Kagome System Research Articles

Electronic correlations in the normal state of the kagome superconductor KV3Sb5

Recently, intensive studies have revealed fascinating physics, such as charge density wave and superconducting states, in the newly synthesized kagome-lattice materials ${A\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ $(A=\text{K}, \mathrm{Rb}, \mathrm{Cs})$. Despite the rapid progress, fundamental aspects such as the magnetic properties and electronic correlations in these materials have not been clearly understood yet. Here, based on density functional theory plus single-site dynamical mean-field theory calculations, we investigate the correlated electronic structure and magnetic properties of the ${\mathrm{KV}}_{3}{\mathrm{Sb}}_{5}$ family materials in the normal state. We show that these materials are good metals with weak local correlations. The obtained Pauli-like paramagnetism and the absence of local moments are consistent with a recent experiment. We reveal that the band crossings around the Fermi level form three groups of nodal lines protected by the spacetime inversion symmetry, each carrying a quantized $\ensuremath{\pi}$ Berry phase. Our result suggests that the local correlation strength in these materials appears to be too weak to generate unconventional superconductivity, and nonlocal electronic correlation might be crucial in this kagome system.

Orbital Chern Insulator and Quantum Phase Diagram of a Kagome Electron System with Half-Filled Flat Bands.

We study the quantum phase diagram of electrons on kagome lattice with half-filled lowest flat bands by considering the antiferromagnetic Heisenberg interaction J, and short-range Coulomb interaction V. In the weak J regime, we identify a fully spin-polarized phase. The presence of finite V drives a spontaneous chiral current, which makes the system an orbital Chern insulator by contributing an orbital magnetization. Such an out-of-plane orbital magnetization allows the presence of a Chern insulating phase independent of the spin orientation in contrast to the spin-orbit coupling induced Chern insulator that disappears with in-plane ferromagnetism constrained by symmetry. Such a symmetry difference provides a criterion to distinguish the physical origin of topological responses in kagome systems. The orbital Chern insulator is robust against small coupling J. By further increasing J, we find that the ferromagnetic topological phase is suppressed, which first becomes partially polarized and then enters a nonmagnetic phase with spin and charge nematicity. The frustrated flat band allows the spin and Coulomb interaction to play an essential role in determining the quantum phases.

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카고메 시스템을 활용한 비내진 저층 RC 구조물의 내진성능평가

Emergent chiral spin ordering and anomalous Hall effect in a kagome lattice at a 13 filling

The study of electronic and magnetic properties of kagome lattice has been an active research area searching for topological phases of matters. In particular, the kagome system with transition metal stannides and etc exhibit interesting anomalous Hall effects driven by ferromagnetic or non-collinear magnetic ordering. In this paper, motivated by these pioneer works, we study strongly correlated spin-orbit coupled electrons in kagome lattice at 1/3 filling. Using both Hartree-Fock approach and effective model analysis, we report quantum phase transitions accompanied with distinct charge and magnetic ordered phases. Especially, for strongly interacting limit, we discover new types of 1(2)-pinned metallic states which are understood by effective localized electron models. Furthermore, when spin-orbit coupling is present, it turns out that such pinned metallic states open a wide region of Chern insulating phase with chiral spin ordering. Thus, quantum anomalous Hall effect is expected with emergent scalar spin chirality. Our theory provides a theoretical platform of strongly interacting kagome metal which is applicable to transition metal stannides.

Turbulent hydrodynamics in strongly correlated Kagome metals

A current challenge in condensed matter physics is the realization of strongly correlated, viscous electron fluids. These fluids can be described by holography, that is, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canonical system considered for realizations has been graphene. In this work, we show that Kagome systems with electron fillings adjusted to the Dirac nodes provide a much more compelling platform for realizations of viscous electron fluids, including non-linear effects such as turbulence. In particular, we find that in Scandium Herbertsmithite, the fine-structure constant, which measures the effective Coulomb interaction, is enhanced by a factor of about 3.2 as compared to graphene. We employ holography to estimate the ratio of the shear viscosity over the entropy density in Sc-Herbertsmithite, and find it about three times smaller than in graphene. These findings put the turbulent flow regime described by holography within the reach of experiments.

