We report $^{23}$Na and $^{59}$Co nuclear magnetic (NMR) and quadrupolar resonance (NQR) studies for the $x=2/3$ phase of the lamellar oxide Na$_{x}$CoO$_{2}$, which allowed us to establish reliably the atomic order of the Na layers and their stacking between the CoO$_{2}$ slabs. We evidence that the Na$^{+}$ order stabilizes filled non magnetic Co$^{3+}$ ions on 25% of the cobalt sites arranged in a triangular sublattice. The transferred holes are delocalized on the 75% complementary cobalt sites which unexpectedly display a planar cobalt kagomé structure. These experimental results resolve a puzzling issue by precluding localized moments pictures for the magnetic properties. They establish that the quasi ferromagnetic properties result from a narrow band connecting a frustrated arrangement of atomic orbitals, and open the route to unravel through similar studies the electronic properties of the diverse ordered phases of sodium cobaltates.
The complex iridium oxide Na3Ir3O8 with a B-site ordered spinel structure was synthesized in single crystalline form, where the chiral hyper-kagome lattice of Ir atoms, as observed in the spin-liquid candidate Na4Ir3O8, was identified. The average valence of Ir is 4.33+ and, therefore, Na3Ir3O8 can be viewed as a doped analogue of the hyper-kagome spin liquid with Ir4+. The transport measurements showed that Na3Ir3O8 is in fact a semi-metal. The electronic structure calculation demonstrated that the strong spin-orbit coupling of Ir yields the semi-metallic state out of an otherwise band insula…
The kagome lattice is a fertile platform to explore topological excitations with both Fermi-Dirac and Bose-Einstein statistics. While relativistic Dirac Fermions and flat-bands have been discovered in the electronic structure of kagome metals, the spin excitations have received less attention. Here we report inelastic neutron scattering studies of the prototypical kagome magnetic metal FeSn. The spectra display well-defined spin waves extending up to 120 meV. Above this energy, the spin waves become progressively broadened, reflecting interactions with the Stoner continuum. Using linear spin w…
We report the results of ac and dc magnetic susceptibility and isothermal magnetization measurements (T= 2-300 K) on the single crystals of a metallic kagome lattice, Tb3Ru4Al12, reported recently to undergo reentrant magnetism with the onset of long range antiferromagnetic order below (TN=) 22K. The magnetization data obtained on the crystal with the c-axis orientation along magnetic-field reveal spin-glass-like characteristics near 17 K (below TN). However, for the orientation along basal plane, such glassy anomalies are not observable above 2 K. In this respect, this compound behaves like a…
The geometrical frustration nature of the kagome lattice makes it a great host to flat electronic band, non-trivial topological properties, and novel magnetisms. Metallic kagome antiferromagnet YMn$_{6}$Sn$_{6}$ exhibits the topological Hall effect (THE) when an in-plane magnetic field is applied. THE is typically associated with the nanometer-sized non-coplanar spin structure of skyrmions in non-centrosymmetric magnets with large Dzyaloshinskii-Moriya interaction. Here we use single crystal neutron diffraction to determine the field/temperature dependence of the magnetic structure in YMn$_{6}…
We present the results of neutron diffraction studies on polycrystals of a metallic kagome lattice, Tb3Ru4Al12, reported recently to undergo reentrant magnetism, with the onset of long range antiferromagnetic order below (TN=) 22 K and spin-glass features below about 17 K. The present results reveal long-range antiferromagnetic order of an incommensurate type with the moments oriented along c-axis at all temperatures below TN. There are however notable changes in the T dependence of propagation vector along b-axis across 17 K. An observation of interest is that there is no decrease of intensit…
In two-dimensional (2D) metallic kagome lattice materials, destructive interference of electronic hopping pathways around the kagome bracket can produce nearly localized electrons, and thus electronic bands that are flat in momentum space. When ferromagnetic order breaks the degeneracy of the electronic bands and splits them into the spin-up majority and spin-down minority electronic bands, quasiparticle excitations between the spin-up and spin-down flat bands should form a narrow localized spin-excitation Stoner continuum coexisting with well-defined spin waves in the long wavelengths. Here w…
We investigate the characteristics of the metallic phase near the Mott transition in the Kagomé lattice Hubbard model using the cellular dynamical mean field theory. By calculating the specific heat and spin correlation functions, we demonstrate that the quasiparticles show anomalous properties in the metallic phase close to the Mott transition. We find clear evidence for the multi-band heavy quasiparticles in the specific heat, which gives rise to unusual temperature dependence of the spin correlation functions.
