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2D conjugated metal–organic frameworks (2D c‐MOFs) are emerging as unique electroactive materials for electronics and spintronics. The structural design and discovery of Kagome‐type 2D c‐MOFs exhibiting a metallic state are of paramount significance, yet remain rarely explored. Here, the solution synthesis of benzenehexol‐based 2D c‐MOFs based is presented on the tetrahydroxy‐1,4‐quinone (THQ) ligand. This study shows that controlling the pH of the reaction system to ≈7.5 yields an energetically favorable nonporous Cu3(C6O6) with a Kagome lattice, while at a pH of ≈10, the known porous Cu3(C6O6)2 with a honeycomb lattice is obtained. The crystal structures of both Cu3(C6O6)2 and Cu3(C6O6) are resolved with near‐atomic precision (resolution, 1.8 Å) using an imaging technique. Unlike the p‐type semiconducting behavior of Cu3(C6O6)2, theoretical studies identify Cu3(C6O6) as a metal due to its unique structural topology. The metallic state of Cu3(C6O6) is experimentally validated by terahertz time‐domain spectroscopy (THz‐TDS), which shows an increase in conductivity upon cooling. Scattering‐type scanning near‐field optical microscopy (s‐SNOM) measurements further support these findings by revealing an increase in normalized reflectivity with decreasing temperature. This work provides a new avenue for tailoring the structural topology of 2D c‐MOFs to attain the Kagome lattice and metallic state. [ABSTRACT FROM AUTHOR]

The appearance of van Hove singularities near the Fermi level leads to prominent phenomena, including superconductivity, charge density wave, and ferromagnetism. Here a bilayer Kagome lattice with multiple van Hove singularities is designed and a novel borophene with such lattice (BK‐borophene) is proposed by the first‐principles calculations. BK‐borophene, which is formed via three‐center two‐electron (3c–2e) σ‐type bonds, is predicted to be energetically, dynamically, thermodynamically, and mechanically stable. The electronic structure hosts both conventional and high‐order van Hove singularities in one band. The conventional van Hove singularity resulting from the horse saddle is 0.065 eV lower than the Fermi level, while the high‐order one resulting from the monkey saddle is 0.385 eV below the Fermi level. Both the singularities lead to the divergence of electronic density of states. Besides, the high‐order singularity is just intersected to a Dirac‐like cone, where the Fermi velocity can reach 1.34 × 106 m s−1. The interaction between the two Kagome lattices is critical for the appearance of high‐order van Hove singularities. The novel bilayer Kagome borophene with rich and intriguing electronic structure offers an unprecedented platform for studying correlation phenomena in quantum material systems and beyond. [ABSTRACT FROM AUTHOR]

Here we review scanning tunneling microscopy research on the surface determination for various types of kagome materials, including 11-type (CoSn, FeSn, FeGe), 32-type (Fe3Sn2), 13-type (Mn3Sn), 135-type (AV3Sb5, A = K, Rb, Cs), 166-type (TbMn6Sn6, YMn6Sn6 and ScV6Sn6), and 322-type (Co3Sn2S2 and Ni3In2Se2). We first demonstrate that the measured step height between different surfaces typically deviates from the expected value of ±0.4 ∼0.8Å, which is owing to the tunneling convolution effect with electronic states and becomes a serious issue for Co3Sn2S2 where the expected Sn-S interlayer distance is 0.6Å. Hence, we put forward a general methodology for surface determination as atomic step geometry imaging, which is fundamental but also experimentally challenging to locate the step and to image with atomic precision. We discuss how this method can be used to resolve the surface termination puzzle in Co3Sn2S2. This method provides a natural explanation for the existence of adatoms and vacancies, and beyond using unknown impurity states, we propose and use designer layer-selective substitutional chemical markers to confirm the validity of this method. Finally, we apply this method to determine the surface of a new kagome material Ni3In2Se2, as a cousin of Co3Sn2S2, and we image the underlying kagome geometry on the determined Se surface above the kagome layer, which directly visualizes the p-d hybridization physics. We emphasize that this general method does not rely on theory, but the determined surface identity can provide guidelines for first-principles calculations with adjustable parameters on the surface-dependent local density of states and quasi-particle interference patterns. [ABSTRACT FROM AUTHOR]

Abstract Here we review scanning tunneling microscopy research on the surface determination for various types of kagome materials, including 11-type (CoSn, FeSn, FeGe), 32-type (Fe3Sn2), 13-type (Mn3Sn), 135-type (AV3Sb5, A = K, Rb, Cs), 166-type (TbMn6Sn6, YMn6Sn6 and ScV6Sn6), and 322-type (Co3Sn2S2 and Ni3In2Se2). We first demonstrate that the measured step height between different surfaces typically deviates from the expected value of ±0.4 ∼0.8Å, which is owing to the tunneling convolution effect with electronic states and becomes a serious issue for Co3Sn2S2 where the expected Sn-S interlayer distance is 0.6Å. Hence, we put forward a general methodology for surface determination as atomic step geometry imaging, which is fundamental but also experimentally challenging to locate the step and to image with atomic precision. We discuss how this method can be used to resolve the surface termination puzzle in Co3Sn2S2. This method provides a natural explanation for the existence of adatoms and vacancies, and beyond using unknown impurity states, we propose and use designer layer-selective substitutional chemical markers to confirm the validity of this method. Finally, we apply this method to determine the surface of a new kagome material Ni3In2Se2, as a cousin of Co3Sn2S2, and we image the underlying kagome geometry on the determined Se surface above the kagome layer, which directly visualizes the p-d hybridization physics. We emphasize that this general method does not rely on theory, but the determined surface identity can provide guidelines for first-principles calculations with adjustable parameters on the surface-dependent local density of states and quasi-particle interference patterns.