Magnetic topological kagome systems

The authors introduce a new class of topological systems driven by the Hund's coupling mechanism associated to Mott physics. The paper establishes a link between the core magnetism on the Kagome lattice and the occurrence of topological energy Bloch bands. This research is motivated by the recently discovered quantum material Co3Sn2S2.

First and second order topological phases on ferromagnetic breathing kagome lattice

In this work, topological properties of a ferromagnetic Heisenberg model on a breathing kagome lattice are investigated extensively in the presence of Dzyaloshinskii–Moriya interaction. While the kagome ferromagnet hosts only a single first order topological phase, the breathing kagome system exhibits multiple first and second order topological phases along with their coexistence. Magnon dispersion relation is obtained by using linear spin wave theory. Flat band and Dirac cones are obtained in the absence of Dzyaloshinskii–Moriya interaction. A topological phase diagram is presented where several first and second order phases as well as their overlap are identified. Values of thermal Hall conductivity for all the first order phases are obtained. Distinct first order phases are characterized by different sets of Chern numbers in association with the necessary chiral edge states in accordance to the first order bulk-boundary-correspondence rule. Second order phase is characterized by polarization along with the emergence of corner states. Violation of the second order bulk-corner-correspondence rule has been noted in some regions.

Kagome metal-organic frameworks as a platform for strongly correlated electrons

By using first-principles calculations we put forward the Cu-dicyanoanthracene lattice as a platform to investigate strong electronic correlations in the family of Kagome metal-organic frameworks. We show that the low-energy model is composed by molecular orbitals which arrange themselves in a typical Kagome lattice at n = 2/3 filling, where the Fermi level lies at the Dirac point. The Coulomb interaction matrix expressed in this molecular orbitals basis, as obtained by large-scale constrained random-phase approximation calculations, is characterized by local U and non-local parameters exceeding more than ten times the Kagome bandwidth. For such Kagome systems, our findings suggest the possible emergence of peculiar electron–electron collective phenomena, such as an exotic valence bond solid order characterized by modulated bond strengths.

Intrinsic transverse field in frustrated quantum Ising magnets: Physical origin and quantum effects

Transverse field Ising model is a common model in quantum magnetism and is often illustrated as an example for quantum phase transition. Its physical origin in quantum magnets, however, is actually not quite well-understood. The quantum mechanical properties of this model on frustrated systems are not well-understood either. We here clarify the physical origin, both extrinsic one and intrinsic one, for the transverse field of the quantum Ising model, and then explain the quantum effects in the Kagome system. We discuss the quantum plaquette order and the quantum phase transition out of this ordered state in the rare-earth Kagome magnets. Our specific results can find their relevance in the rare-earth tripod Kagome magnets.

Magnon topology and thermal Hall effect in trimerized triangular lattice antiferromagnet

The non-trivial magnon band topology and its consequent responses have been extensively studied in two-dimensional magnetisms. However, the triangular lattice antiferromagnet (TLAF), the best-known frustrated two-dimensional magnet, has received less attention than the closely related Kagome system, because of the spin-chirality cancellation in the umbrella ground state of the undistorted TLAF. In this work, we study the band topology and the thermal Hall effect (THE) of the TLAF with (anti-)trimerization distortion under the external perpendicular magnetic field using the linearized spin wave theory. We show that the spin-chirality cancellation is removed in such case, giving rise to the non-trivial magnon band topology and the finite THE. Moreover, the magnon bands exhibit band topology transitions tuned by the magnetic field. We demonstrate that such transitions are accompanied by the logarithmic divergence of the first derivative of the thermal Hall conductivity. Finally, we examine the above consequences by calculating the THE in the hexagonal manganite YMnO$_3$, well known to have anti-trimerization.

