Low-dimensional metal-organic frameworks: a pathway to design, explore and tune magnetic structures

The magnetic structure adopted by a material relies on symmetry, the hierarchy of exchange interactions between magnetic ions and local anisotropy. A direct pathway to control the magnetic interactions is to enforce dimensionality within the material, from zero-dimensional isolated magnetic ions, one-dimensional (1D) spin-chains, two-dimensional (2D) layers to three-dimensional (3D) order. Being able to design a material with a specific dimensionality for the phenomena of interest is non-trivial. While many advances have been made in the area of inorganic magnetic materials, organic compounds offer distinct and potentially more fertile ground for material design. In particular magnetic metal-organic frameworks (mMOFs) combine magnetism with non-magnetic property functionality on the organic linkers within the structural framework, which can further be tuned with mild perturbations of pressure and field to induce phase transitions. Here, it is examined how neutron scattering measurements on mMOFs can be used to directly determine the magnetic structure when the magnetic ions are in a 2D layered environment within the wider 3D crystalline framework. The hydrated formate, in deuterated form, Co(DCOO)2·2D2O, which was one of the first magnetic MOFs to be investigated with neutron diffraction, is reinvestigated as an exemplar case.

Spin Gapless Quantum Materials and Devices

Quantum materials, with nontrivial quantum phenomena and mechanisms, promise efficient quantum technologies with enhanced functionalities. Quantum technology is held back because a gap between fundamental science and its implementation is not fully understood yet. In order to capitalize the quantum advantage, a new perspective is required to figure out and close this gap. In this review, spin gapless quantum materials, featured by fully spin-polarized bands and the electron/hole transport, are discussed from the perspective of fundamental understanding and device applications. Spin gapless quantum materials can be simulated by minimal two-band models and could help to understand band structure engineering in various topological quantum materials discovered so far. It is explicitly highlighted that various types of spin gapless band dispersion are fundamental ingredients to understand quantum anomalous Hall effect. Based on conventional transport in the bulk and topological transport on the boundaries, various spintronic device aspects of spin gapless quantum materials as well as their advantages in different models for topological field effect transistors are reviewed.

The Promise of Soft-Matter-Enabled Quantum Materials

The field of quantum materials has experienced rapid growth over the past decade, driven by exciting new discoveries with immense transformative potential. Traditional synthetic methods to quantum materials have, however, limited the exploration of architectural control beyond the atomic scale. By contrast, soft matter self-assembly can be used to tailor material structure over a large range of length scales, with a vast array of possible form factors, promising emerging quantum material properties at the mesoscale. This review explores opportunities for soft matter science to impact the synthesis of quantum materials with advanced properties. Existing work at the interface of these two fields is highlighted, and perspectives are provided on possible future directions by discussing the potential benefits and challenges which can arise from their bridging.

Transition-Metal Interlink Neural Network: Machine Learning of 2D Metal-Organic Frameworks with High Magnetic Anisotropy

Two-dimensional (2D) metal-organic framework (MOF) materials with large perpendicular magnetic anisotropy energy (MAE) are important candidates for high-density magnetic storage. The MAE-targeted high-throughput screening of 2D MOFs is currently limited by the time-consuming electronic structure calculations. In this study, a machine learning model, namely, transition-metal interlink neural network (TMINN) based on a database with 1440 2D MOF materials is developed to quickly and accurately predict MAE. The well-trained TMINN model for MAE successfully captures the general correlation between the geometrical configurations and the MAEs. We explore the MAEs of 2583 other 2D MOFs using our trained TMINN model. From these two databases, we obtain 11 unreported 2D ferromagnetic MOFs with MAEs over 35 meV/atom, which are further demonstrated by the high-level density functional theory calculations. Such results show good performance of the extrapolation predictions of TMINN. We also propose some simple design rules to acquire 2D MOFs with large MAEs by building a Pearson correlation coefficient map between various geometrical descriptors and MAE. Our developed TMINN model provides a powerful tool for high-throughput screening and intentional design of 2D magnetic MOFs with large MAE.

Tunable topological electronic states in the honeycomb-kagome lattices of nitrogen/oxygen-doped graphene nanomeshes

The rich and exotic electronic properties of graphene nanomeshes (GNMs) have been attracting interest due to their superiority to pristine graphene. Using first-principles calculations, we considered three graphene meshes doped with nitrogen and oxygen atoms (C10N3, C9N4 and C10O3). The electronic band structures of these GNMs in terms of the proximity of the Fermi level featured a two-dimensional (2D) honeycomb-kagome lattice with concurrent kagome and Dirac bands. The position of the Fermi level can be regulated by the doping ratio, resulting in different topological quantum states, namely topological Dirac semimetals and Dirac nodal line (DNL) semimetals. More interestingly, the adsorption of rhenium (Re) atoms in the voids of the C10N3 (Re@ C10N3) GNMs induced quantum anomalous Hall (QAH) states, as verified by the nonzero Chern numbers and chiral edge states. These GNMs offer a promising platform superior to pristine graphene for regulating multiple topological states.