The recent discoveries of surprisingly large anomalous Hall effect (AHE) in antiferromagnets have attracted much attention due to their promising use in spintronics devices. However, such AHE‐hosting antiferromagnetic materials are rare in nature. Herein, it is demonstrated that Mn2.4Ga, a Fermi‐level‐tuned kagome antiferromagnet, has a large anomalous Hall conductivity of ≈150 Ω−1 cm−1 at room temperature that surpasses the usual high values (i.e., 20–50 Ω−1 cm−1) observed so far in two outstanding kagome antiferromagnets, Mn3Sn and Mn3Ge. Although the triangular spin structure of Mn2.4Ga shows a weak net magnetic moment of ≈0.05 µB per formula unit, it guarantees a nonzero Berry curvature in the kagome plane. Moreover, the anomalous Hall conductivity exhibits a sign reversal with the rotation of a small magnetic field that can be ascribed to the field‐controlled chirality of the spin triangular structure. This theoretical calculations further suggest that the large AHE in Mn2.4Ga originates from a significantly enhanced Berry curvature associated with the tuning of the Fermi level close to the Weyl points. These properties, together with the ability to manipulate moment orientations using a moderate external magnetic field, make Mn2.4Ga extremely exciting for future antiferromagnetic spintronics. [ABSTRACT FROM AUTHOR]

The superconducting ground state of kagome metals AV3Sb5 (where A stands for K, Rb, or Cs) emerges from an exotic charge density wave (CDW) state that potentially breaks both rotational and time reversal symmetries. However, the specifics of the Cooper pairing mechanism, and the nature of the interplay between these two states remain elusive, largely due to the lack of momentum-space (k-space) superconducting energy gap structure. By implementing Bogoliubov quasiparticle interference (BQPI) imaging, we obtain k-space information on the multiband superconducting gap structure ΔSCi(k) in pristine CsV3Sb5. We show that the estimated energy gap on the vanadium d x y / x 2 − y 2 orbital is anisotropic but nodeless, with a minimal value located near the M point. Interestingly, a comparison of ΔSCi(k) with the CDW gap ΔCDWi(k) obtained by angle-resolved photoemission spectroscopy (ARPES) reveals direct k-space competition between these two order parameters, i.e., the opening of a large (small) CDW gap at a given momentum corresponds to a small (large) superconducting gap. When the long-range CDW order is suppressed by replacing vanadium with titanium, we find a nearly isotropic energy gap on both the V and Sb bands. This information will be critical for identifying the microscopic pairing mechanism and its interplay with intertwined electronic orders in this kagome superconductor family. [ABSTRACT FROM AUTHOR]

Computer simulation of two-dimensional colloidal systems, in which interactions between particles are induced and controlled by an external rotating magnetic field, has been performed. The effective interaction potential of particles, along with the conventional pair potential, includes also three-particle interaction. It is shown that one of the parameters of the potential—field precession angle—radically changes the character of particle interaction and the phase diagram. In particular, at small angles the system behaves like a two-dimensional system with a purely repulsive soft-disk potential, whereas at large angles it behaves like a generalized Lennard-Jones system with the (nm)-potential; the presence of the three-particle part of potential reduces the temperature of the gas–liquid critical point. At intermediate field precession angles the phase diagram contains melting lines of triangular crystals of high and low density, between which a phase with a Kagome lattice was found. Our results serve an important guide for future experiments and simulation of colloidal systems, as well as for solving many problems in the fields of "soft" matter, physical chemistry, chemical physics, photonics, and materials science [ABSTRACT FROM AUTHOR]

Kagome magnets with diverse topological quantum responses are crucial for next-generation topological engineering. The anisotropic magnetism and band evolution induced by ferromagnetic phase transition (FMPT) is reported in a newly discovered titanium-based kagome ferromagnet SmTi3Bi4, which features a distorted Ti kagome lattice and Sm atomic zig-zag chains. Temperature-dependent resistivity, heat capacity, and magnetic susceptibility reveal a ferromagnetic ordering temperature Tc of 23.2 K. A large magnetic anisotropy, observed by applying the magnetic field along three crystallographic axes, identifies the b axis as the easy axis. Angle-resolved photoemission spectroscopy with first-principles calculations unveils the characteristic kagome motif, including the Dirac point at the Fermi level and multiple van Hove singularities. Notably, a band splitting and gap closing attributed to FMPT is observed, originating from the exchange coupling between Sm 4f local moments and itinerant electrons of the kagome Ti atoms, as well as the time-reversal symmetry breaking induced by the long-range ferromagnetic order. Considering the large in-plane magnetization and the evolution of electronic structure under the influence of ferromagnetic ordering, such materials promise to be a new platform for exploring the intricate electronic properties and magnetic phases based on the kagome lattice. [ABSTRACT FROM AUTHOR]

Abstract The appearance of van Hove singularities near the Fermi level leads to prominent phenomena, including superconductivity, charge density wave, and ferromagnetism. Here a bilayer Kagome lattice with multiple van Hove singularities is designed and a novel borophene with such lattice (BK‐borophene) is proposed by the first‐principles calculations. BK‐borophene, which is formed via three‐center two‐electron (3c–2e) σ‐type bonds, is predicted to be energetically, dynamically, thermodynamically, and mechanically stable. The electronic structure hosts both conventional and high‐order van Hove singularities in one band. The conventional van Hove singularity resulting from the horse saddle is 0.065 eV lower than the Fermi level, while the high‐order one resulting from the monkey saddle is 0.385 eV below the Fermi level. Both the singularities lead to the divergence of electronic density of states. Besides, the high‐order singularity is just intersected to a Dirac‐like cone, where the Fermi velocity can reach 1.34 × 106 m s−1. The interaction between the two Kagome lattices is critical for the appearance of high‐order van Hove singularities. The novel bilayer Kagome borophene with rich and intriguing electronic structure offers an unprecedented platform for studying correlation phenomena in quantum material systems and beyond.

Abstract Geometrically perfect S = ½ kagome lattices with frustrated magnetism are typically electrical insulators. Electron or hole doping is predicted to induce an exotic conducting state including superconductivity. Herein, an unconventional strategy of doping an S = ½ kagome lattice CoCu3(OH)6Cl2 is adopted – a structural analogue of a well‐known quantum spin liquid (QSL) candidate herbertsmithite (ZnCu3(OH)6Cl2) – by integrating it with reduced graphene oxide (rGO) via in situ redox chemistry. Such an integration drastically enhances the electrical conductivity, resulting in the transformation of an insulator to a semiconductor, corroborating the respective density of states obtained from the density functional theory calculations. Estimation of the magnetic moments, data on the Hall‐effect measurements, Bader charge analysis, and photoemission signals, altogether provide a bold signature of remote hole doping in CoCu3(OH)6Cl2 by rGO. The remote doping provides an alternative to the site doping approach to impart exotic electronic properties in spin liquid candidates, specifically, the generation of topological states like Dirac metal is envisioned.

