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Tuning the flat bands of the kagome metal CoSn with Fe, In, or Ni doping

We report CoSn is a Pauli paramagnet with relatively flat d bands centered about 100 meV below the Fermi energy, E F . Single crystals of CoSn lightly doped with Fe, In, or Ni are investigated using x-ray and neutron scattering, magnetic susceptibility and magnetization, AC susceptibility, specific heat, and resistivity measurements. Within the rigid-band approximation, hole doping with a few percent of Fe or In should move the flat bands closer to E F , whereas electron doping with Ni should move the flat bands further away from E F . We provide evidence that this indeed occurs. Fe and In doping drive CoSn toward magnetism, while Ni doping suppresses CoSn's already weak magnetic response. The resulting ground state is different for Fe versus In doping. For Fe-doped crystals, Co 1-x Fe x Sn, with 0.02< x <0.27, the magnetic and specific-heat data are consistent with the formation of a spin glass, with a glass temperature, T g , ranging from 1 K for x = 0.02 to 10 K for x = 0.27. Powder and single-crystal neutron diffraction found no evidence of long-range magnetic order below T g for samples with x ≈ 0.17. For In-doped crystals, CoSn 1-y In y , both the magnetic susceptibility and the Sommerfeld coefficient, γ, increase substantially relative to pure CoSn, but with no clear indication of a magnetic transition for 0.05< y <0.2. CoSn crystals doped with Ni (Co 0.93 Ni 0.07 Sn) have a significantly smaller magnetic susceptibility and γ than pure CoSn, consistent with flat bands further from E F .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

CoSn-type NiIn1–xSbx (0 ≤ x ≤ 0.17): Site-Selective Substitution, Electronic Structure, Chemical Bonding, and Structural Transformation

CoSn-type intermetallic compounds have emerged as a model platform for Kagome-derived flat-band physics, where subtle chemical perturbations can strongly influence electronic structure and phase stability. Here, we present a combined experimental and theoretical study of Sb-substitution in CoSn-type NiIn1–xSbx (0 ≤ x ≤ 0.17) to elucidate the interplay between site selectivity, solubility limit, chemical bonding, and electronic structure. Rietveld refinements on Neutron powder diffraction data confirmed the selective Sb-substitution at the electron-rich In2 (2d) site forming the honeycomb substructure, while the In1 (1a) site within the Kagome layer remains exclusively occupied by In. Density functional theory (DFT) calculations revealed that pristine CoSn-type NiIn hosts Ni 3d-dominated flat bands near the Fermi level (EF), originating from the Kagome-like Ni substructure. Partial replacement of In by Sb within the honeycomb layer alters these flat-band features below EF, reducing the density of states and suppressing the flat-band topology near the Fermi level. Orbital-resolved electronic structure and chemical-bonding analyses show that Sb-substitution enhances Ni-p-block (In/Sb) covalency and optimizes charge compensation, stabilizing the CoSn-type structure up to the solubility limit x ≈ 0.17. Beyond the limit, the higher-Sb compositions show satellite reflections consistent with an incommensurately modulated phase. These results establish a link between site-selective chemical substitution, bonding optimization, and flat-band electronic structure evolution, providing fundamental insights into how chemical substitution influences the electronic properties of Kagome-based intermetallic compounds.

Roy, Nilanjan [National Institute of Technology Si↗

Spin excitations in metallic kagome lattice FeSn and CoSn

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 we report inelastic neutron scattering studies of spin excitations in 2D metallic kagome lattice antiferromagnetic FeSn and paramagnetic CoSn, where angle resolved photoemission spectroscopy experiments found spin-polarized and nonpolarized flat bands, respectively, below the Fermi level. Our measurements on FeSn and CoSn reveal well-defined spin waves extending above 140 meV and correlated paramagnetic scattering around Γ point below 90 meV, respectively. In addition, we observed non-dispersive excitations at ~170 meV and ~360 meV arising mostly from hydrocarbon scattering of the CYTOP-M used to glue the samples to aluminum holder. Therefore, our results established the evolution of spin excitations in FeSn and CoSn, and identified anomalous flat modes overlooked by the neutron scattering community for many years.