Recently the unusual metallic state with a substantially non-uniform distribution of a charge and mag\-ne\-tic density in CoO$_2$ planes was found experimentally in the Na$_x$CoO$_2$ compound with $x>0.6$. We have investigated an origin of such electron disproportionation in the lamellar sodium cobaltates by calculating the ion states as a function of a strength of the electron correlations in the $d$(Co)-shells within the GGA+U approximation for the system with a realistic crystal structure. It was found that the nonuniformity of spin and charge densities are induced by an ordering of the sod…
Motivated by the recent discovery of metallic kagome lattice materials, AV$_{3}$Sb$_{5}$ (A=K, Rb, Cs), we investigate the ground state of the half-filled kagome lattice Hubbard model by employing the density-matrix renormalization group (DMRG) method. We identify a metal-insulator transition around $U \thicksim U_{c1}$ and four distinct phases as a function of $U/t$ on narrower cylinders, including a metallic phase at $U < U_{c1}$, two insulating intermediate phases: a translational symmetry breaking phase at $U_{c1} < U < U_{c2}$ and a quantum spin liquid phase at $U_{c2} < U < U_{c3}$, and …
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 mag…
In order to study the magnetic properties of frustrated metallic systems, we present Quantum Monte Carlo data on the magnetic susceptibility of the Hubbard model on triangular and Kagome lattices. We show that the underlying lattice structure is important, and determines the nature and the doping dependence of the magnetic fluctuations. In particular, in the doped Kagome case we find strong short-range magnetic correlations, which makes the metallic Kagome systems a promising field for studies of superconductivity.
We report on novel magnetic and electronic properties of SrCo6O11 that exhibits a unique stepwise magnetization and its relevant magnetotransport phenomena investigated by the site-selective 59Co nuclear magnetic resonance (NMR) at zero and applied magnetic fields. This compound is composed of three Co sites in the unit cell, i.e., Co(1) in the metallic Kagome layer, a Co(2) dimerized pillar between the layers and Co(3) in the triangular lattice. Zero-field NMR spectra have revealed that large local moments at the Co(3) sites are magnetically ordered without any trace of bulk magnetization M a…
Effect of geometrical frustration in strongly-correlated metallic region is studied for the Hubbard model on the kagome lattice at half filling by a cluster extension of the dynamical mean-field theory combined with a continuous-time auxiliary-field quantum Monte Carlo method. We find that the electron correlation enhances the spin chirality in both vector and scalar channels. The chirality grows as decreasing temperature and exhibits a peak at a low temperature, indicating a new energy scale under strong correlation. The peak temperature is considerably lower than that for the local spin mome…
The kagome Hubbard model (KHM) is a paradigmatic example of a frustrated two-dimensional model. While its strongly correlated regime, described by a Heisenberg model, is of topical interest due to its enigmatic prospective spin-liquid ground state, the weakly and moderately correlated regimes remain largely unexplored. Motivated by the rapidly growing number of metallic kagome materials (e.g., Mn$_3$Sn, Fe$_3$Sn$_2$, FeSn, Co$_3$Sn$_2$S$_2$, Gd$_3$Ru$_4$Al$_{12}$), we study the respective regimes of the KHM by means of three complementary numerical methods: the dynamical mean-field theory (DMF…
Kagome-lattice materials have attracted tremendous interest due to the broad prospect for seeking superconductivity, quantum spin liquid states, and topological electronic structures. Among them, the transition-metal kagome lattices are high-profile objects for the combination of topological properties, rich magnetism, and multiple-orbital physics. Here we report an inelastic neutron scattering study on the spin dynamics of a kagome-lattice antiferromagnetic metal Fe$_{0.89}$Co$_{0.11}$Sn. Although the magnetic excitations can be observed up to $\sim$250 meV, well-defined spin waves are only i…
Recently, transition-metal-based kagome metals have aroused much research interest as a novel platform to explore exotic topological quantum phenomena. Here we report on the synthesis, structure, and physical properties of a bilayer kagome lattice compound V3Sb2. The polycrystalline V3Sb2 samples were synthesized by conventional solid-state-reaction method in a sealed quartz tube at temperatures below 850 Celsius degree. Measurements of magnetic susceptibility and resistivity revealed consistently a density-wave-like transition at Tdw ~ 160 K with a large thermal hysteresis, even though some s…
