Tunable anomalous Hall conductivity through volume-wise magnetic competition in a topological kagome magnet

The Impact of Hydrostatic Pressure on the Structural, Mechanical, Thermal, and Optoelectronic Characteristics of the RbV3Sb5 Kagome Compound: Ab initio Approach

We studied the RbV3Sb5 kagome compound's structural, mechanical, thermal, and optoelectronic properties. Mulliken and Hirshfeld population analysis found ionic and covalent connections in RbV3Sb5. The Born stability criterion shows that pure RbV3Sb5 is mechanically stable. The precise measurement of 3.96 indicates that our sample has higher machinability at 20 GPa. Low anticipated hardness of RbV3Sb5 suggests it can be used as a soft solid lubricant. Hardness ratings rise with pressure, however there are exceptions. Pressure causes large nonmonotonic changes in RbV3Sb5's anisotropic characteristics. A comparable 20 GPa Zener anisotropic value, RbV3Sb5 has the highest. The structure's projected Debye temperature at 0 GPa is 284.39 K, indicating softness. Dispersion curves with negative frequencies suggest ground state structural dynamical instability. The structure has no negative-energy phonon branches under 10 GPa stress. From band structure and density of state analysis, the structure behaves metallically under hydrostatic pressure. Also, the structure has maximal ultra-violet conductivity and absorption. The absorption coefficient, conductivity, and loss function plots show uniform patterns at all pressures. As pressure rises, these graphs' peaks blue shift.

Depth-dependent study of time-reversal symmetry-breaking in the kagome superconductor AV3Sb5

The breaking of time-reversal symmetry (TRS) in the normal state of kagome superconductors AV3Sb5 stands out as a significant feature, but its tunability is unexplored. Using low-energy muon spin rotation and local field numerical analysis, we study TRS breaking as a function of depth in single crystals of RbV3Sb5 (with charge order) and Cs(V0.86Ta0.14)3Sb5 (without charge order). In the bulk of RbV3Sb5 (>33 nm from the surface), we observed an increase in the internal magnetic field width in the charge-ordered state. Near the surface (<33 nm), the muon spin relaxation rate is significantly enhanced and this effect commences at temperatures significantly higher than the onset of charge order. In contrast, no similar field width enhancement was detected in Cs(V0.86Ta0.14)3Sb5, either in the bulk or near the surface. These observations indicate a strong connection between charge order and TRS breaking and suggest that TRS breaking can occur prior to long-range charge order.

Microscopic probing of the superconducting and normal state properties of Ta2V3.1Si0.9 by muon spin rotation

The two-dimensional kagome lattice is an experimental playground for novel physical phenomena, from frustrated magnetism and topological matter to chiral charge order and unconventional superconductivity. A newly identified kagome superconductor, Ta2V3.1Si0.9 has recently gained attention for possessing a record high critical temperature, T C = 7.5 K for kagome metals at ambient pressure. In this study we conducted a series of muon spin rotation measurements to delve deeper into understanding the superconducting and normal state properties of Ta2V3.1Si0.9. We demonstrate that Ta2V3.1Si0.9 is a bulk superconductor with either a s+s-wave or anisotropic s-wave gap symmetry, and has an unusual paramagnetic shift in response to external magnetic fields in the superconducting state. Additionally, we observe an exceptionally low superfluid density - a distinctive characteristic of unconventional superconductivity - which remarkably is comparable to the superfluid density found in hole-doped cuprates. In its normal state, Ta2V3.1Si0.9 exhibits a significant increase in the zero-field muon spin depolarisation rate, starting at approximately 150 K, which has been observed in other kagome-lattice superconductors, and therefore hints at possible hidden magnetism. These findings characterise Ta2V3.1Si0.9 as an unconventional superconductor and a noteworthy new member of the vanadium-based kagome material family.

Tunable Anomalous Hall Effect in a Kagomé Ferromagnetic Weyl Semimetal

Emerging from the intricate interplay of topology and magnetism, the giant anomalous Hall effect (AHE) is the most known topological property of the recently discovered kagomé ferromagnetic Weyl semimetal Co3Sn2S2 with the magnetic Co atoms arranged on a kagomé lattice. Here it is reported that the AHE in Co3Sn2S2 can be fine-tuned by an applied magnetic field orientated within ≈2° of the kagomé plane, while beyond this regime, it stays unchanged. Particularly, it can vanish in magnetic fields parallel to the kagomé plane and even decrease in magnetic fields collinear with the spin direction. This tunable AHE can be attributed to local spin switching enabled by the geometrical frustration of the magnetic kagomé lattice, revealing that spins in a kagomé ferromagnet change their switching behavior as the magnetic field approaches the kagomé plane. These results also suggest a versatile way to tune the properties of a kagomé magnet.