36 MATERIALS SCIENCE↗

Flat bands in the CoSn-type compounds

Quantum interference on the kagome lattice generates electronic bands with narrow bandwidth, called flat bands. Crystal structures incorporating this lattice can host strong electron correlations with nonstandard ingredients, but only if these bands lie at the Fermi level. In the six compounds with the CoSn structure type (FeGe, FeSn, CoSn, NiIn, RhPb, and PtTl) the transition metals form a kagome lattice. The two iron variants are robust antiferromagnets so we focus on the latter four and investigate their thermodynamic and transport properties. We consider these results and calculated band structures to locate and characterize the flat bands in these materials. Finally, we propose that CoSn and RhPb deserve the community's attention for exploring flat-band physics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Chemical Control of Magnetism in the Kagome Metal CoSn 1 – x In x : Magnetic Order from Nonmagnetic Substitutions

As a two-dimensional structural motif, the kagome net produces many interesting magnetic and electronic properties. In particular, this lattice produces flat electronic bands with a large density of states. When the chemical potential is positioned within these flat bands, electronic instabilities can result. For the kagome metal CoSn, this alignment is not realized, the flat bands are completely filled, and the compound is a Pauli paramagnet. For this study, we have grown crystals and powders of CoSn 1 – x In x and shown that replacing Sn with In moves the chemical potential into the flat band region, as expected from simple electron counting. This is supported by band structure calculations, heat capacity measurements, and angle-resolved photoemission spectroscopy. The increased density of states results in the emergence of antiferromagnetic order evidenced by magnetic susceptibility, Mössbauer spectroscopy, and neutron diffraction data. The Néel temperature reaches a maximum of 32 K. The emergence of magnetic order when introducing a nonmagnetic element into a nonmagnetic kagome metal is striking. This work provides clear evidence that flat bands arising from electronically frustrated lattices in bulk crystals provide a new and powerful way to realize correlated ground states controlled by crystal chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Materials Data on CoSn by Materials Project

CoSn crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Co is bonded in a 10-coordinate geometry to four equivalent Co and six Sn atoms. All Co–Co bond lengths are 2.65 Å. There are four shorter (2.61 Å) and two longer (2.65 Å) Co–Sn bond lengths. There are two inequivalent Sn sites. In the first Sn site, Sn is bonded in a 9-coordinate geometry to six equivalent Co atoms. In the second Sn site, Sn is bonded in a hexagonal planar geometry to six equivalent Co atoms.

36 MATERIALS SCIENCE↗

Orbital-selective Dirac fermions and extremely flat bands in frustrated kagome-lattice metal CoSn

Layered kagome-lattice 3d transition metals are emerging as an exciting platform to explore the frustrated lattice geometry and quantum topology. However, the typical kagome electronic bands, characterized by sets of the Dirac-like band capped by a phase-destructive flat band, have not been clearly observed, and their orbital physics are even less well investigated. Here, we present close-to-textbook kagome bands with orbital differentiation physics in CoSn, which can be well described by a minimal tight-binding model with single-orbital hopping in Co kagome lattice. The capping flat bands with bandwidth less than 0.2 eV run through the whole Brillouin zone, especially the bandwidth of the flat band of out-of-plane orbitals is less than 0.02 eV along Γ-M. The energy gap induced by spin-orbit interaction at the Dirac cone of out-of-plane orbitals is much smaller than that of in-plane orbitals, suggesting orbital-selective character of the Dirac fermions.