Magnetocaloric effect in the triangulated Kagome lattice Cu9Cl2(cpa)6

The spin frustrated magnetism of the 2-D molecular magnet material Cu9Cl2(cpa)6 (cpa = anion of 2-carboxypentonic acid), abbreviated as CPA, has been the subject of experimental and theoretical studies that suggest this Heisenberg lattice may be among the most frustrated of materials, along with other Kagome, garnet and pyrochlore systems. The CPA framework is a triangles-in-triangles, or a triangulated-Kagome-lattice (TKL) for which M(T,H) phase diagrams rich in topologically induced spin-liquid states should result from deliberate chemical manipulations. While the spin frustrated topology of CPA makes it of interest for the fundamental physics of quantum spin liquids (QSLs), we report here that the low temperature magnetothermodynamic properties also make it of interest for the study of the magnetocaloric effect (MCE). Highly frustrated materials that do not have clearly distinctive first- or second-order phase transitions can have MCEs due to the persistent entropy of low-lying eigenstates with large degrees of degeneracy. We present field-dependent data up to H = 1T that allow estimates for the MCE of CPA to be calculated from magnetization and demonstrate that a H-T phase boundary exists for temperatures above T = 2K in applied fields below H = 1T. When taken in combination with the phase boundary discovered in the heat capacity data below T = 2K, as well as synthetic results that demonstrate CPA can be taken as a broad materials class, the presence of this second phase boundary suggest chemical variations should present tremendous opportunity to design additional materials. The synthetic challenge will be to produce high quality crystals with consistent, well-understood chemical compositions.

Tuning of a Kagome Magnet: Insulating Ground State in Ga‐Substituted Cu4(OH)6Cl2

Here, a successful synthesis method of the series GaxCu4–x(OD)6Cl2 with substitutions up to x = 0.8 is presented. The compound remains a frustrated kagome system with an insulating ground state similar to herbertsmithite for these substitutions, as the additional charge of Ga3+ is most likely bound to additional OH− and Cl−. Besides infrared measurements, we present magnetic and specific‐heat data down to 2 K for selected samples with . With increasing x the long‐range magnetic order is suppressed, similar to what is observed in the series ZnxCu4–x(OH)6Cl2, indicating that Ga goes predominantly to the inter‐plane position of the layered crystal structure. The reduction of the frozen magnetic fraction with increasing substitution is followed by muon spin relaxation (μSR) measurements. 69,71Ga nuclear magnetic resonance (NMR) was applied as a local probe for Ga induced disorder. One well resolved Ga NMR line of moderate width is found for each isotope across the phase diagram which indicates a rather homogeneous distribution of the Ga isotopes on a single site in the lattice.

Canonical-Ensemble Calculations of the Magnetic Susceptibility for a Spin-1/2 Spherical Kagome Cluster With Dzyaloshinskii–Moriya Interactions by Using Microcanonical Thermal Pure Quantum States

For the spherical kagome system {W <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">72</sub> V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">30</sub> }, which is a magnetic cluster with 30 V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4+</sup> ions, recent experimental and theoretical studies on the magnetization process at low temperatures have indicated that Dzyaloshinskii-Moriya interaction is an important ingredient in this material. In this paper, we use microcanonical thermal pure quantum (mTPQ) states to calculate the temperature dependence of the magnetic susceptibility and compare our calculated results with an existing experimental susceptibility. These mTPQ states are generated to reproduce the smooth microcanonical ensemble, which is difficult from the canonical ensemble. We show that adequate choice of a parameter in the generation procedure of mTPQ states leads to the same temperature dependence as the canonical ensemble.