Endless Dirac nodal lines and high mobility in kagome semimetal Ni3In2Se2: a theoretical and experimental study

Kagome-lattice crystal is crucial in quantum materials research, exhibiting unique transport properties due to its rich band structure and the presence of nodal lines and rings. Here, we investigate the electronic transport properties and perform first-principles calculations for Ni3In2Se2kagome topological semimetal. First-principles calculations of the band structure without the inclusion of spin-orbit coupling (SOC) shows that three bands are crossing the Fermi level (EF), indicating the semi-metallic nature. With SOC, the band structure reveals a gap opening of the order of 10 meV.Z2index calculations suggest the topologically nontrivial natures (ν0;ν1ν2ν3) = (1;111) both without and with SOC. Our detailed calculations also indicate six endless Dirac nodal lines and two nodal rings with aπ-Berry phase in the absence of SOC. The temperature-dependent resistivity is dominated by two scattering mechanisms:s-dinterband scattering occurs below 50 K, while electron-phonon (e-p) scattering is observed above 50 K. The magnetoresistance (MR) curve aligns with the theory of extended Kohler's rule, suggesting multiple scattering origins and temperature-dependent carrier densities. A maximum MR of 120% at 2 K and 9 T, with a maximum estimated mobility of approximately 3000 cm2V-1s-1are observed. Ni3In2Se2is an electron-hole compensated topological semimetal, as we have carrier density of electron (ne) and hole (nh) arene≈nh, estimated from Hall effect data fitted to a two-band model. Consequently, there is an increase in the mobility of electrons and holes, leading to a higher carrier mobility and a comparatively higher MR. The quantum interference effect leading to the two dimensional (2D) weak antilocalization effect (-σxx∝ln(B)) manifests as the diffusion of nodal line fermions in the 2D poloidal plane and the associated encircling Berry flux of nodal-line fermions.

Atomically Thin Kagome-Structured Co9Te16 Achieved through Self-Intercalation and Its Flat Band Visualization

Kagome materials have recently garnered substantial attention due to the intrinsic flat band feature and the stimulated magnetic and spin-related many-body physics. In contrast to their bulk counterparts, two-dimensional (2D) kagome materials feature more distinct kagome bands, beneficial for exploring novel quantum phenomena. Herein, we report the direct synthesis of an ultrathin kagome-structured Co-telluride (Co9Te16) via a molecular beam epitaxy (MBE) route and clarify its formation mechanism from the Co-intercalation in the 1T-CoTe2 layers. More significantly, we unveil the flat band states in the ultrathin Co9Te16 and identify the real-space localization of the flat band states by in situ scanning tunneling microscopy/spectroscopy (STM/STS) combined with first-principles calculations. A ferrimagnetic order is also predicted in kagome-Co9Te16. This work should provide a novel route for the direct synthesis of ultrathin kagome materials via a metal self-intercalation route, which should shed light on the exploration of the intriguing flat band physics in the related systems.

Chiral and flat-band magnetic quasiparticles in ferromagnetic and metallic kagome layers

Magnetic kagome metals are a promising platform to develop unique quantum transport and optical phenomena caused by the interplay between topological electronic bands, strong correlations, and magnetic order. This interplay may result in exotic quasiparticles that describe the coupled electronic and spin excitations on the frustrated kagome lattice. Here, we observe novel elementary magnetic excitations within the ferromagnetic Mn kagome layers in TbMn6Sn6 using inelastic neutron scattering. We observe sharp, collective acoustic magnons and identify flat-band magnons that are localized to a hexagonal plaquette due to the special geometry of the kagome layer. Surprisingly, we observe another type of elementary magnetic excitation; a chiral magnetic quasiparticle that is also localized on a hexagonal plaquette. The short lifetime of localized flat-band and chiral quasiparticles suggest that they are hybrid excitations that decay into electronic states.

Hidden magnetism uncovered in a charge ordered bilayer kagome material ScV6Sn6

Charge ordered kagome lattices have been demonstrated to be intriguing platforms for studying the intertwining of topology, correlation, and magnetism. The recently discovered charge ordered kagome material ScV6Sn6 does not feature a magnetic groundstate or excitations, thus it is often regarded as a conventional paramagnet. Here, using advanced muon-spin rotation spectroscopy, we uncover an unexpected hidden magnetism of the charge order. We observe an enhancement of the internal field width sensed by the muon ensemble, which takes place within the charge ordered state. More importantly, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. Taken together with the hidden magnetism found in AV3Sb5 (A = K, Rb, Cs) and FeGe kagome systems, our results suggest ubiqitous time-reversal symmetry-breaking in charge ordered kagome lattices.