36 MATERIALS SCIENCE↗

Topological flat bands in frustrated kagome lattice CoSn

Electronic flat bands in momentum space, arising from strong localization of electrons in real space, are an ideal stage to realize strongly-correlated phenomena. Theoretically, the flat bands can naturally arise in certain geometrically frustrated lattices, often with nontrivial topology if combined with spin-orbit coupling. Here, we report the observation of topological flat bands in frustrated kagome metal CoSn, using angle-resolved photoemission spectroscopy and band structure calculations. Throughout the entire Brillouin zone, the bandwidth of the flat band is suppressed by an order of magnitude compared to the Dirac bands originating from the same orbitals. The frustration-driven nature of the flat band is directly confirmed by the chiral d-orbital texture of the corresponding real-space Wannier functions. Spin-orbit coupling opens a large gap of 80 meV at the quadratic touching point between the Dirac and flat bands, endowing a nonzero Z2 invariant to the flat band. These findings demonstrate that kagome-derived flat bands are a promising platform for novel emergent phases of matter at the confluence of strong correlation and topology.

36 MATERIALS SCIENCE↗

Materials Data on CoSn(PO4)2 by Materials Project

Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations

36 MATERIALS SCIENCE↗

Anomalies in the electromagnetic response and peculiarities of the domain structure in the magnetic Weyl semimetal Co 3⁢ Sn 2 ⁢S 2

In this paper, we present a comprehensive study of magnetic properties of Co 3 ⁢Sn 2 ⁢S 2 (CoSnS) crystals using macroscopic characterization and observations of the domain structure (DS) in a wide range of easy- and hard-axis fields (𝐻) and temperatures (𝑇). From macroscopic measurements, we derive temperature dependences of the basic magnetic parameters of the material [saturation magnetization 𝑀 𝑠 ⁡(𝑇), uniaxial anisotropy constant 𝐾⁡(𝑇), and exchange stiffness 𝐴⁡(𝑇)] and, based on them, calculate the thermodynamic magnetization 𝑀⁡(𝐻,𝑇) curves and DS parameters for pinning-free samples. We find important qualitative and quantitative differences between the theory and experiment defined by the efficient pinning of domain walls (DWs) in our samples. It turns out that, already at temperatures close to the ferromagnetic transition 𝑇 𝑐 , the DW dynamics falls into the heavy creep regime, resulting in a strong deferral of the DS adjustment into the equilibrium state. Here, we suggest that specific magnetic defects, responsible for pinning and causing field-tuned reproducible domain nucleation patterns observed in our high-quality samples, are pointlike. Recently found magnetic polarons formed around vacancies and impurities, which carry strong diamagnetic moments of spin-orbit nature and are intrinsic for CoSnS and expected in other Weyl semimetals, are a possible source of pinning yielding peculiar 𝑀⁡(𝐻,𝑇) response of CoSnS.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Confined Room-Temperature Ferromagnetism in Kagome (Fe 3 Sn 2 /CoSn) Superlattices

We reveal the presence of robust ferromagnetism in topological kagome (Fe 3 Sn 2 /CoSn) ×n superlattices via polarized neutron reflectivity (PNR) and magnetization measurements. Using molecular beam epitaxy, we have synthesized superlattices of alternating ferromagnetic Fe 3 Sn 2 and paramagnetic CoSn layers, the interfacial integrity of which is confirmed using scanning transmission electron microscopy. Magnetization depth profiles, obtained by fitting the PNR data, confirm the presence of ferromagnetism in the confined Fe 3 Sn 2 layers at room temperature, with minimal thickness dependence down to 2 nm. A net magnetization is found in the near-surface region of CoSn, which we attribute to surface oxidation. Our results demonstrate that superlattice engineering is a means to confine ferromagnetism in kagome metals, enabling future studies of thickness-dependent anomalous Hall and Nernst effects as well as spin-dependent transport and tunneling in device structures.

kagome metals↗

Simultaneous Development of Antiferromagnetism and Local Symmetry Breaking in a Kagome Magnet (Co 0.45 Fe 0.55 )Sn