Mott transition and ferrimagnetism are studied in the Hubbard model on the anisotropic kagomé lattice using the variational cluster approximation and the phase diagram at zero temperature and half-filling is analyzed. The ferrimagnetic phase rapidly grows as the geometric frustration is relaxed, and the Mott insulator phase disappears in moderately frustrated region, showing that the ferrimagnetic fluctuations stemming from the relaxation of the geometric frustration is enhanced by the electron correlations. In metallic phase, heavy fermion behavior is observed and mass enhancement factor is c…
The Hubbard model on the Kagomé lattice is investigated in a metallic phase at half-filling. By introducing anisotropic electron hopping on the lattice, we control geometrical frustration and clarify how the lattice geometry affects physical properties. By means of the fluctuation exchange (FLEX) approximation, we calculate the spin and charge susceptibilities, the one-particle spectral function, the quasi-particle renormalization factor, and the Fermi velocity. It is found that geometrical frustration of the Kagomé lattice suppresses the instability to various ordered states through the stron…
A multi-orbital model for a CoO_2-layer in Na_xCoO_2 is derived. In this model the kinetic energy for the degenerate t_2g-orbitals is given by indirect hopping over oxygen, leading naturally to the concept of four inter-penetrating Kagome lattices. Local Coulomb interaction couples the four lattices and an effective Hamiltonian for the interaction in the top band can be written in terms of fermionic operators with four different flavors. Focusing on charge and spin density instabilities, a big variety of possible metallic states with spontaneously broken symmetry are found. These states lead t…
We report magnetic behavior of two intermetallics-based kagome lattices, Tb3Ru4Al12 and Er3Ru4Al12, crystallizing in the Gd3Ru4Al12-type hexagonal crystal structure, by measurements in the range 1.8-300 K with bulk experimental techniques (ac and dc magnetization, heat-capacity and magnetoresistance). The main finding is that the Tb compound, known to order antiferromagnetically below (T_N=) 22 K, shows glassy characteristics at lower temperatures (<15K), thus characterizing this compound as a re-entrant spin-glass. The data reveal that glassy phase is quite complex and is of a cluster type. S…
Topological magnon is a vibrant research field gaining more and more attention in the past few years. Among many theoretical proposals and limited experimental studies, ferromagnetic Kagome lattice emerges as one of the most elucidating systems. Here we report neutron scattering studies of YMn6Sn6, a metallic system consisting of ferromagnetic Kagome planes. This system undergoes a commensurate-to-incommensurate antiferromagnetic phase transition upon cooling with the incommensurability along the out-of-plane direction. We observe magnon band gap opening at the symmetry-protected K points and …
We study the Hubbard model with time-reversal invariant flux and spin-orbit coupling and position-dependent onsite energies on the kagome lattice, using numerical and analytical methods. In particular, we perform calculations using real space dynamical mean-field theory (R-DMFT). To study the topological properties of the system, we use the topological Hamiltonian approach. We obtain a rich phase diagram: for weak and intermediate interactions, depending on the model parameters, the system is in the band insulator, topological insulator, or metallic phase, while for strong interactions the sys…
Electronic topology in metallic kagome compounds is under intense scrutiny. We present transport experiments in Na2/3CoO2 in which the Na order differentiates a Co kagome sub-lattice in the triangular CoO2 layers. Hall and magnetoresistance (MR) data under high fields give evidence for the coexistence of light and heavy carriers. At low temperatures, the dominant light carrier conductivity at zero field is suppressed by a B-linear MR suggesting Dirac like quasiparticles. Lifshitz transitions induced at large B and T unveil the lower mobility carriers. They display a negative B^2 MR due to scat…