Observation of Termination-Dependent Topological Connectivity in a Magnetic Weyl Kagome Lattice

Engineering surfaces and interfaces of materials promises great potential in the field of heterostructures and quantum matter designers, with the opportunity to drive new many-body phases that are absent in the bulk compounds. Here, we focus on the magnetic Weyl kagome system Co3Sn2S2 and show how for the terminations of different samples the Weyl points connect differently, still preserving the bulk-boundary correspondence. Scanning tunneling microscopy has suggested such a scenario indirectly, and here, we probe the Fermiology of Co3Sn2S2 directly, by linking it to its real space surface distribution. By combining micro-ARPES and first-principles calculations, we measure the energy-momentum spectra and the Fermi surfaces of Co3Sn2S2 for different surface terminations and show the existence of topological features depending on the top-layer electronic environment. Our work helps to define a route for controlling bulk-derived topological properties by means of surface electrostatic potentials, offering a methodology for using Weyl kagome metals in responsive magnetic spintronics.

Tunable unconventional kagome superconductivity in charge ordered RbV3Sb5 and KV3Sb5

Unconventional superconductors often feature competing orders, small superfluid density, and nodal electronic pairing. While unusual superconductivity has been proposed in the kagome metals AV3Sb5, key spectroscopic evidence has remained elusive. Here we utilize pressure-tuned and ultra-low temperature muon spin spectroscopy to uncover the unconventional nature of superconductivity in RbV3Sb5 and KV3Sb5. At ambient pressure, we observed time-reversal symmetry breaking charge order below [Formula: see text] 110 K in RbV3Sb5 with an additional transition at [Formula: see text] 50 K. Remarkably, the superconducting state displays a nodal energy gap and a reduced superfluid density, which can be attributed to the competition with the charge order. Upon applying pressure, the charge-order transitions are suppressed, the superfluid density increases, and the superconducting state progressively evolves from nodal to nodeless. Once optimal superconductivity is achieved, we find a superconducting pairing state that is not only fully gapped, but also spontaneously breaks time-reversal symmetry. Our results point to unprecedented tunable nodal kagome superconductivity competing with time-reversal symmetry-breaking charge order and offer unique insights into the nature of the pairing state.

Visualization of Tunable Weyl Line in A-A Stacking Kagome Magnets

Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena, in which the delicate interplay between frustrated crystal structure, magnetization, and spin-orbit coupling (SOC) can engender highly tunable topological states. Here, utilizing angle-resolved photoemission spectroscopy, the Weyl lines are directly visualized with strong out-of-plane dispersion in the A-A stacked kagome magnet GdMn₆ Sn₆ . Remarkably, the Weyl lines exhibit a strong magnetization-direction-tunable SOC gap and binding energy tunability after substituting Gd with Tb and Li, respectively. These results not only illustrate the magnetization direction and valence counting as efficient tuning knobs for realizing and controlling distinct 3D topological phases, but also demonstrate AMn₆ Sn₆ (A = rare earth, or Li, Mg, or Ca) as a versatile material family for exploring diverse emergent topological quantum responses.

Exploration of the physical properties of the newly synthesized kagome superconductor LaIr3Ga2 using different exchange-correlation functionals

LaIr₃Ga₂ is a kagome superconductor with a superconducting temperature (T_c) of 5.16 K. Here, we present the physical properties of the LaIr₃Ga₂ kagome superconductor computed via the DFT method wherein six different exchange-correlation functionals were used. The lattice parameters obtained using different functionals are reasonable, with a slight variation compared to experimental values. The bonding nature was explored. The elastic constants (C_ij), moduli (B, G, Y), and Vickers hardness (H_v) were computed to disclose the mechanical behavior. The H_v values were estimated to be 2.56-3.16 GPa using various exchange-correlation functionals, indicating the softness of the kagome material. The Pugh ratio, Poisson's ratio, and Cauchy pressure revealed the ductile nature. In addition, mechanical stability was ensured based on the estimated elastic constants. The anisotropic mechanical behavior was confirmed via different anisotropic indices. The Debye temperature (Θ_D), melting temperature (T_m), and minimum thermal conductivity (k_min) were calculated to characterize the thermal properties and predict the potential of LaIr₃Ga₂ as a thermal barrier coating material. The electronic density of states was investigated in detail. The McMillan equation was used to estimate T_c, and the electron-phonon coupling constant (λ) was calculated to explore the superconducting nature. The important optical constants were also calculated to explore its possible optoelectronic applications. The values of reflectivity in the IR-visible region are about 62% to 80%, indicating that the compound under study is suitable as a coating to reduce solar heating. The obtained parameters were compared with previously reported parameters, where available.