CoSn and FeSn, two kagome-lattice metals, have recently attracted significant attention as hosts of electronic flat bands and emergent physical properties. However, current understandings of their physical properties are limited to knowledge of the average crystal structure. Here, we report the Fe-doping induced coemergence of the antiferromagentic (AFM) order and local symmetry breaking in (Co 0.45 Fe 0.55 )Sn. Rietveld analysis on the neutron and synchrotron X-ray diffraction data indicates A-type antiferromagnetic order with the moment pointing perpendicular to the kagome layers, associated with the anomaly in the MSn(1) 2 Sn(2) 4 (M = Co/Fe) octahedral distortion and the lattice constant c. Reverse Monte Carlo (RMC) modeling of the synchrotron X-ray total scattering results captured the subtle local orthorhombic distortion involving off-axis displacements of Sn(2). Our results indicate that the stable hexagonal lattice above T N becomes unstable once the A-type AFM order is formed below T N . Here we argue that the local symmetry breaking has a magnetic origin, since the spatially varied M–Sn(2) bond lengths arise from out-of-plane magnetic exchange coupling J c via the exchange pathway M–Sn(2)–M. Our study provides comprehensive information on the crystal structure in both long-range scale and local scale, unveiling unique coupling between AFM order, octahedral distortion, and hidden local symmetry breaking.

36 MATERIALS SCIENCE↗

Fermion–boson many-body interplay in a frustrated kagome paramagnet

Kagome-nets, appearing in electronic, photonic and cold-atom systems, host frustrated fermionic and bosonic excitations. However, it is rare to find a system to study their fermion–boson many-body interplay. Here we use state-of-the-art scanning tunneling microscopy/spectroscopy to discover unusual electronic coupling to flat-band phonons in a layered kagome paramagnet, CoSn. We image the kagome structure with unprecedented atomic resolution and observe the striking bosonic mode interacting with dispersive kagome electrons near the Fermi surface. At this mode energy, the fermionic quasi-particle dispersion exhibits a pronounced renormalization, signaling a giant coupling to bosons. Through the self-energy analysis, first-principles calculation, and a lattice vibration model, we present evidence that this mode arises from the geometrically frustrated phonon flat-band, which is the lattice bosonic analog of the kagome electron flat-band. Our findings provide the first example of kagome bosonic mode (flat-band phonon) in electronic excitations and its strong interaction with fermionic degrees of freedom in kagome-net materials.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Measurements of the quantum geometric tensor in solids

Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is a core aspect of contemporary physics. The quantum geometric tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state. The imaginary part of the QGT is the well-known Berry curvature, which plays an integral role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence recently, giving rise to a new set of quantum geometric phenomena such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. Here, in this work, we develop a framework to measure the QGT in crystalline solids using polarization-, spin- and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in the kagome metal CoSn, which hosts topological flat bands. Establishing this momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.

36 MATERIALS SCIENCE↗

Stabilizing homogeneous CaMn6Sn6via oscillatory crystal growth: structural complexity in a kagome metal

CaMn6Sn6 is a member of the large family of Mn-based kagome metals derived by filling voids of the prototypical CoSn structure. We observed Ca-deficiency and structural complexity, with approximately 10% deficiency of calcium relative to the ideal 166 stoichiometry. These features are common in related Ca-based materials. We find that growth conditions stabilize different phases with varying Curie temperatures. Diffraction and magnetization measurements reveal that conventional growth profiles yield inhomogeneity both within and between crystals in a given batch, whereas an oscillatory temperature profile promotes homogeneous crystals that adopt a superstructure beyond the parent hexagonal structure type. We present the physical properties of crystals grown using the oscillatory approach. The crystals are highly conductive, with a c-axis residual resistivity ratio ρ(300 K)/ρ(2 K) exceeding 100 and a positive, linear magnetoresistance at base temperature. Magnetically, the crystals are quite similar to MgMn6Sn6, with easy-plane ferromagnetic behavior and a Curie temperature of TC ≈ 237 K. These results highlight the critical role of growth conditions in stabilizing homogeneous crystals of complex phases such as Ca0.9Mn6Sn6. The oscillatory growth approach provides an effective route for accessing the intrinsic properties of this complex material and may be broadly useful for the growth of related kagome systems.