Compounds with a kagome lattice exhibit intriguing properties and the charge density wave (CDW) adds an additional layer of interest to research on them. In this study, we investigate the temperature and magnetic field dependent electrical properties under a chemical substitution and hydrostatic pressure of ScV6Sn6, a non-magnetic CDW compound. Substituting 5% Cr at the V site or applying 1.5 GPa of pressure shifts the CDW from 92 K to ∼ 50 K. This shift is attributed to the movement of the imaginary phonon band, as revealed by the phonon dispersion relation. The longitudinal and Hall resistivities respond differently under these stimuli. The magnetoresistance (MR) retains its quasilinear behavior under pressure, but it becomes quadratic after Cr substitution. The anomalous Hall-like behavior of the parent compound persists up to the respective CDW transition under pressure, after which it decreases sharply. In contrast, the longitudinal and Hall resistivities of Cr substituted compounds follow a two-band model and originate from the multi carrier effect. These results clearly highlight the role of phonon contributions in the CDW transition and call for further investigation into the origin of the anomalous Hall-like behavior in the parent compound. [ABSTRACT FROM AUTHOR]

Compounds with a kagome lattice exhibit intriguing properties and the charge density wave (CDW) adds an additional layer of interest to research on them. In this study, we investigate the temperature and magnetic field dependent electrical properties under a chemical substitution and hydrostatic pressure of ScV6Sn6, a non-magnetic CDW compound. Substituting 5% Cr at the V site or applying 1.5 GPa of pressure shifts the CDW from 92 K to ∼ 50 K. This shift is attributed to the movement of the imaginary phonon band, as revealed by the phonon dispersion relation. The longitudinal and Hall resistivities respond differently under these stimuli. The magnetoresistance (MR) retains its quasilinear behavior under pressure, but it becomes quadratic after Cr substitution. The anomalous Hall-like behavior of the parent compound persists up to the respective CDW transition under pressure, after which it decreases sharply. In contrast, the longitudinal and Hall resistivities of Cr substituted compounds follow a two-band model and originate from the multi carrier effect. These results clearly highlight the role of phonon contributions in the CDW transition and call for further investigation into the origin of the anomalous Hall-like behavior in the parent compound. [ABSTRACT FROM AUTHOR]

In this work we studied the vortex-configuration in a mesoscopic superconducting square in presence of an external magnetic field H applied parallel to its surface vector. We study the magnetization curves in a complete loop, the magnretic induction and the superconducting-electron density for the sample considering Neumann boundary conditions for the order parameter, via length Gennes extrapolation (b → ∞). The sample presents a pinnin center as a Kagome-type laticce at different critical temperature. We solve the generalized time-dependent Ginzburg-Landau equations for a two-condensate system using the Link-variable method considering a Field-Cooling process. Our results show that the vortices are always located at the pinning centers in non-conventional configurations, due to cuopling used. [ABSTRACT FROM AUTHOR]

In this work we studied the vortex-configuration in a mesoscopic superconducting square in presence of an external magnetic field H applied parallel to its surface vector. We study the magnetization curves in a complete loop, the magnretic induction and the superconducting-electron density for the sample considering Neumann boundary conditions for the order parameter, via length Gennes extrapolation . The sample presents a pinnin center as a Kagome-type laticce at different critical temperature. We solve the generalized time-dependent Ginzburg-Landau equations for a two-condensate system using the Link-variable method considering a Field-Cooling process. Our results show that the vortices are always located at the pinning centers in non-conventional configurations, due to cuopling used.

Magnetic materials could realize the intriguing quantum anomalous Hall effect and metal-to-insulator transition when combined with band topology or electronic correlation, which have broad prospects in quantum information, spintronics, and valleytronics. Here, we propose the approach of designing novel two-dimensional (2D) magnetic states via d-orbital-based superatomic lattices. Specifically, we chose triangular zirconium dichloride disks as superatoms to construct the honeycomb superatomic lattices. Using first-principles calculations, we identified a series of 2D magnetic states with varying sizes of superatoms. We found the non-uniform stoichiometries and geometric effect of superatomic lattice give rise to spin-polarized charges arranged in different magnetic configurations, containing ferromagnetic coloring triangles, antiferromagnetic honeycomb, and ferromagnetic kagome lattices. Attractively, these magnetic states are endowed with nontrivial band topology or strong correlation, forming an ideal Chern insulator or antiferromagnetic Dirac Mott insulator. Our work not only reveals the potential of d-orbital-based superatoms for generating unusual magnetic configurations, but also supplies a new avenue for material engineering at the nanoscale. [ABSTRACT FROM AUTHOR]

Abstract Controllably fabricating low-dimensional systems and unraveling their exotic states at the atomic scale is a pivotal step for the construction of quantum functional materials with emergent states. Here, by utilizing the elaborated molecular beam epitaxy growth, we obtain various FexSey phases beyond the single-layer FeSe/SrTiO3 films. A synthetic strategy of lowering substrate temperature with superfluous Se annealing is implemented to achieve various stoichiometric FeSe-derived phases, ranging from 1:1 to 5:8. The phase transitions and electronic structure of these FexSey phases are systematically characterized by atomic resolution scanning tunneling microscopy measurements. We observe the long-ranged antiferromagnetic order of the Fe4Se5 phase by spin-polarized signals with striped patterns, which is also verified by their magnetic response of phase shift between adjacent domains. The electronic doping effect in insulating Fe4Se5 and the kagome effect in metallic Fe5Se8 are also discussed, where the kagome lattice is a promising structure to manifest both spin frustration of d electrons in a quantum-spin-liquid phase and correlated topological states with flat-band physics. Our study provides promising opportunities for constructing artificial superstructures with tunable building blocks, which is helpful for understanding the emergent quantum states and their correlation with competing orders in the FeSe-based family.