Anomalous depinning of magnetic domain walls within the ferromagnetic phase of the Weyl semimetal Co3Sn2S2

We report bulk magnetization measurements and spatially resolved measurements of magnetic domains inCo3Sn2S2single crystals. The results indicate that a previously reported magnetic anomaly around 130 K is due to an anomalous domain wall depinning upon cooling. Our measurements also reveal a hysteresis between field-cooled-cooling and field-cooled-warming magnetization curves acquired under a constant magnetic field below 300 Oe. This observation rules out the possibility that the anomaly stems from a second-order phase transition. Our results further suggest that changes in the shape of hysteresis loops from 5 to 170 K are caused by an unusual temperature-dependent domain nucleation field that changes sign around 130 K. The Kerr rotation images of the magnetic domains confirm that the domain walls depin between 120 and 140 K.

Topological kagome magnets and superconductors

A kagome lattice naturally features Dirac fermions, flat bands and van Hove singularities in its electronic structure. The Dirac fermions encode topology, flat bands favour correlated phenomena such as magnetism, and van Hove singularities can lead to instabilities towards long-range many-body orders, altogether allowing for the realization and discovery of a series of topological kagome magnets and superconductors with exotic properties. Recent progress in exploring kagome materials has revealed rich emergent phenomena resulting from the quantum interactions between geometry, topology, spin and correlation. Here we review these key developments in this field, starting from the fundamental concepts of a kagome lattice, to the realizations of Chern and Weyl topological magnetism, to various flat-band many-body correlations, and then to the puzzles of unconventional charge-density waves and superconductivity. We highlight the connection between theoretical ideas and experimental observations, and the bond between quantum interactions within kagome magnets and kagome superconductors, as well as their relation to the concepts in topological insulators, topological superconductors, Weyl semimetals and high-temperature superconductors. These developments broadly bridge topological quantum physics and correlated many-body physics in a wide range of bulk materials and substantially advance the frontier of topological quantum matter.

Correlation driven near-flat band Stoner excitations in a Kagome magnet

Among condensed matter systems, Mott insulators exhibit diverse properties that emerge from electronic correlations. In itinerant metals, correlations are usually weak, but can also be enhanced via geometrical confinement of electrons, that manifest as ‘flat’ dispersionless electronic bands. In the fast developing field of topological materials, which includes Dirac and Weyl semimetals, flat bands are one of the important components that can result in unusual magnetic and transport behaviour. To date, characterisation of flat bands and their magnetism is scarce, hindering the design of novel materials. Here, we investigate the ferromagnetic Kagomé semimetal Co3Sn2S2 using resonant inelastic X-ray scattering. Remarkably, nearly non-dispersive Stoner spin excitation peaks are observed, sharply contrasting with the featureless Stoner continuum expected in conventional ferromagnetic metals. Our band structure and dynamic spin susceptibility calculations, and thermal evolution of the excitations, confirm the nearly non-dispersive Stoner excitations as unique signatures of correlations and spin-polarized electronic flat bands in Co3Sn2S2. These observations serve as a cornerstone for further exploration of band-induced symmetry-breaking orders in topological materials.

Local spectroscopic evidence for a nodeless magnetic kagome superconductor CeRu2

We report muon spin rotation (µSR) experiments on the microscopic properties of superconductivity and magnetism in the kagome superconductor CeRu₂withTc≃5 K. From the measurements of the temperature-dependent magnetic penetration depthλ, the superconducting order parameter exhibits nodeless pairing, which fits best to an anisotropics-wave gap symmetry. We further show that theTc/λ^-2ratio is comparable to that of unconventional superconductors. Furthermore, the powerful combination of zero-field (ZF)-µSR and high-fieldµSR has been used to uncover magnetic responses across three characteristic temperatures, identified asT1∗≃110 K,T2∗≃65 K, andT3∗≃40 K. Our experiments classify CeRu₂as an exceedingly rare nodeless magnetic kagome superconductor.

Disorder- and Topology-Enhanced Fully Spin-Polarized Currents in Nodal Chain Spin-Gapless Semimetals

Recently discovered high-quality nodal chain spin-gapless semimetals MF_{3} (M=Pd, Mn) feature an ultraclean nodal chain in the spin up channel residing right at the Fermi level and displaying a large spin gap leading to a 100% spin polarization of transport properties. Here, we investigate both intrinsic and extrinsic contributions to anomalous and spin transport in this class of materials. The dominant intrinsic origin is found to originate entirely from the gapped nodal chains without the entanglement of any other trivial bands. The side-jump mechanism is predicted to be negligibly small, but intrinsic skew scattering enhances the intrinsic Hall and Nernst signals significantly, leading to large values of respective conductivities. Our findings open a new material platform for exploring strong anomalous and spin transport properties in magnetic topological semimetals.