Multipolar edge states in the anisotropic kagome antiferromagnet

Excitations of ordered insulating magnets gain renewed interest due to their potential topological properties and the natural realization of magnetic analogues of the celebrated topological models. In this paper we go beyond these parallels and explore what else is there in the unconventional excitations of quantum magnets. We study the topologically nontrivial multiplet excitations of the antiferromagnetic spin-1/2 kagome system with strong breathing anisotropy and Dzyaloshinskii-Moriya interaction. We show that in the chiral magnetic ground state the excitations can be characterized by a spin-1/2 doublet and a spin-3/2 quartet. With the use of magnetic field we can tune the quartet through a band touching topological phase transition, when a novel spin-3/2 Dirac cone is formed by the touching of four bands. In the topologically nontrivial regime the spin-3/2 bands have large Chern numbers -3, -1, 1, 3. In an open system the emerging chiral edge states naturally inherit the multipolar characters and we find novel quadrupolar edge modes.

Continuous degeneracy of the fcc kagome lattice with magnetic dipolar interactions

Results are presented on analytic and computational analyses of the spin states associated with a 3D fcc lattice composed of ABC stacked kagome planes of magnetic ions with only long-range dipole-dipole interactions. Extending previous work on the 2D kagome system, where discrete six-fold discrete degeneracy of the ground state was revealed [Holden et al. Phys. Rev. B 91, 224425 (2015)], we show that the 3D lattice exhibits a continuous degeneracy characterized by just two spherical angles involving six sublattice spin vectors. Application of a Heat Bath Monte Carlo algorithm shows that thermal fluctuations reduce this degeneracy at very low temperature in an order-by-disorder process. A magnetic field applied along directions of high symmetry also results in lifting the continuous degeneracy to a subset of states from the original set of ground states. Metropolis Monte Carlo simulation results are also presented on the temperature and system size dependence of the energy, specific heat, and magnetization, providing evidence for a phase transition at T $\simeq$ 0.38 (in units of the dipole strength). The results can be relevant to a class of magnetic compounds having the AuCu$_3$ crystal structure.

Coupled magnetic and ferroelectric states in the distorted honeycomb system Fe4Ta2O9

We report on the magnetic, thermodynamic, dielectric, and pyroelectric measurements on the hitherto unreported Fe${_4}$Ta${_2}$O${_9}$. This system is seen to exhibit a series of magnetic transitions, many of which are coupled to the emergence of ferroelectric order, making Fe${_4}$Ta${_2}$O${_9}$ the only genuine multiferroic in its material class. We suggest that the observed properties arise as a consequence of an effective reduction in the dimensionality of the magnetic lattice, with the magnetically active Fe${^{2+}}$ ions preferentially occupying a quasi 2D buckled honeycomb structure. The low temperature $H$-$T$ phase diagram of Fe${_4}$Ta${_2}$O${_9}$ reveals a rich variety of coupled magnetic and ferroelectric phases, in similarity with that observed in the distorted Kagome systems.

Neutron diffraction study and theoretical analysis of the antiferromagnetic order and the diffuse scattering in the layered kagome system CaBaCo2Fe2O7

The hexagonal swedenborgite, CaBaCo$_2$Fe$_2$O$_7$, is a chiral frustrated antiferromagnet, in which magnetic ions form alternating Kagome and triangular layers. We observe a long range $\sqrt{3} \times \sqrt{3}$ antiferromagnetic order setting in below $T_N = 160$ K by neutron diffraction on single crystals of CaBaCo$_2$Fe$_2$O$_7$. Both magnetization and polarized neutron single crystal diffraction measurements show that close to $T_N$ spins lie predominantly in the $ab$-plane, while upon cooling the spin structure becomes increasingly canted due to Dzyaloshinskii-Moriya interactions. The ordered structure can be described and refined within the magnetic space group $P31m^\prime$. Diffuse scattering between the magnetic peaks reveals that the spin order is partial. Monte Carlo simulations based on a Heisenberg model with two nearest-neighbor exchange interactions show a similar diffuse scattering and coexistence of the $\sqrt{3} \times \sqrt{3}$ order with disorder. The coexistence can be explained by the freedom to vary spins without affecting the long range order, which gives rise to ground-state degeneracy. Polarization analysis of the magnetic peaks indicates the presence of long-period cycloidal spin correlations resulting from the broken inversion symmetry of the lattice, in agreement with our symmetry analysis.