Topological photonic insulators provide a novel approach to achieve high-efficiency terahertz transmissions due to the presence of the topological edge states. In this work, the frequency ranges of the topological edge states can be controlled by varying the radius of rods in the kagome lattice and the distance between them. In addition, a gap can be generated between two different frequency ranges and the frequency selecting functions can be realized by constructing different types of domains. Similarly, sandwich a non-trivial photonic crystal between two trivial ones also capable of frequency selection for its topological edge states. Our findings suggest that this work has significant potential for applications in photonic integrated devices.

Controllably fabricating low-dimensional systems and unraveling their exotic states at the atomic scale is a pivotal step for the construction of quantum functional materials with emergent states. Here, by utilizing the elaborated molecular beam epitaxy growth, we obtain various FexSey phases beyond the single-layer FeSe/SrTiO3 films. A synthetic strategy of lowering substrate temperature with superfluous Se annealing is implemented to achieve various stoichiometric FeSe-derived phases, ranging from 1:1 to 5:8. The phase transitions and electronic structure of these FexSey phases are systematically characterized by atomic resolution scanning tunneling microscopy measurements. We observe the long-ranged antiferromagnetic order of the Fe4Se5 phase by spin-polarized signals with striped patterns, which is also verified by their magnetic response of phase shift between adjacent domains. The electronic doping effect in insulating Fe4Se5 and the kagome effect in metallic Fe5Se8 are also discussed, where the kagome lattice is a promising structure to manifest both spin frustration of d electrons in a quantum-spin-liquid phase and correlated topological states with flat-band physics. Our study provides promising opportunities for constructing artificial superstructures with tunable building blocks, which is helpful for understanding the emergent quantum states and their correlation with competing orders in the FeSe-based family. [ABSTRACT FROM AUTHOR]

We present a brief review of experimental and theoretical papers on studies of electron transport and magnetic properties in manganese-based compounds Mn2YZ and Mn3Z (Y = V, Cr, Fe, Co, Ni, etc.; Z = Al, Ge, Sn, Si, Pt, etc.). It has been shown that in the electronic subsystem of Mn2YZ compounds, the states of a half-metallic ferromagnet and a spin gapless semiconductor can arise with the realization of various magnetic states, such as a ferromagnet, a compensated ferrimagnet, and a frustrated antiferromagnet. Binary compounds of Mn3Z have the properties of a half-metallic ferromagnet and a topological semimetal with a large anomalous Hall effect, spin Hall effect, spin Nernst effect, and thermal Hall effect. Their magnetic states are also very diverse: from a ferrimagnet and an antiferromagnet to a compensated ferrimagnet and a frustrated antiferromagnet, as well as an antiferromagnet with a kagome-type lattice. It has been demonstrated that the electronic and magnetic properties of such materials are very sensitive to external influences (temperature, magnetic field, external pressure), as well as the processing method (cast, rapidly quenched, nanostructured, etc.). Knowledge of the regularities in the behavior of the electronic and magnetic characteristics of Mn2YAl and Mn3Z compounds can be used for applications in micro- and nanoelectronics and spintronics. [ABSTRACT FROM AUTHOR]

In this work, we study the effect of electron doping on the kagome superconductor CsV3Sb5. Single crystals and powders of CsV3Sb5−xTex are synthesized and characterized via magnetic susceptibility, nuclear quadrupole resonance, and x-ray diffraction measurements, where we observe a slight suppression of the charge density wave transition temperature and superconducting temperature with the introduction of electron dopants. In contrast to hole doping, both transitions survive relatively unperturbed up to the solubility limit of Te within the lattice. A comparison is presented between the electronic phase diagrams of electron- and hole-tuned CsV3Sb5.

Two-dimensional (2D) semiconducting silicon (Si) is significant for the development of micro/nanoelectronics because of their compatibility with the current Si-based technology and the advantages common to 2D electronic materials. Here, by focusing on the kagome lattice (KL), we design a set of semiconducting 2D KL-Si for nanoscale field-effect transistor (FET) applications. First-principles calculations demonstrate that both stable geometric properties and tunable semiconducting electronic properties can be obtained for the 2D KL-Si with different thicknesses. The 2D KL-Si features electronic band gaps ranging from 2.82 to 1.36 eV as a function of increasing the layer thickness and hole/electron mobility as large as about 103 cm2·V–1·s–1. By applying the KL-Si to nanoscale FETs, we obtain giant negative differential resistances with peak-valley ratios over 107 and excellent switching performance fulfilling the requirements of the International Technology Roadmap for Semiconductors. Our study demonstrates the importance of kagome topology in the design of 2D Si crystals with excellent semiconducting properties as well as their promising application in nanoelectronic devices. [ABSTRACT FROM AUTHOR]

Compounds with a kagome lattice exhibit intriguing properties and the charge density wave (CDW) adds an additional layer of interest to research on them. In this study, we investigate the temperature and magnetic field dependent electrical properties under a chemical substitution and hydrostatic pressure of ScV _6 Sn _6 , a non-magnetic CDW compound. Substituting 5% Cr at the V site or applying 1.5 GPa of pressure shifts the CDW from 92 K to ∼ 50 K. This shift is attributed to the movement of the imaginary phonon band, as revealed by the phonon dispersion relation. The longitudinal and Hall resistivities respond differently under these stimuli. The magnetoresistance (MR) retains its quasilinear behavior under pressure, but it becomes quadratic after Cr substitution. The anomalous Hall-like behavior of the parent compound persists up to the respective CDW transition under pressure, after which it decreases sharply. In contrast, the longitudinal and Hall resistivities of Cr substituted compounds follow a two-band model and originate from the multi carrier effect. These results clearly highlight the role of phonon contributions in the CDW transition and call for further investigation into the origin of the anomalous Hall-like behavior in the parent compound.