Hidden Local Symmetry Breaking in a Kagome-Lattice Magnetic Weyl Semimetal

Exploring the relationship between intriguing physical properties and structural complexity is a central topic in studying modern functional materials. Co₃Sn₂S₂, a newly discovered kagome-lattice magnetic Weyl semimetal, has triggered intense interest owing to the intimate coupling between topological semimetallic states and peculiar magnetic properties. However, the origins of the magnetic phase separation and spin glass state below T_C in this ordered compound are two unresolved yet important puzzles in understanding its magnetism. Here, we report the discovery of local symmetry breaking surprisingly co-emerges with the onset of ferromagnetic order in Co₃Sn₂S₂, by a combined use of neutron total scattering and half-polarized neutron diffraction. An anisotropic distortion of the cobalt kagome lattice at the atomic/nano level is also found, with distinct distortion directions among the two Co1 and four Co2 atoms. The mismatch of local and average symmetries occurs below T_C, indicating that Co₃Sn₂S₂ evolves to an intrinsically lattice disordered system when the ferromagnetic order is established. The local symmetry breaking with intrinsic lattice disorder provides new understanding of the puzzling magnetic properties. Our density functional theory (DFT) calculation indicates that the local symmetry breaking is expected to reorient local ferromagnetic moments, unveiling the existence of the ferromagnetic instability associated with the lattice instability. Furthermore, DFT calculation unveils that the local symmetry breaking could affect the Weyl property by breaking the mirror plane. Our findings highlight the fundamentally important role that the local symmetry breaking plays in advancing our understanding on the magnetic and topological properties in Co₃Sn₂S₂, which may draw attention to explore the overlooked local symmetry breaking in Co₃Sn₂S₂, its derivatives and more broadly in other topological Dirac/Weyl semimetals and kagome-lattice magnets.

Competing Magnetic Phases in LnSbTe (Ln = Ho and Tb)

The interplay between a topological electronic structure and magnetism may result in intricate physics. In this work, we describe a case of rather peculiar coexistence or competition of several magnetic phases below seemingly single antiferromagnetic transition in LnSbTe (Ln = Ho and Tb) topological semimetals, the magnetic members of the ZrSiS/PbFCl structure type (space group P4/nmm). Neutron diffraction experiments reveal a complex multi-step order below T_N = 3.8 K (Ln = Ho) and T_N = 6.4 K (Ln = Tb). Magnetic phases can be described using four propagation vectors k₁ = (¹/₂ 0 0) and k₂ = (¹/₂ 0 ¹/₄) at a base temperature of 1.7 K, which transform into incommensurate vectors k₁' = (¹/₂ - δ 0 0) and k₃ = (¹/₂ - δ 0 ¹/₂) at elevated temperatures in both compounds. Together with the refined models of magnetic structures, we present the group theoretical analysis of magnetic symmetry of the proposed solutions. These results prompt further investigations of the relation between the electronic structure of those semimetals and the determined antiferromagnetic ordering existing therein.

Uncovering the Kagome Ferromagnet within a Family of Metal-Organic Frameworks

Kagome networks of ferromagnetically or antiferromagnetically coupled magnetic moments represent important models in the pursuit of a diverse array of novel quantum and topological states of matter. Here, we explore a family of Cu²⁺-containing metal-organic frameworks (MOFs) bearing kagome layers pillared by ditopic organic linkers with the general formula Cu₃(CO₃)₂(x)₃·2ClO₄ (MOF-x), where x is 1,2-bis(4-pyridyl)ethane (bpe), 1,2-bis(4-pyridyl)ethylene (bpy), or 4,4'-azopyridine (azpy). Despite more than a decade of investigation, the nature of the magnetic exchange interactions in these materials remained unclear, meaning that whether the underlying magnetic model is that of an kagome ferromagnet or antiferromagnet is unknown. Using single-crystal X-ray diffraction, we have developed a chemically intuitive crystal structure for this family of materials. Then, through a combination of magnetic susceptibility, powder neutron diffraction, and muon-spin spectroscopy measurements, we show that the magnetic ground state of this family consists of ferromagnetic kagome layers that are coupled antiferromagnetically via their extended organic pillaring linkers.

Observation of a phase transition within the domain walls of ferromagnetic Co3Sn2S2

The ferromagnetic phase of Co3Sn2S2 is widely considered to be a topological Weyl semimetal, with evidence for momentum-space monopoles of Berry curvature from transport and spectroscopic probes. As the bandstructure is highly sensitive to the magnetic order, attention has focused on anomalies in magnetization, susceptibility and transport measurements that are seen well below the Curie temperature, leading to speculation that a “hidden” phase coexists with ferromagnetism. Here we report spatially-resolved measurements by Kerr effect microscopy that identify this phase. We find that the anomalies coincide with a deep minimum in domain wall (DW) mobility, indicating a crossover between two regimes of DW propagation. We demonstrate that this crossover is a manifestation of a 2D phase transition that occurs within the DW, in which the magnetization texture changes from continuous rotation to unidirectional variation. We propose that the existence of this 2D transition deep within the ferromagnetic state of the bulk is a consequence of a giant quality factor for magnetocrystalline anisotropy unique to this compound. This work broadens the horizon of the conventional binary classification of DWs into Bloch and Néel walls, and suggests new strategies for manipulation of domain walls and their role in electron and spin transport.

