinct functional 2D materials into heterostructures naturally emerged that provides unprecedented platforms for exploring new physics that are not accessible in a single 2D material or 3D heterostructures. Along with the rapid development of controllable, scalable, and programmed synthesis techniques of high-quality 2D heterostructures, various heterostructure devices with extraordinary performance have been designed and fabricated, including tunneling transistors, photodetectors, and spintronic devices. In this review, we present a summary of the latest progresses in fabrications, properties, and applications of different types of 2D heterostructures, followed by the discussions on present challenges and perspectives of further investigations.

2D Oxide Nanomaterials to Address the Energy Transition and Catalysis

2D oxide nanomaterials constitute a broad range of materials, with a wide array of current and potential applications, particularly in the fields of energy storage and catalysis for sustainable energy production. Despite the many similarities in structure, composition, and synthetic methods and uses, the current literature on layered oxides is diverse and disconnected. A number of reviews can be found in the literature, but they are mostly focused on one of the particular subclasses of 2D oxides. This review attempts to bridge the knowledge gap between individual layered oxide types by summarizing recent developments in all important 2D oxide systems including supported ultrathin oxide films, layered clays and double hydroxides, layered perovskites, and novel 2D-zeolite-based materials. Particular attention is paid to the underlying similarities and differences between the various materials, and the subsequent challenges faced by each research community. The potential of layered oxides toward future applications is critically evaluated, especially in the areas of electrocatalysis and photocatalysis, biomass conversion, and fine chemical synthesis. Attention is also paid to corresponding novel 3D materials that can be obtained via sophisticated engineering of 2D oxides.

Magnetic proximity effect induced spin-dependent electronic structure in two-dimensional SnO by half-metallic monolayer CrN ferromagnet

The electronic structure and magnetic anisotropy of a 2D SnO/CrN heterostructure can be tailored by strains and interlayer distances.

Quantum theory of spin waves for helical ground states in a hollandite lattice

We perform spin-wave analysis of classical ground states of a model Hamiltonian proposed earlier (Mandal et al 2014 Phys. Rev. B 90 104420) for [Formula: see text] compounds. It is known that the phase diagram of the hollandite lattice (lattice of [Formula: see text] compounds) consists of four different helical phases (FH, A2H, C2H, CH phase) in the space of model parameters [Formula: see text]. The spin wave dispersion shows presence of gapless mode which interpolates between quadratic to linear depending on phases and values of J _i . In most cases, the second lowest mode shows the existence of a roton-like minima mainly from [Formula: see text] to [Formula: see text] and [Formula: see text] to [Formula: see text] path and it appears at the value of [Formula: see text] for constant [Formula: see text]. Few higher modes also show similar minima. Each helical phase has its characteristic traits which can be used to determine the phases itself. The analytical expressions of eigenmodes at high symmetry points are obtained which can be utilized to extract the values of J _i . Density of states, specific heat and susceptibilities at low temperature have been studied within spin-wave approximation. The specific heat shows departure from T ^1.5(3) dependence found in three-dimensional unfrustrated ferromagnetic(anti-ferromagnetic) system which seems to be the signature of incommensurate helical phase. The parallel susceptibility is maximum for FH phase and minimum for CH phase at low temperature. The perpendicular susceptibility is found to be independent of temperature at very low temperature. Our study can be used to compare experiments on magnon spectrum, elastic neutron scattering, and finite temperature properties mentioned above for clean [Formula: see text] system as well as determining the values of J _i .

Surface Vacancy-Induced Switchable Electric Polarization and Enhanced Ferromagnetism in Monolayer Metal Trihalides

Monolayer chromium triiodide (CrI₃), as the thinnest ferromagnetic material demonstrated in experiment [ Huang et al. Nature 2017 , 546 , 270 ], opens up new opportunities for the application of two-dimensional (2D) materials in spintronic nanodevices. Atom-thick 2D materials with switchable electric polarization are now urgently needed for their rarity and important roles in nanoelectronics. Herein, we unveil that surface I vacancies not only enhance the intrinsic ferromagnetism of monolayer CrI₃ but also induce switchable electric polarization. I vacancies bring about an out-of-plane polarization without breaking the nonmetallic nature of CrI₃. Meanwhile, the induced polarization can be reversed in a moderate energy barrier, arising from the unique porosity of CrI₃ that contributes to the switch of I vacancies between top and bottom surfaces. Engineering 2D switchable polarization through surface vacancies is also applicable to many other metal trihalides, which opens up a new and general way toward pursuing low-dimensional multifunctional nanodevices.

MBene (MnB): a new type of 2D metallic ferromagnet with high Curie temperature

We extend the 2D MXene family into the boride world, namely, MBenes. High-throughput calculations screen twelve MBenes with excellent stability. Among them, 2D MnB MBene exhibits robust metallic ferromagnetism (∼3.2 μ_B per Mn atom) and high Curie temperature (345 K). After functionalization with the -F and -OH groups, the ferromagnetic ground state of 2D MnB is well preserved. The Curie temperature is increased to 405 and 600 K, respectively, providing a novel and feasible strategy to tailor the T_C of 2D magnetic materials.