We present a comprehensive investigation of the superconducting properties of ZrRe 2 , a Re-based hexagonal Laves compounds. ZrRe 2 crystallizes in a C14-type structure (space group P6 3 /mmc), where the Re atoms form a breathing Kagome lattice, with cell parameters a = b = 5.2682(5) Å and c = 8.63045 Å. Through transport measurements, the superconducting transition is observed with T c o n s e t = 6.44 K and T c z e r o = 6.06 K. In magnetization measurements(ZFC-FC) superconducting transition occurs at 6.12 K. The measured lower and upper critical fields are 6.27 mT and 7.84 T, respectively. Measurements of the specific heat capacity confirm the presence of bulk superconductivity, with a normalized specific heat change of Δ C e / γ T c = 1.63 and an electron-phonon strength of λ e p = 0.69. DFT calculations revealed that the band structure of ZrRe 2 is intricate and without van Hove singularity. [ABSTRACT FROM AUTHOR]

• Single-crystal samples were prepared using a new methodology. • The compound can be regarded as a new system charactered by the K atom embedded in the Kagome system Na 5 Co 15.5 Te 6 O 36. • Magnetization measurements reveal ferromagnetic correlations and an enhanced abnormal hysteresis loop. In this paper, we report the structural, magnetic and specific heat properties of a new compound Na 2.67 K 1.33 Pb 0.67 Co 15.33 Te 6 O 36 (NKPCTO). The compound can be regarded as a new system charactered by the K and Pb atom embedded in the Kagome system Na 5 Co 15.5 Te 6 O 36 (NCTO). In the new structure, we find that the disordered occupations of the Na and Co(3) atoms is irrelevant to K atom site, and Pb has same site with K. The ground state is proposed to have an effective S = 1/2 due to the 3d7 Co2+ ion in octahedral coordination and considerable spin–orbit coupling. Magnetic and specific heat data uncover that only an antiferromagnetic phase transition develops in NKPCTO at 49 K. There are also ferromagnetic correlations above the Neel temperature, as well as anomalous hysteresis loops and multiple field-induced magnetic transitions at low temperatures. [ABSTRACT FROM AUTHOR]

Modulating the electron interaction and magnetic domains is an essential strategy to evoke novel physical properties, both for fundamental research and for related magnetic applications. The emerging annealing process attracted attention due to its capability of tuning the magnetic performance, but it has been rarely studied. Herein, we conducted hydrogen annealing on the Weyl semimetallic Co 3 Sn 2 S 2 and investigated the magnetic interaction, critical behavior, and magnetocaloric effect (MCE). Hydrogen-annealed Co 3 Sn 2 S 2 (HA-Co 3 Sn 2 S 2) exhibits a distinct anisotropy-dependent magnetic behavior, where a typical second-order transition with an easy magnetization process is observed under H // c. However, a frustrated magnetic state composed of ferromagnetic (FM), antiferromagnetic (AFM), and/or spin glass phases is observed when H // ab. Critical analyses illustrate that the ground state of HA-Co 3 Sn 2 S 2 lies between the 3D-Ising model and the Mean-filed model, indicating the presence of both long-range and short-range magnetic interactions in the system. Additionally, we found that HA-Co 3 Sn 2 S 2 exhibits an enhanced saturation magnetization (M s) and magnetic refrigeration capacity, both showing anisotropic dependence, compared to the pristine Co 3 Sn 2 S 2. Our work develops hydrogen annealing to modulate electron coupling and magnetic domains, paving the way for further studies of anisotropic magnetic behavior and applications in magnetic refrigeration. • The high-quality single crystal Co 3 Sn 2 S 2 is synthesized and is further annealed under the hydrogen atmosphere. • A significant enhancement of M s and magnetic refrigeration capacity is obtained, with strong anisotropic dependence. • The ground state of HA-Co 3 Sn 2 S 2 is between the 3D-Ising model and the Mean-filed model. [ABSTRACT FROM AUTHOR]

The Kagome lattice is rich in unique electronic and magnetic properties, such as flat band, superconductivity, charge density waves, and so on. In this paper, the magnetic properties, flat and Dirac bands of monolayer Mn 3 Sn 3 Se 2 with Kagome lattice are investigated based on first-principles calculations. A total of four magnetic configurations are considered, and the intrinsic ground state of Mn 3 Sn 3 Se 2 is identified as the ferromagnetic state. Strain has a significant effect on its magnetic ground state, which changes to an in-plane AFM state when the tensile strain exceeds 5 %. Monolayer Mn 3 Sn 3 Se 2 has an out-of-plane magnetic anisotropy of up to 0.777 meV, and the Curie temperature is 528 K. The band structure of the FM state is shown to be metallic, and spin polarized flat and Dirac bands appear near the Fermi level, which are degenerate. Monolayer Mn 3 Sn 3 Se 2 changes to half-metallic when a strain of 1%–2% is applied. Strain and correlation effects can significantly alter the flatness of flat band and the relative energy with Dirac bands. These results not only enrich the family of two-dimensional ferromagnets, but also provide a reference for studying the regulation of flat and Dirac bands. • The intrinsic Mn 3 Sn 3 Se 2 monolayer is room-temperature ferromagnetic metal. • The Curie temperature is 528 K and out-of-plane MAE is 0.777 meV. • A tensile strain of 1 %∼2 % makes it a half-metal. • There are flat band and Dirac point near the Fermi level, which are degenerate. • U-value and strain can regulate the degeneracy and the flatness of flat band. [ABSTRACT FROM AUTHOR]

A new compound NaMn 3 (SeO 3) 2 (HSeO 3) 6 was obtained by a conventional hydrothermal method. This compound crystallizes in a trigonal system with space group R -3, exhibiting a typical kagomé structure, where the kagomé layers are composed of [MnO 6 ] octahedra linked by [SeO 3 ] groups. Magnetic susceptibility measurements confirm that this compound exhibits a ferromagnetic transition at ∼13 K, as further confirmed by the heat capacity data. The magnetic entropy was estimated, indicating that the system may release almost the entire entropy at low temperature. The compound NaMn 3 (SeO 3) 2 (HSeO 3) 6 shows a typical kagomé layered structure and exhibits ferromagnetic transition at ∼13 K. [Display omitted] • A new selenite compound NaMn 3 (SeO 3) 2 (HSeO 3) 6 was synthesized by a conventional hydrothermal method. • This compound has a unique layered structure featuring regular S = 2 kagomé planes. • The compound was found to exhibits ferromagnetic transition at ∼13 K by magnetic and heat capacity measurements. [ABSTRACT FROM AUTHOR]