May, Andrew [ORNL] (ORCID:0000000307778539)↗

Magnetic order and physical properties of the kagome metal UNb 6 ⁢Sn 6

The 𝑅⁢𝑀 6 ⁢𝑋 6 family of materials (𝑅 = rare-earth, 𝑀 = transition metal, 𝑋 = Ga, Si, Ge, Sn) produces an array of emergent phenomena, such as charge density waves, intrinsic Hall effects, and complex magnetic order, due to its kagome net of transition metal atoms, its local-moment magnetic anisotropies, and its extensive chemical tunability. Here, in this study, we report UNb 6⁢ Sn 6 , a new “166” material containing both an actinide and a 4⁢𝑑 transition metal, along with its nonmagnetic analog ThNb6⁢Sn6, to investigate the properties of a 5⁢𝑓−4⁢𝑑 electron 166 system. UNb 6 ⁢Sn 6 crystallizes in the hexagonal 𝑃⁢6/𝑚⁢𝑚⁢𝑚 space group with a small degree of disorder due to shifts in the size of the CoSn-like cages along the 𝑐 axis. Upon cooling at zero magnetic field, the material undergoes two magnetic phase transitions at 𝑇 2 = 46K and 𝑇 N = 43K. The low-temperature, zero-field phase is an antiferromagnet with ordered uranium moments and a k = (0,0,1/2) propagation vector determined by neutron diffraction. Remarkably, with a magnetic field applied along the 𝑐 axis, five additional magnetic transitions occur, evidenced by magnetization and resistivity data, before the moment saturates at 2.62 𝜇 B /U at 2 K and ≥ 13.6T. In two magnetic phase regions, the Hall resistivity of UNb 6⁢ Sn 6 significantly deviates from the magnetization, suggesting that the phases have a large Berry curvature or a change in the Fermi surface. The unknown magnetic ordering of the field-dependent phases of UNb 6⁢ Sn 6 demonstrates the complexity of the 5⁢𝑓−4⁢𝑑 166 system and encourages further study of its properties.

36 MATERIALS SCIENCE↗

Structural modulation, physical properties, and electronic band structure of the kagome metal UCr 6 ⁢Ge 6

The chemical flexibility of the 𝑅⁢𝑀 6 ⁢𝑋 6 stoichiometry, where an 𝑓-block element is intercalated in the CoSn structure type, allows for the tuning of flatbands associated with kagome lattices to the Fermi level and for emergent phenomena due to interactions between the 𝑓- and 𝑑-electron lattices. Yet, 5⁢𝑓 members of the “166” compounds are underrepresented compared with 4⁢𝑓 members. In this work, we report single-crystal growth of UCr 6 ⁢Ge 6 , which crystallizes in a monoclinically distorted Y 0.5⁢ Co 3 ⁢Ge 3 -type structure. The real-space character of the modulation, which is unique within the 𝑅⁢𝑀 6 ⁢𝑋 6 family, is approximated by a 3×1×2 supercell of the average monoclinic cell. The compound has kagome-lattice flatbands near the Fermi level and a moderately enhanced electronic heat capacity, as evidenced by its low-temperature Sommerfeld coefficient (𝛾=86.5 mJ mol −1 K −2 ) paired with band structure calculations. The small, isotropic magnetization and featureless resistivity of UCr 6 ⁢Ge 6 suggest itinerant uranium 5⁢𝑓 electrons and Pauli paramagnetism. Angle-resolved photoemission spectroscopy results provide evidence for uranium 5⁢𝑓 weight at the Fermi level and for a flatband near the Fermi level associated with the chromium 3⁢𝑑 kagome lattice. The isotropic magnetic behavior of the uranium 5⁢𝑓 electrons starkly contrasts with localized behavior in other uranium 166 compounds, highlighting the high tunability of the magnetic ground state across the material family.

36 MATERIALS SCIENCE↗