Motivated by recent experiment on the Na$_4$Ir$_3$O$_8$ compound we study the Hubbard model on the "hyper-kagome lattice", which forms a three-dimensional network of corner sharing triangles, using dynamical cluster approximation (DCA) method with $N_c$=12 combined with the continuous-time quantum Monte Carlo (CT QMC) method. The system undergoes a Mott transition if the Hubbard interaction $U/W$ ($W$ is the bandwidth) exceeds the value of 1.2 for $T$=0.1 and displays reentrant behavior due to competition between the magnetic correlation and the kinetic energy of electrons due to the geometric…
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 $(Γ$ point) appear. The flat bands can be of different nature. Most of them are tangent to the dispersive bands at the cent…
First order phase transitions, where one phase replaces another by virtue of a simple crossing of free energies, are best known between solids, liquids and vapours, but they also occur in a wide range of other contexts, including even elemental magnets. The key challenges are to establish whether a phase transition is indeed first order, and then to determine how the new phase emerges because this will determine thermodynamic and electronic properties. Here we meet both challenges for the spin reorientation transition in the topological metallic ferromagnet Fe3Sn2. Our magnetometry and variabl…
A ferromagnet with spin anisotropies on the 2D Kagome lattice is theoretically studied. This is a typical example of the flat-band ferromagnet. The Berry phase induced by the tilting of the spins opens the band gap and quantized Hall conductance σ_{xy}=\pm e^2/h is realized without external magnetic field. This is the most realistic chiral spin state based on the ferromagnetism. We also discuss the implication of our results to anomalous Hall effect observed in the metallic pyrochlore ferromagnets R_2Mo_2O_7(R=Nd, Sm, Gd).
We present the results of first-principle calculations using the Vienna Ab-initio Simulation Package (VASP) for a new class of organometallics labeled TM3C6O6 (TM =Sc, Ti, V, Cr, Fe, Co, Ni and Cu) in the form of planar, two-dimensional, periodic free-standing layers. These materials, which can be produced by on-surface coordination on metallic surfaces, have a kagome lattice of TM ions. Calculating the structural properties, we show that all considered materials have local magnetic moments in the ground state, but four of them (with Fe, Co, Ni and Cu) show spin-crossover behavior by changing …
Triple-${\bf Q}$ collinear state with compensated ferrimagnetic nature on frustrated kagome lattice
Department of Earth and Space Science, Graduate School of Science, The University of Osaka（大阪大学理学研究科地球宇宙科学系）；Molecular Photoscience Research Center, Kobe University（神户大学分子光科学研究中心）
The magnetization process of single crystals of the metallic kagomé ferromagnet Co3Sn2S2 was carefully measured via magnetization and AC susceptibility. Field-dependent anomalous transitions in the magnetization indicate a low-field unconventionally ordered phase stabilized just below TC. The magnetic phase diagrams in applied fields along different crystallographic directions were determined. The magnetic relaxation process studied in frequencies covering five orders of magnitude from 0.01 to 1000 Hz indicates characteristic relaxation times of several seconds at the boarders of the anomalous…
Orbital-specific Itinerancy and Localization in a Kagome Magnet
Institute of Metal Physics（金属物理研究所）；Ural Federal University（乌拉尔联邦大学）；National Synchrotron Radiation Research Center（国家同步辐射研究中心）；National Tsing Hua University（国立清华大学）；Rutgers University（罗格斯大学）
Kagome lattice offers unique opportunities for the exploration of unusual quantum states of correlated electrons. Here, we report on the observation of superconductivity in a kagome single crystal Pd3P2S8 when a semiconducting to metallic transition is driven by pressure. High-pressure resistance measurements show that the metallization and superconductivity are simultaneously observed at about 11 GPa. With increasing pressure, the superconducting critical temperature Tc is monotonously enhanced from 2.6 K to a maximum 7.7 K at ~52 GPa. Interestingly, superconductivity retains when the pressur…