Quantum correlation in the antiferromagnetic XXZ model on kagome lattice and non-Hermitian tight binding model on kagome lattice are investigated. For the Hermitian XXZ model on kagome lattice, the calculations are performed for different extensions of the model with single-ion anisotropy and out-of-plane Dzyaloshinskii–Moriya interaction (DMI). We get the von Neumann entropy as a function of the DMI interaction, anisotropy and single-ion anisotropy with aim to verify the effect of these corrections that occurs in real magnetic systems on quantum correlation. Moreover, the effect of DMI interaction, anisotropy and single-ion anisotropy is investigated on concurrence and entanglement negativity as well. For the non-Hermitian tight binding model on kagome lattice, we analyzed quantum correlation using the entanglement negativity as entanglement measure which is more adequate in this case. [ABSTRACT FROM AUTHOR]

The analysis of graphs and networks is a multidisciplinary research field from its origin. As such, it has been extensively used also in biomedicine, cheminformatics, and in bioinformatics, where approaches based on graph descriptors have been offered for communicating with the numerous challenging tasks. In quantitative structure-activity (QSAR) and quantitative structure-property (QSPR) relationships studies, graph invariants are used to forecast the biological activities and properties of nanomaterials. In these studies, degree-based topological descriptors have founded comprehensive acceptance among the different types of descriptors, because of the ease of generation and the speed with which these calculations can be performed. In this article, we first compute the M-polynomials of 2D kagome lattice and then derive the closed form of various significant topological degree-based indices in terms of the M-polynomials and partition techniques. Furthermore, we sketch surfaces that show the dependence of some topological indices on the parameters of the structure. [ABSTRACT FROM AUTHOR]

Kagome lattice, made of corner-sharing triangles, provides an excellent platform for hosting exotic topological quantum phases. Here, we report the observation of large anomalous Hall effect and topological Hall effect in the Kagome lattice material Yb 0.90 Mn 6 Ge 3.25 Ga 0.39 single crystal. Compared to the antiferromagnetic pristine compound YbMn 6 Ge 6 , Yb 0.90 Mn 6 Ge 3.25 Ga 0.39 has an easy plane ferromagnetic structure below 361 K and presents a spin-reorientation transition at 218 K. An intrinsic anomalous Hall conductivity with the value of 604.2 Ω-1·cm-1 is obtained in Yb 0.90 Mn 6 Ge 3.25 Ga 0.39 , which is the largest in RMn 6 X 6 (X = Ge and Sn) family. Besides, a remarkable topological Hall signal is also observed near room temperature. The topological Hall resistivity of Yb 0.90 Mn 6 Ge 3.25 Ga 0.39 is determined to be -1.86 μΩ·cm at 280 K under μ 0 H = 0.3 T. Our results indicate that Yb 0.90 Mn 6 Ge 3.25 Ga 0.39 may be an excellent platform to study the relationship between the magnetic and electronic structure and to explore novel quantum phenomenon. [Display omitted] [ABSTRACT FROM AUTHOR]

The concept of orbital angular momentum (OAM) has garnered significant attention from researchers since its discovery, with a steady uncovering of its properties over the past three decades. Initially overlooked, the role of OAM in the optical vortex lattice (OVL) has gained prominence due to recent scholarly efforts. This study delves into the modification of OAM by employing controlled topological charge to generate high-order OVL. Furthermore, it explores the Talbot effect within the context of multi-beam interference. The findings indicate that the interference of three beams of light results in the formation of both Kagome and Super-honeycomb lattices, whereas the interference of four beams leads to the emergence of the Lieb lattice. This research offers novel insights into light interference and light field regulation and its application. •Research explores OAM modifications using controlled topological charge for high-order OVL generation. • Highlights the growing importance of OAM in optical sciences, especially in complex OVL creation. • Demonstrates Talbot effect with multi-beam interference, revealing Kagome and Super-honeycomb lattice formation from three beams. • Shows four-beam interference leading to Lieb lattice emergence, advancing light interference and field regulation insights. [ABSTRACT FROM AUTHOR]

A wider scope in topological semimetals accelerates various attractive quantum phenomena for the last two decades. We here report the detailed investigation of magnetic Co3Sn2S2 Weyl semimetal based on the cobalt accompanied kagome lattice for the first time. We emphasize the highly motivated theoretical and experimental analyses in each topological terms of Co3Sn2S2 that led to intensifying emergent topological materials with inherent properties, particularly in the pursuance of magnetic rich quantum anomalous Hall effect. We additionally highlight the Co3Sn2S2 surface band structure, recognized in the diverse fields of study from the perception of topological properties to modern electrochemistry approaches. From materials perspective, this typical kagome Co3Sn2S2 Weyl semimetal alone has extensively covered more enriching nontrivial surface states than topological insulators and nonmagnetic semimetals even in the absence of magnetic field and external strain. Some specific examples include Weyl nodes linked flat band magnetism, a large anomalous Hall effect, anomalous Hall angle, giant magnetooptical effect, and thermomagnetic Nernst effect. In addition, we selectively extend the review on the undisputed surface band characteristics of Co3Sn2S2, by which a major concept of magnetic Weyl semimetal could hierarchically meet the contemporary quantum phenomena. This strongly led to more focus on nontrivial magnetic topological studies for gaining insightful perspectives.