Robust Dirac spin gapless semiconductors in a two-dimensional oxalate based organic honeycomb-kagome lattice

Two-dimensional (2D) ferromagnetic materials with intrinsic and robust spin-polarized Dirac cones are of great interest in exploring exciting physics and in realizing spintronic devices. Using comprehensive ab initio calculations, herein we reveal a family of 2D oxalate-based metal-organic frameworks (MOFs) that possess the desired characteristics. We propose that these 2D oxalate-based MOFs may be assembled by oxalate ions (C₂O₄^2-) and two homo-transition metal atoms. We demonstrate that 2D MOFs of Ni₂(C₂O₄)₃ and Re₂(C₂O₄)₃ are intrinsic Dirac spin gapless semiconductors with linear band dispersion, low energy dissipation and high electron carrier velocity. As robust ferromagnets, they also possess large magnetic moments, large perpendicular magnetic anisotropy, and high Curie temperatures, e.g. 208 K for Ni₂(C₂O₄)₃. In particular, spin-orbit coupling triggers a topologically nontrivial band gap of 143 meV in Re₂(C₂O₄)₃, which is promising to realize the quantum anomalous Hall effect at high temperatures.

Multiscale Modeling Strategy of 2D Covalent Organic Frameworks Confined at an Air-Water Interface

Two-dimensional covalent organic frameworks (2D COFs) have attracted attention as versatile active materials in many applications. Recent advances have demonstrated the synthesis of monolayer 2D COF via an air-water interface. However, the interfacial 2D polymerization mechanism has been elusive. In this work, we have used a multiscale modeling strategy to study dimethylmethylene-bridged triphenylamine building blocks confined at the air-water interface to form a 2D COF via Schiff-base reaction. A synergy between the computational investigations and experiments allowed the synthesis of a 2D-COF with one of the linkers considered. Our simulations complement the experimental characterization and show the preference of the building blocks to be at the interface with a favorable orientation for the polymerization. The air-water interface is shown to be a key factor to stabilize a flat conformation when a dimer molecule is considered. The structural and electronic properties of the monolayer COFs based on the two monomers are calculated and show a semiconducting nature with direct bandgaps. Our strategy provides a first step toward the in silico polymerization of 2D COFs at air-water interfaces capturing the initial steps of the synthesis up to the prediction of electronic properties of the 2D material.

Nodal ring spin gapless semiconductor: New member of spintronic materials

INTRODUCTION

Spin gapless semiconductors (SGSs) and nodal ring states (NRSs) have aroused great scientific interest in recent years due to their unique electronic properties and high application potential in the field of spintronics and magnetoelectronics.

OBJECTIVES

Since their advent, all SGSs and NRSs have been predicted in independent materials. In this work, we proposed a novel type of material, nodal ring spin gapless semiconductor (NRSGS), which combines both states of the SGSs and NRSs.

METHODS

The synthesized material Mg2VO4 has been detailed with band structure analysis based on first principle calculations.

RESULTS

Obtained results revealed that there are gapless crossings in the spin-up direction, which are from multiple topological nodal rings located exactly at the Fermi energy level. Mg2VO4 combines the advantages inherited from both NRSs and SGSs in terms of the innumerable gapless points along multiple nodal rings with all linear dispersions and direct contacts. In addition, Mg2VO4 also shows strong robustness against both the spin orbit coupling effect and strain conditions.

CONCLUSION

For the first time, we propose the concept of an NRSGS, and the first such material candidate Mg2VO4 can immediately advance corresponding experimental measurements and even facilitate real applications.