The Magnetic Genome of Two-Dimensional van der Waals Materials

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

Flat-Band-Induced Anomalous Anisotropic Charge Transport and Orbital Magnetism in Kagome Metal CoSn

For solids, the dispersionless flat band has long been recognized as an ideal platform for achieving intriguing quantum phases. However, experimental progress in revealing flat-band physics has so far been achieved mainly in artificially engineered systems represented as magic-angle twisted bilayer graphene. Here, we demonstrate the emergence of flat-band-dominated anomalous transport and magnetic behaviors in CoSn, a paramagnetic kagome-lattice compound. By combination of angle-resolved photoemission spectroscopy measurements and first-principles calculations, we reveal the existence of a kagome-lattice-derived flat band right around the Fermi level. Strikingly, the resistivity within the kagome lattice plane is more than one order of magnitude larger than the interplane one, in sharp contrast with conventional (quasi-) two-dimensional layered materials. Moreover, the magnetic susceptibility under the out-of-plane magnetic field is found to be much smaller as compared with the in-plane case, which is revealed to be arising from the introduction of a unique orbital diamagnetism. Systematic analyses reveal that these anomalous and giant anisotropies can be reasonably attributed to the unique properties of flat-band electrons, including large effective mass and self-localization of wave functions. Our results broaden the already fascinating flat-band physics, and demonstrate the feasibility of exploring them in natural solid-state materials in addition to artificial ones.

Time-reversal symmetry-breaking charge order in a kagome superconductor

The kagome lattice¹, which is the most prominent structural motif in quantum physics, benefits from inherent non-trivial geometry so that it can host diverse quantum phases, ranging from spin-liquid phases, to topological matter, to intertwined orders^2-8 and, most rarely, to unconventional superconductivity^6,9. Recently, charge sensitive probes have indicated that the kagome superconductors AV₃Sb₅ (A = K, Rb, Cs)^9-11 exhibit unconventional chiral charge order^12-19, which is analogous to the long-sought-after quantum order in the Haldane model²⁰ or Varma model²¹. However, direct evidence for the time-reversal symmetry breaking of the charge order remains elusive. Here we use muon spin relaxation to probe the kagome charge order and superconductivity in KV₃Sb₅. We observe a noticeable enhancement of the internal field width sensed by the muon ensemble, which takes place just below the charge ordering temperature and persists into the superconducting state. Notably, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. We further show the multigap nature of superconductivity in KV₃Sb₅ and that the [Formula: see text] ratio (where T_c is the superconducting transition temperature and λ_ab is the magnetic penetration depth in the kagome plane) is comparable to those of unconventional high-temperature superconductors. Our results point to time-reversal symmetry-breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice.

Signatures of Weyl Fermion Annihilation in a Correlated Kagome Magnet

The manipulation of topological states in quantum matter is an essential pursuit of fundamental physics and next-generation quantum technology. Here we report the magnetic manipulation of Weyl fermions in the kagome spin-orbit semimetal Co_{3}Sn_{2}S_{2}, observed by high-resolution photoemission spectroscopy. We demonstrate the exchange collapse of spin-orbit-gapped ferromagnetic Weyl loops into paramagnetic Dirac loops under suppression of the magnetic order. We further observe that topological Fermi arcs disappear in the paramagnetic phase, suggesting the annihilation of exchange-split Weyl points. Our findings indicate that magnetic exchange collapse naturally drives Weyl fermion annihilation, opening new opportunities for engineering topology under correlated order parameters.

Coexistence of structural and magnetic phases in van der Waals magnet CrI3

CrI3 has raised as an important system to the emergent field of two-dimensional van der Waals magnetic materials. However, it is still unclear why CrI3 which has a ferromagnetic rhombohedral structure in bulk, changed to anti-ferromagnetic monoclinic at thin layers. Here we show that this behaviour is due to the coexistence of both monoclinic and rhombohedral crystal phases followed by three magnetic transitions at TC1 = 61 K, TC2 = 50 K and TC3 = 25 K. Each transition corresponds to a certain fraction of the magnetically ordered volume as well as monoclinic and rhombohedral proportion. The different phases are continuously accessed as a function of the temperature over a broad range of magnitudes. Our findings suggest that the challenge of understanding the magnetic properties of thin layers CrI3 is in general a coexisting structural-phase problem mediated by the volume-wise competition between magnetic phases already present in bulk.