The kagome lattice, consisting of interconnected triangles and hexagons uniquely, is an excellent model system for study frustrated magnetism, electronic correlation and topological electronic structure. After an intensive investigation on frustrated magnetism in insulating magnetic kagome lattices, the interplay between charge and spin degrees of freedom via spin-orbital coupling in metallic systems (kagome metals) has become an attractive topic recently. Here, we study centrosymmetric YMn6Sn6 with Mn kagome lattice. We discover that it exhibits giant topological Hall effect near room tempera…
The kagomé lattice is a fruitful source of novel physical states of matter, including the quantum spin liquid and Dirac fermions. Here we report a structural, thermodynamic, and transport study of the two-dimensional kagomé metal-organic frameworks Ni_3(HIB)v2 and Cu_3(HIB)_2 (HIB = hexaiminobenzene). Magnetization measurements yield Curie constants of 1.12 and 0.352 emu K mol f.u.-1 Oe-1 respectively, close to the values expected for ideal S=1 and S=1/2 moments. Weiss temperatures of -20.3 K and -6.52 K, respectively, indicate moderate to weak magnetic interactions. Electrical transport measu…
Sc3Mn3Al7Si5 is a rare example of a correlated metal in which the Mn moments form a kagome lattice. The absence of magnetic ordering to the lowest temperatures suggests that geometrical frustration of magnetic interactions may lead to strong magnetic fluctuations. We have performed inelastic neutron scattering measurements on Sc3Mn3Al7Si5, finding that phonon scattering dominates for energies from ~20 - 50 meV. These results are in good agreement with ab initio calculations of the phonon dispersions and densities of states, and as well reproduce the measured specific heat. A weak magnetic sign…
Frustrated itinerant ferromagnets, with non-collinear static spin structures, are an exciting class of material as their spin chirality can introduce a Berry phase in the electronic scattering and lead to exotic electronic phenomena such as the anomalous Hall effect (AHE). This study presents a reexamination of the magnetic properties of Fe$_3$Sn$_2$, a metallic ferromagnet, based on the 2-dimensional kagome bilayer structure. Previously thought of as a conventional ferromagnet, we show using a combination of SQUID measurements, symmetry analysis and powder neutron diffraction, that Fe$_3$Sn$_…
Motivated by recent experiments on the quantum-spin-liquid candidate material LiZn2Mo3O8, we study a single-band extended Hubbard model on an anisotropic Kagome lattice with the 1/6 electron filling. Due to the partial filling of the lattice, the inter-site repulsive interaction is necessary to generate Mott insulators, where electrons are localized in clusters, rather than at lattice sites. We provide examples of such cluster Mott insulators and study the phase transitions between metallic states and cluster Mott insulators on an anisotropic Kagome lattice. It is shown that these cluster Mott…
Motivated by recent experimental progress on various cluster Mott insulators, we study an extended Hubbard model on a breathing Kagomé lattice with a single electron orbital and $1/6$ electron filling. Two distinct types of cluster localization are found in the cluster Mott regime due to the presence of the electron repulsion between neighboring sites, rather than from the on-site Hubbard interaction in the conventional Mott insulators. We introduce a unified parton construction framework to accommodate both type of cluster Mott insulating phase as well as a trivial Ferm liquid metal and discu…
Motivated by recent experiments in Gd$_3$Ru$_4$Al$_{12}$, we demonstrate the emergence of atomic scale Skyrmions in interacting spins on a breathing kagome lattice with competing nearest neighbor ferromagnetic and next nearest neighbor antiferromagnetic exchange interactions. In the presence of an applied longitudinal magnetic field, the ground state magnetic order evolves from a helical phase at low fields to a Skyrmion phase at intermediate fields before finally entering a polarized phase at high fields. The size of each Skyrmion spans only two unit cells of the lattice, in contrast to tens …
Fermi surface fluctuations and lattice instabilities in the 2D metallic kagome superconductor CsV$_3$Sb$_5$ are elucidated via polarization-resolved Raman spectroscopy. The presence of a weak electronic continuum in high-quality samples marks the cross-over into the charge-density-wave (CDW) ordered phase, while impurity-rich samples promote strong defect-induced electronic scattering processes that affect the coherence of the CDW phase. CDW-induced phonon anomalies appear below $T_{\mathrm{CDW}}$, with emergent $C2$ symmetry for one of the CDW amplitude modes, alluding to nematicity. In conju…