We present a comprehensive study of the magnetocaloric effect (MCE) in a family of kagome magnets with formula R Mn 6 Sn 6 (R =Tb, Ho, Er, and Lu). These materials have a small rare-earth content and tunable magnetic ordering, hence they provide a venue to study the fundamentals of the MCE. We examine the effect of different types of order (ferrimagnetic and antiferromagnetic) and the presence of a metamagnetic transition on the MCE. We extend the study to the high-entropy rare-earth forms of the R Mn 6 Sn 6 family. Our results suggest several guidelines for enhancing the MCE in tunable magnetic materials with small rare-earth content. • The magnetocaloric effect in R Mn 6 Sn 6 depends sensitively on the rare-earth. • R Mn 6 Sn 6 family is a tunable platform to study high temperature MCE. • High-entropy forms are not always a viable path to increase MCE. [ABSTRACT FROM AUTHOR]

The spin–orbit coupling (SOC) effect is the dominant origin of the topological properties in a topological insulator which can be induced and enhanced through various methods. Here we theoretically study the effects of varying SOC on the topological properties of two-dimensional kagome lattice based on the tight-binding approximation. We find that the system can undergo a transition between two non-trivial topological states by tuning the SOC strength. In addition, the topological phase transition can be achieved with a weaker SOC under a uniform tensile strain, which suggests that strain engineering can be used to regulate topological states. Besides, the characteristics of optical spin Hall conductivity are also studied, which supplies an experimental determination to reveal the different topological states. Furthermore, we propose an external mechanical strain modulated spin-switch device, which can generate opposite spin currents under stretch and compressed strain. Our results indicate that with the combination of SOC and strain, kagome lattice materials have potential applications on tunable spintronics and optoelectronic devices.

Recently the Rydberg blockade effect has been utilized to realize quantum spin liquid (QSL) on a kagome lattice. Evidence of QSL has been obtained experimentally by directly measuring non-local string order. In this paper, we report a Bardeen–Cooper–Schrieffer (BCS)-type variational wave function study of the spin liquid state in this model. This wave function is motivated by mapping the Rydberg blockade model to a lattice gauge theory, where the local gauge conservations replace the role of constraints from the Rydberg blockade. We determine the variational parameter from the experimental measurement of the Rydberg atom population. Then we compare the predictions of this deterministic wave function with the experimental measurements of non-local string order. Combining the measurements on both open and closed strings, we extract the fluctuations only associated with the closed-loop as an indicator of the topological order. The prediction from our wave function agrees reasonably well with the experimental data, with only one fitting parameter determined by measurement of Rydberg atom population. Our variational wave function provides a simple and intuitive picture of the QSL in this system that can be generalized to similar spin liquid phases in other lattice geometry.

We consider interaction energies E f [ L ] between a point O ∈ R d , d ≥ 2 , and a lattice L containing O, where the interaction potential f is assumed to be radially symmetric and decaying sufficiently fast at infinity. We investigate the conservation of optimality results for E f when integer sublattices kL are removed (periodic arrays of vacancies) or substituted (periodic arrays of substitutional defects). We consider separately the non-shifted ( O ∈ k L ) and shifted ( O ∉ k L ) cases and we derive several general conditions ensuring the (non-)optimality of a universal optimizer among lattices for the new energy including defects. Furthermore, in the case of inverse power laws and Lennard-Jones-type potentials, we give necessary and sufficient conditions on non-shifted periodic vacancies or substitutional defects for the conservation of minimality results at fixed density. Different examples of applications are presented, including optimality results for the Kagome lattice and energy comparisons of certain ionic-like structures. [ABSTRACT FROM AUTHOR]

In this study, we explored the electronic properties of a two-dimensional (2D) kagome lattice in the presence of an external magnetic field, spin-orbit coupling (SOC), and strain. Our focus was on investigating the energy-dependent behavior of the electronic heat capacity and paramagnetic spin susceptibility in response to changing factors. Employing the Green's function approach, we successfully determined the energy dependence of the electronic heat capacity and paramagnetic susceptibility using the tight-binding model. Notably, at low energies, the electronic heat capacity almost reaches the Schottky anomaly peak, while the paramagnetic susceptibility sharply decreases. Furthermore, we conducted a detailed investigation of the energy-dependent paramagnetic susceptibility and electronic heat capacity of a kagome lattice monolayer, considering the influences of SOC and magnetic field factors. Our investigation of the density of states (DOS) in the presence of SOC suggests that semimetal-to-insulator phase transitions occur. Additionally, throughout our study, we observed variations in the DOS spectrum, indicating the influence of both compressive and tensile strains. We found that these alterations, along with the splitting of levels under different conditions, led to changes in the material's electrical properties. [Display omitted] • Single orbital lattice hopping, tight-binding approach is employed. • By applying SOC, phase transfer from semimetal to insulator is created. • Applying an external magnetic field creates a band gap. • The paramagnetic susceptibility demonstrated a decreasing trend in low energy. • In low temperatures, an upward trend for the heat capacity is observed. [ABSTRACT FROM AUTHOR]

Interfacial structural transformations arising from solute segregation play a crucial role in the performance of materials. However, these micro-transitions are often difficult to reveal due to their buried nature. Here, in a typical Mg-rare-earth model system, we present the discovery of interfacial Kagome lattice transitions triggered by segregation of solutes coupled with bi-crystalline lattice interactions, in three types of partially coherent tilt grain boundaries (GBs), using atomic-resolution scanning transmission electron microscopy observations plus theoretical calculations. The results demonstrate that the minimization of GB elastic strain is responsible for the selective segregation of solutes at interfacial specific sites, resulting in a confined phase transition of the embedded triangular-quadrilateral (10 1 ¯ 1) Mg lattice to a topological hexagonal-triangular Kagome lattice via atomic shuffling. Furthermore, the pressure-temperature conditions that trigger such interfacial Kagome lattice transitions have also been determined. These findings not only enrich the transition pathways formed by the Kagome lattice but also provide a bottom-up approach for investigating interfacial structural transformations induced by solute/impurity segregation in polycrystalline materials. [Display omitted] [ABSTRACT FROM AUTHOR]

The frustrated magnets exhibiting kagome geometries and the investigation of their structure-property relationships have garnered substantial attention as potential candidates for quantum spin liquid (QSL). In this study, β -Mn 2 (OH) 3 Cl nanosheets with distorted kagome geometries were synthesized via a solid-state reaction, and low-temperature magnetic measurements revealed a spin-glass-like magnetic phase transition around 40 K in the frustrated β -Mn 2 (OH) 3 Cl. A pressure-induced structural phase transition was further realized by employing in situ synchrotron X-ray diffraction, leading to a hexagonal crystal structure with a nearly perfect kagome lattice of magnetic Mn2+ ions. High-pressure Raman and UV–vis absorption measurements indicates that the topological evolution can be attributed to the synergistic effects of pressure driven internal hydrogen bonds and the intrinsic Jahn-Teller effects. This study provides a strategy for synthesizing candidate compounds of QSL and sheds light on the mechanism underlying the topological evolution of kagome lattices under high pressure. [Display omitted] • β -Mn 2 (OH) 3 Cl nanosheets were synthesized via a solid-state reaction and exhibited spin glass behavior at low temperatures. • β -Mn 2 (OH) 3 Cl undergoes an irreversible phase transition under high pressure to form a nearly perfect kagome lattice. • The hydrogen bonding and the Jahn-Teller effect are key factors in its high-pressure structural transition of β -Mn 2 (OH) 3 Cl. [ABSTRACT FROM AUTHOR]