Unconventional chiral charge order in kagome superconductor KV3Sb5

Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics^1-4. A charge-density-wave-like order with orbital currents has been proposed for achieving the quantum anomalous Hall effect^5,6 in topological materials and for the hidden phase in cuprate high-temperature superconductors^7,8. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy to discover an unconventional chiral charge order in a kagome material, KV₃Sb₅, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2 × 2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2 × 2 charge modulation exhibits an intensity reversal in real space, signalling charge ordering. At the impurity-pinning-free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Theoretical analysis of our experiments suggests a tantalizing unconventional chiral charge density wave in the frustrated kagome lattice, which can not only lead to a large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity.

Unusual Exchange Couplings and Intermediate Temperature Weyl State in Co_{3}Sn_{2}S_{2}

Understanding magnetism and its possible correlations to topological properties has emerged to the forefront as a difficult topic in studying magnetic Weyl semimetals. Co_{3}Sn_{2}S_{2} is a newly discovered magnetic Weyl semimetal with a kagome lattice of cobalt ions and has triggered intense interest for rich fantastic phenomena. Here, we report the magnetic exchange couplings of Co_{3}Sn_{2}S_{2} using inelastic neutron scattering and two density functional theory (DFT) based methods: constrained magnetism and multiple-scattering Green's function methods. Co_{3}Sn_{2}S_{2} exhibits highly anisotropic magnon dispersions and linewidths below T_{C}, and paramagnetic excitations above T_{C}. The spin-wave spectra in the ferromagnetic ground state is well described by the dominant third-neighbor "across-hexagon" J_{d} model. Our density functional theory calculations reveal that both the symmetry-allowed 120° antiferromagnetic orders support Weyl points in the intermediate temperature region, with distinct numbers and the locations of Weyl points. Our study highlights the important role Co_{3}Sn_{2}S_{2} can play in advancing our understanding of kagome physics and exploring the interplay between magnetism and band topology.

Chirality-Dependent Hall Effect and Antisymmetric Magnetoresistance in a Magnetic Weyl Semimetal

Weyl semimetals host a variety of exotic effects that have no counterpart in conventional materials, such as the chiral anomaly and magnetic monopole in momentum space. These effects give rise to unusual transport properties, including a negative magnetoresistance and a planar Hall effect, etc. Here, we report a new type of Hall and magnetoresistance effect in a magnetic Weyl semimetal. Unlike antisymmetric (with respect to either magnetic field or magnetization) Hall and symmetric magnetoresistance in conventional materials, the discovered magnetoresistance and Hall effect are antisymmetric in both magnetic field and magnetization. We show that the Berry curvature, the tilt of the Weyl node, and the chiral anomaly synergically produce these phenomena. Our results reveal a unique property of Weyl semimetals with broken time reversal symmetry.

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.

Unconventional critical behaviors at the magnetic phase transition of Co3Sn2S2 kagomé ferromagnet

Co₃Sn₂S₂ has generated a growing interest as a rare example of the highly uniaxial anisotropic kagomé ferromagnet showing a combination of frustrated-lattice magnetism and topology. Recently, via precise measurements of the magnetization and AC susceptibility we have found a low-field anomalous magnetic phase (A-phase) with very slow spin dynamics that appears just below the Curie temperature (T _C). The A-phase hosts high-density domain bubbles after cooling through T _C as revealed in a previous in-situ Lorentz-TEM study. Here, we present further signatures of the anomalous magnetic transition (MT) at T _C revealed by a study of the critical behaviors of the magnetization and magnetocaloric effect using a high-quality single crystal. Analyses of numerous magnetization isotherms around T _C (≃177 K) using different approaches (the modified Arrot plot, Kouvel-Fisher method and magnetocaloric effect) result in consistent critical exponents that do not satisfy the theoretical predictions of standard second-order-MT models. Scaling analyses for the magnetization, magnetic entropy change and field-exponent of the magnetic entropy change, all consistently show low-field deviations below T _C from the universal curves. Our results reveal that the MT of Co₃Sn₂S₂ can not be explained as a conventional second-order type and suggest an anomalous magnetic state below T _C.

Field-Modulated Anomalous Hall Conductivity and Planar Hall Effect in Co3Sn2S2 Nanoflakes

Time-reversal-symmetry-breaking Weyl semimetals (WSMs) have attracted great attention recently because of the interplay between intrinsic magnetism and topologically nontrivial electrons. Here, we present anomalous Hall and planar Hall effect studies on Co₃Sn₂S₂ nanoflakes, a magnetic WSM hosting stacked Kagome lattice. The reduced thickness modifies the magnetic properties of the nanoflake, resulting in a 15-time larger coercive field compared with the bulk, and correspondingly modifies the transport properties. A 22% enhancement of the intrinsic anomalous Hall conductivity (AHC), as compared to bulk material, was observed. A magnetic field-modulated AHC, which may be related to the changing Weyl point separation with magnetic field, was also found. Furthermore, we showed that the PHE in a hard magnetic WSM is a complex interplay between ferromagnetism, orbital magnetoresistance, and chiral anomaly. Our findings pave the way for a further understanding of exotic transport features in the burgeoning field of magnetic topological phases.