Recent progress, challenges, and prospects in emerging group-VIA Xenes: synthesis, properties and novel applications

The discovery of graphene (G) attracted considerable attention to the study of other novel two-dimensional materials (2DMs), which is identified as modern day "alchemy" since researchers are converting the majority of promising periodic table elements into 2DMs. Among the family of 2DMs, the newly invented monoelemental, atomically thin 2DMs of groups IIIA-VIA, called "Xenes" (where, X = IIIA-VIA group elements, and "ene" is the Latin word for nanosheets (NSs)), are a very active area of research for the fabrication of future nanodevices with high speed, low cost and elevated efficiency. Currently, any novel structure of 2DMs from the typical Xenes will probably be applicable in electronic technology. Analysis of their possible highly sensitive synthesis and characterization present opportunities for theoretically examining proposed 2D-Xenes with atomic precision in ideal circumstances, thus providing theoretical predictions for experimental support. Several theoretically predicted and experimentally synthesized 2D-Xene materials have been investigated for the group-VIA elements (tellurene (2D-Te), and selenene (2D-Se)), which are similar to topological insulators (TIs), thus potentially rendering them suitable materials for application in upcoming nanodevices. Although the investigation and device application of these materials are still in their infancy, theoretical studies and a few experiment-based investigations have proven that they are complementary to conventional (i.e., layered bulk-derived) 2DMs. This review focuses on the synthesis of novel group-VIA Xenes (2D-Te and 2D-Se) and summarizes the current development in understanding their basic properties, with the current advancement in signifying device applications. Lastly, the future research prospects, further advanced applications and associated shortcomings of the group-VIA Xenes are summarized and highlighted.

Spin-Gapless Semiconductors

The spin-gapless semiconductors (SGSs) are a new class of zero-gap materials which have fully spin polarized electrons and holes. They bridge the zero-gap materials and the half-metals. The band structures of the SGSs can have two types of energy dispersion: Dirac linear dispersion and parabolic dispersion. The Dirac-type SGSs exhibit fully spin polarized Dirac cones, and offer a platform for massless and fully spin polarized spintronics as well as dissipationless edge states via the quantum anomalous Hall effect. With fascinating spin and charge states, they hold great potential for spintronics. There have been tremendous efforts worldwide to find suitable candidates for SGSs. In particular, there is an increasing interest in searching for Dirac type SGSs. In the past decade, a large number of Dirac or parabolic type SGSs have been predicted by density functional theory, and some parabolic SGSs have been experimentally demonstrated. The SGSs hold great potential for spintronics, electronics, and optoelectronics with high speed and low-energy consumption. Here, both the Dirac and the parabolic types of SGSs in different material systems are reviewed and the concepts of the SGS, novel spin and charge states, and the potential applications of SGSs in next-generation spintronic devices are outlined.

Mirror symmetry origin of Dirac cone formation in rectangular two-dimensional materials

The Dirac cone (DC) band structure of graphene was thought to be unique to the hexagonal symmetry of its honeycomb lattice. However, two-dimensional (2D) materials possessing rectangular unit cells, e.g. unitary 6,6,12-graphyne and binary t1/t2-SiC, were also found to have DC band features. In this work, a "mirror symmetry parity coupling (MSPC)" mechanism is proposed to elaborate on the DC formation process of 6,6,12-graphyne with the tight-binding method combined with density functional calculations. First, atoms of unit cells are divided into two groups, each of which possesses its own mirror symmetry. Second, wave atom functions within each group are combined into two sets of normalized orthogonal wave functions with an odd and even parity symmetry, respectively, followed by couplings among intragroups and intergroups. The MSPC mechanism, in general, can explain the origins of the DC band structures of a category of 2D materials possessing mirror symmetry and rectangular or hexagonal unit cells. The important role of symmetry analysis, especially mirror symmetry, in understanding DC formation is demonstrated, which may serve as a critical design criterion for novel DC materials.

Glide Mirror Plane Protected Nodal-Loop in an Anisotropic Half-Metallic MnNF Monolayer

Two-dimensional (2D) nodal-loop (NL) semimetals have attracted tremendous attention for their abundant physics and potential device applications, whereas the realization of gapless NL semimetals robust against spin-orbit coupling (SOC) remains a big challenge. Recently, breakthroughs have been made with the realization of gapless NL semimetals in 2D half-metallic materials, where NLs were protected by a horizontal mirror plane symmetry. Here we first propose an alternative nonsymmorphic horizontal glide mirror plane symmetry which could protect the NLs in 2D materials. On the basis of comprehensive first-principles calculations and symmetry analysis, we found that the glide mirror symmetry together with intrinsic out-of-plane spin polarization can protect the NL against SOC in a half-metallic semimetal, namely, the MnNF monolayer. Moreover, we predict that the MnNF monolayer has strong anisotropic characteristics, tunable band structure by changing the magnetization direction, and 100% spin-polarized transport properties. Our work not only provides a novel 2D half-metallic semimetal with strong anisotropy but also broadens the scope of 2D nodal-loop materials.