Muon spin relaxation study of spin dynamics in the extended kagome systems YBaCo4O7+δ (δ=0,0.1)

We present muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) measurements of the extended kagome systems ${\mathrm{YBaCo}}_{4}{\mathrm{O}}_{7+\ensuremath{\delta}}$ ($\ensuremath{\delta}=0,0.1$), comprising two interpenetrating kagome sublattice of $\mathrm{Co}{(\mathrm{I})}^{3+}$ ($S=3/2$) and a triangle sublattice of $\mathrm{Co}{(\mathrm{II})}^{2+}$ ($S=2$). The zero- and longitudinal-field $\ensuremath{\mu}\mathrm{SR}$ spectra of the stoichiometric compound ${\mathrm{YBaCo}}_{4}{\mathrm{O}}_{7}$ unveil that the triangular subsystem orders at ${T}_{N}=101$ K. In contrast, the muon spin relaxation rate pertaining to the kagome subsystem shows persistent spin dynamics down to $T=20$ K and then a sublinear decrease $\ensuremath{\lambda}(T)\ensuremath{\sim}{T}^{0.66(5)}$ on cooling towards $T=4$ K. In addition, the introduction of interstitial oxygen ($\ensuremath{\delta}=0.1$) is found to drastically affect the magnetism. For the fast-cooling experiment ($g10$ K/min), ${\mathrm{YBaCo}}_{4}{\mathrm{O}}_{7.1}$ enters a regime characterized by persistent spin dynamics below 90 K. For the slow-cooling experiment (1 K/min), evidence is obtained for the phase separation into interstitial oxygen-poor and oxygen-rich regions with distinct correlation times. The observed temperature, cooling rate, and oxygen content dependencies of spin dynamics are discussed in terms of a broad range of spin-spin correlation times, relying on a different degree of frustration between the kagome and triangle sublattices as well as of oxygen migration.

A bird’s eye view on the flat and conic band world of the honeycomb and Kagome lattices: towards an understanding of 2D metal-organic frameworks electronic structure

We present a thorough tight-binding analysis of the band structure of a wide variety of lattices belonging to the class of honeycomb and Kagome systems including several mixed forms combining both lattices. The band structure of these systems are made of a combination of dispersive and flat bands. The dispersive bands possess Dirac cones (linear dispersion) at the six corners (K points) of the Brillouin zone although in peculiar cases Dirac cones at the center of the zone point) appear. The flat bands can be of different nature. Most of them are tangent to the dispersive bands at the center of the zone but some, for symmetry reasons, do not hybridize with other states. The objective of our work is to provide an analysis of a wide class of so-called ligand-decorated honeycomb Kagome lattices that are observed in a 2D metal-organic framework where the ligand occupy honeycomb sites and the metallic atoms the Kagome sites. We show that the px-py graphene model is relevant in these systems and there exists four types of flat bands: Kagome flat (singly degenerate) bands, two kinds of ligand-centered flat bands (A2 like and E like, respectively doubly and singly degenerate) and metal-centered (three fold degenerate) flat bands.

Flat bands and Dirac cones in breathing lattices

In breathing pyrochlores and kagomes, couplings between neighbouring tetrahedra and triangles are free to differ. Breathing lattices thus offer the possibility to explore a different facet of the rich physics of these systems. Here we consider nearest-neighbour classical Heisenberg interactions, both ferromagnetic and antiferromagnetic, and study how the anisotropy of breathing lattices modifies the mode spectrum of pyrochlore and kagome systems. The nature and degeneracy of the flat bands are shown to be preserved for any value of the anisotropy. These flat bands can coexist with Dirac nodes at the point when the model becomes particle-hole symmetric. We also derive the nature of the ground state for the breathing kagome lattice, which bears a spontaneous chirality when neighbouring triangles are alternatively ferromagnetic and antiferromagnetic.