Localized spin-orbit polaron in magnetic Weyl semimetal Co3Sn2S2

The kagome lattice Co₃Sn₂S₂ exhibits the quintessential topological phenomena of a magnetic Weyl semimetal such as the chiral anomaly and Fermi-arc surface states. Probing its magnetic properties is crucial for understanding this correlated topological state. Here, using spin-polarized scanning tunneling microscopy/spectroscopy (STM/S) and non-contact atomic force microscopy (nc-AFM) combined with first-principle calculations, we report the discovery of localized spin-orbit polarons (SOPs) with three-fold rotation symmetry nucleated around single S-vacancies in Co₃Sn₂S_2. The SOPs carry a magnetic moment and a large diamagnetic orbital magnetization of a possible topological origin associated relating to the diamagnetic circulating current around the S-vacancy. Appreciable magneto-elastic coupling of the SOP is detected by nc-AFM and STM. Our findings suggest that the SOPs can enhance magnetism and more robust time-reversal-symmetry-breaking topological phenomena. Controlled engineering of the SOPs may pave the way toward practical applications in functional quantum devices.

Kagome lattice material Co₃Sn₂S₂ is identified as a magnetic Weyl semimetal and its magnetic properties are less studied. Here, the authors observe localized spin-orbit polarons nucleated around single S-vacancies carrying a large diamagnetic orbital magnetism in Co₃Sn₂S₂.

Spin-orbit quantum impurity in a topological magnet

Quantum states induced by single-atomic impurities are at the frontier of physics and material science. While such states have been reported in high-temperature superconductors and dilute magnetic semiconductors, they are unexplored in topological magnets which can feature spin-orbit tunability. Here we use spin-polarized scanning tunneling microscopy/spectroscopy (STM/S) to study the engineered quantum impurity in a topological magnet Co3Sn2S2. We find that each substituted In impurity introduces a striking localized bound state. Our systematic magnetization-polarized probe reveals that this bound state is spin-down polarized, in lock with a negative orbital magnetization. Moreover, the magnetic bound states of neighboring impurities interact to form quantized orbitals, exhibiting an intriguing spin-orbit splitting, analogous to the splitting of the topological fermion line. Our work collectively demonstrates the strong spin-orbit effect of the single-atomic impurity at the quantum level, suggesting that a nonmagnetic impurity can introduce spin-orbit coupled magnetic resonance in topological magnets.

Electronic correlations and flattened band in magnetic Weyl semimetal candidate Co3Sn2S2

The interplay between electronic correlations and topological protection may offer a rich avenue for discovering emergent quantum phenomena in condensed matter. However, electronic correlations have so far been little investigated in Weyl semimetals (WSMs) by experiments. Here, we report a combined optical spectroscopy and theoretical calculation study on the strength and effect of electronic correlations in a magnet Co₃Sn₂S₂. The electronic kinetic energy estimated from our optical data is about half of that obtained from single-particle ab initio calculations in the ferromagnetic ground state, which indicates intermediate-strength electronic correlations in this system. Furthermore, comparing the energy and side-slope ratios between the interband-transition peaks at high energies in the experimental and single-particle-calculation-derived optical conductivity spectra with the bandwidth-renormalization factors obtained by many-body calculations enables us to estimate the Coulomb-interaction strength (U ∼ 4 eV) in Co₃Sn₂S₂. Besides, a sharp experimental optical conductivity peak at low energy, which is absent in the single-particle-calculation-derived spectrum but is consistent with the optical conductivity peaks obtained by many-body calculations with U ∼ 4 eV, indicates that an electronic band connecting the two Weyl cones is flattened by electronic correlations and emerges near the Fermi energy in Co₃Sn₂S₂. Our work paves the way for exploring flat-band-generated quantum phenomena in WSMs.

Exchange biased anomalous Hall effect driven by frustration in a magnetic kagome lattice

Co[Formula: see text]Sn[Formula: see text]S[Formula: see text] is a ferromagnetic Weyl semimetal that has been the subject of intense scientific interest due to its large anomalous Hall effect. We show that the coupling of this material's topological properties to its magnetic texture leads to a strongly exchange biased anomalous Hall effect. We argue that this is likely caused by the coexistence of ferromagnetism and geometric frustration intrinsic to the kagome network of magnetic ions, giving rise to spin-glass behavior and an exchange bias.