Strain-tunable magnetic anisotropy in two-dimensional Dirac half-metals: nickel trihalides

The recent discovery of intrinsic two-dimensional (2D) ferromagnetism has sparked intense interest due to the potential applications in spintronics. Magnetic anisotropy energy defines the stability of magnetization in a specific direction with respect to the crystal lattice and is an important parameter for nanoscale applications. In this work, using first-principles calculations we predict that 2D NiX3 (X = Cl, Br, and I) can be a family of intrinsic Dirac half-metals characterized by a band structure with an insulator gap in one spin channel and a Dirac cone in the other. The combination of 100% spin polarization and massless Dirac fermions renders the monolayer NiX3 a superior candidate material for efficient spin injection and high spin mobility. The NiX3 is dynamically and thermodynamically stable up to high temperature and the magnetic moment of about 1 μ B per Ni3+ ion is observed with high Curie temperature and large magnetic anisotropy energy. Moreover, detailed calculations of their energetics, atomic structures, and electronic structures under the influence of a biaxial strain ε have been carried out. The magnetic anisotropy energy also exhibits a strain dependence in monolayer NiX3. The hybridization between Ni d xy and d x 2-y 2 orbitals gives the largest magnetic anisotropy contribution, whether for the off-plane magnetized NiCl3 (NiBr3) or the in-plane magnetized NiI3. The outstanding attributes of monolayer NiX3 will substantially broaden the applicability of 2D magnetism for a wide range of applications.

Palladium (III) Fluoride Bulk and PdF3/Ga2O3/PdF3 Magnetic Tunnel Junction: Multiple Spin-Gapless Semiconducting, Perfect Spin Filtering, and High Tunnel Magnetoresistance

Spin-gapless semiconductors (SGSs) with Dirac-like band crossings may exhibit massless fermions and dissipationless transport properties. In this study, by applying the density functional theory, novel multiple linear-type spin-gapless semiconducting band structures were found in a synthesized R3−c-type bulk PdF₃ compound, which has potential applications in ultra-fast and ultra-low power spintronic devices. The effects of spin-orbit coupling and on-site Coulomb interaction were determined for the bulk material in this study. To explore the potential applications in spintronic devices, we also performed first-principles combined with the non-equilibrium Green’s function for the PdF₃/Ga₂O₃/PdF₃ magnetic tunnel junction (MTJ). The results suggested that this MTJ exhibits perfect spin filtering and high tunnel magnetoresistance (~5.04 × 10⁷).

Rhombohedral Lanthanum Manganite: A New Class of Dirac Half-Metal with Promising Potential in Spintronics

Dirac half-metals have drawn great scientific interests in spintronics because of their outstanding physical properties such as the large spin polarization and massless Dirac fermions. By using first-principles calculations, we investigate the perovskite-type lanthanum manganite (LaMnO₃) as a novel Dirac half-metal. Specifically, LaMnO₃ displays multiple linear band crossings in the spin-up direction, while it has a large band gap (∼5 eV) in the spin-down orientation. The intriguing linear band dispersions guarantee the ultrafast electron transport and the significant band differences between spin up and down directions promise the realization of 100% spin-polarized current and the extremely low energy consumption. Such a spin-polarized Dirac material is rare among perovskite-type compounds. By adopting the mean-field theory, the estimated Curie temperature T_c is 438.4 K. Importantly, the LaMnO₃ crystal has been experimentally realized 2 decades ago, which facilitates the future experimental validation. With the novel spin-polarized electronic properties and the high possibility of experimental fabrication, LaMnO₃ is ideal for the spintronic application.

Na2C monolayer: a novel 2p Dirac half-metal with multiple symmetry-protected Dirac cones

A Dirac half-metal material, which has a gapped band structure in one spin channel but Dirac cones in the other, combines two intriguing properties of 100% spin polarization and massless Dirac fermions and has recently started to attract increasing attention. In this work, using first-principles calculations we predict that the disodium carbide (Na2C) monolayer is an intrinsic 2p Dirac half-metal material with 12 fully spin-polarized and symmetry-protected Dirac cones, and a slightly gapped (53 meV) spin-polarized nodal line coexisting in one spin channel, leaving the other spin channel insulated with a gap of 1.9 eV. There are two kinds of Dirac cones in Na2C, protected by different crystalline symmetries, both of which are robust against biaxial strains (±5%) and spin-orbit coupling effects, with Fermi velocities of up to 5.2 × 105 m s-1. Ferromagnetism is mainly contributed to by the unpaired 2p electrons in the carbon, with a Curie temperature estimated to be 382 K, and the origin of the 2p magnetism could be explained by the superexchange mechanism between C2- anions with the Na+ cation as a bridge. Our results not only indicate a promising candidate for high-speed spintronic devices, but also reveal the hidden mechanism of the origin of symmetric protection and ferromagnetic exchange interactions in a Dirac semi-metal, which would provide a feasible strategy for the design of Dirac materials.