We investigate the anisotropic magnetic response in a kagome antiferromagnetic compound Fe 1- x Co x Sn (x = 0, 0.04, 0.06, 0.14). The magnetic behaviors of three distinct spin orderings, namely the planar, tilted, and axial spin states, are examined under various conditions, including doping rate, temperature, and magnetic fields. We confirm that the magnetic susceptibility of all three spin states has significant anisotropy, which depends on both the magnitude and direction of the applied magnetic field. The planar and axial states show scaling behavior in magnetic susceptibility, while the tilted state does not. Furthermore, employing the differential magnetic susceptibility, we observe that the axial spins display discontinuous spin-flop transitions, while the planar and tilted spins exhibit a continuous spin reorientation. The magnetic phase diagrams, summarizing our observations, highlight the anisotropic nature of magnetic behaviors in the Fe 1- x Co x Sn system. These diagrams clearly show that the magnetic responses are not overlapping and follow distinct mechanisms in their interaction with magnetic fields. We suggest that the axial state may arise due to the dopants as an obstacle within the kagome lattice, as evidenced by similar magnetic behaviors in Fe 0.96 Ni 0.06 Sn. [Display omitted] ● Magnetic phase diagrams of AFM Fe 1- x Co x Sn (x < 0.14) single crystals are proposed. ● The influence of magnetic fields on planar, tilted, and axial orderings is examined. ● Magnetic susceptibility can be scaled only in planar and axial spin states. ● Axial spins undergo spin-flops, while planar and tilted spins continuously change. ● The axial state may arise due to the dopants as an obstacle within the kagome lattice. [ABSTRACT FROM AUTHOR]

We investigate the magnetisation and internal energy of the David star in the Kagome lattice by the effective field theory developed by Kaneyoshi. First-order, Second-order and successive phase transitions are observed for different spin-down orientations. Spin-down orientation of identical atoms causes a second-order phase transition, spin-down orientation of different atoms causes a first-order and successive phase transitions. Minimum internal energy is obtained as UDavid star =−5 for all spin-up orientations, whereas it increases (UDavid star > −5) for at least one spin-down orientation. For spin-down orientation of A↑–A↓, internal energy becomes zero at a certain temperature and we call this temperature 'zero internal energy temperature (Tzie)'. At T < Tzie=1.99, internal energy is positive, whereas it is negative for other spin states. Therefore, spin-induced minimum internal energy broken is observed except for all spin-up (A↑, B↑ and C↑) cases. [ABSTRACT FROM AUTHOR]

This paper details the nonlinear design of adaptive lattices by determination and enhancement of compliant modes and optimizing the designed structure for delivering high amplitude actuation. The particular focus is the kagome lattice geometry—a pattern with some unique and useful actuation properties. Developing a novel design tool, the stiffness matrix of the beam assembly is calculated using a developed second-order geometrically nonlinear beam finite element formulation allowing large rotations. Based on this formulation in conjunction with singular value decomposition of the stiffness matrix, the modal optimization technique reduces the continuous structure with many degrees of freedom to a small number of low energy modes, which form the basis of designing the adaptive structure. For delivering high-amplitude actuation, the designed structure needs to be re-optimized due to changes in the nonlinear stiffness matrix under large deformation. This is performed via Bayesian optimization and by removing some internal members of the lattice. The integrity and feasibility of the optimum design is guaranteed via defining some constraints on removed members. [ABSTRACT FROM AUTHOR]

The magnon band topology due to the Dzyaloshinskii–Moriya interaction (DMI) and its relevant topological thermal Hall effect has been extensively studied in kagome lattice magnets. In this theoretical investigation, we report a new mechanism for phase transitions between topological phases of magnons in kagome ferromagnets by tuning the anisotropic nearest-neighbor ferromagnetic interaction and DMI. Using the linear spin-wave theory, we calculate the Chern number and thermal Hall conductivity of magnons in low temperature regime. We show the magnon band structures and magnonic edge states in each topological phase. From the topological phase diagram, we find a sign reversal of the thermal Hall conductivity upon tuning the modulation factors. We explicitly demonstrate the correspondence of thermal Hall conductivity with the propagation direction of the magnonic edge states. Finally, we discuss candidate materials as experimental realizations of our theoretical model.

The high-field regime of the spin-s XXZ antiferromagnet on the kagome lattice gives rise to macroscopically degenerate ground states thanks to a completely flat lowest single-magnon band. The corresponding excitations can be localized on loops in real space and have been coined "localized magnons". Thus, the description of the many-body ground states amounts to characterizing the allowed classical loop configurations and eliminating the quantum mechanical linear relations between them. Here, we investigate this loop-gas description on finite kagome lattices with open boundary conditions and compare the results with exact diagonalization for the spin-1/2 XY model on the same lattice. We find that the loop gas provides an exact account of the degenerate ground-state manifold while a hard-hexagon description misses contributions from nested loop configurations. The densest packing of the loops corresponds to a magnon crystal that according to the zero-temperature magnetization curve is a stable ground state of the spin-1/2 XY model in a window of magnetic fields of about 4% of the saturation field just below this saturation field. We also present numerical results for the specific heat obtained by the related methods of thermal pure quantum (TPQ) states and the finite-temperature Lanczos method (FTLM). For a field in the stability range of the magnon crystal, one finds a low-temperature maximum of the specific heat that corresponds to a finite-temperature phase transition into the magnon crystal at low temperatures. [ABSTRACT FROM AUTHOR]