Exploring the geometric, magnetic and electronic properties of Hofmann MOFs for drug delivery

The geometric, magnetic, and electronic properties and the drug capturing abilities of Hofmann-type metal organic frameworks (MOFs) were examined using theoretical calculations. The detailed theoretical calculations predicted that the Hofmann sheet can have two different conformations, planar and twisted. The Ni-Co sheet was the most stable among the systems studied, whereas the Ni-Fe sheet was the least stable. All of the sheets were magnetic spin semiconductors, having Dirac-like and dispersionless bands, which give rise to a major spatial separation between the charge carriers upon excitation. After treatment with bidentate ligands, such as pyrazine and bipyridine, these sheets produce a three dimensional cage-like structure, which is efficient for capturing small drug molecules, e.g., fluorouracil and niacin. This study shows that the magnetic metal atom and ligand structure have a significant effect on the drug capturing abilities of these systems. Therefore, these systems may be a tunable host system for drug delivery.

Zr2Si: an antiferromagnetic Dirac MXene

The antiferromagnetic ground state of Zr₂Si MXene was determined to exhibit anisotropic Dirac cones with Fermi velocities comparable to that in graphene.

Origins of Dirac cone formation in AB3 and A3B (A, B = C, Si, and Ge) binary monolayers

Compared to the pure two-dimensional (2D) graphene and silicene, the binary 2D system silagraphenes, consisting of both C and Si atoms, possess more diverse electronic structures depending on their various chemical stoichiometry and arrangement pattern of binary components. By performing calculations with both density functional theory and a Tight-binding model, we elucidated the formation of Dirac cone (DC) band structures in SiC₃ and Si₃C as well as their analogous binary monolayers including SiGe₃, Si₃Ge, GeC₃, and Ge₃C. A “ring coupling” mechanism, referring to the couplings among the six ring atoms, was proposed to explain the origin of DCs in AB₃ and A₃B binary systems, based on which we discussed the methods tuning the SiC₃ systems into self-doped systems. The first-principles quantum transport calculations by non-equilibrium Green’s function method combined with density functional theory showed that the electron conductance of SiC₃ and Si₃C lie between those of graphene and silicene, proportional to the carbon concentrations. Understanding the DC formation mechanism and electronic properties sheds light onto the design principles for novel Fermi Dirac systems used in nanoelectronic devices.

Dirac spin-gapless semiconductors: promising platforms for massless and dissipationless spintronics and new (quantum) anomalous spin Hall effects

It is proposed that the new generation of spintronics should be ideally massless and dissipationless for the realization of ultra-fast and ultra-low-power spintronic devices. We demonstrate that the spin-gapless materials with linear energy dispersion are unique materials that can realize these massless and dissipationless states. Furthermore, we propose four new types of spin Hall effects that consist of spin accumulation of equal numbers of electrons and holes having the same or opposite spin polarization at the sample edge in Hall effect measurements, but with vanishing Hall voltage. These new Hall effects can be classified as (quantum) anomalous spin Hall effects. The physics for massless and dissipationless spintronics and the new spin Hall effects are presented for spin-gapless semiconductors with either linear or parabolic dispersion. New possible candidates for Dirac-type or parabolic-type spin-gapless semiconductors are proposed in ferromagnetic monolayers of simple oxides with either honeycomb or square lattices.

Origins of Dirac cones and parity dependent electronic structures of α-graphyne derivatives and silagraphynes

Compared with graphene, graphyne and its derivatives possess more diversified atomic configurations and richer electronic structures including Dirac cones (DCs) and metallic features depending on the parity of the number of sp carbon atoms of graphynes. This report described conceptually the process of DC formation of α-graphyne within a tight-binding framework parameterized from density functional calculations. We propose a "triple coupling" mechanism elucidating the DC formation and some flat bands of α-graphynes where the couplings among the three sp carbon chain atoms are critical. The extension of this mechanism further explains the origins of DCs of silagraphynes and the parity dependent electronic structures of α-graphyne derivatives with extended sp carbon chains. Understanding these origins helps in tuning electronic properties in the design of C or C-Si based nanoelectronic devices.

Coronene-based metal–organic framework: a theoretical exploration

A new coronene-based 2D metal–organic framework with interesting magnetic and electronic and remarkable spin-filtering properties has been proposed.