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Flat bands in the CoSn-type compounds

William R. Meier, Mao-Hua Du, Satoshi Okamoto, Narayan Mohanta, Andrew F. May, Michael A. McGuire, Craig A. Bridges, German D. Samolyuk, and Brian C. Sales
Phys. Rev. B 102, 075148 – Published 31 August 2020
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  • INTRODUCTION
  • METHODS
  • RESULTS
  • DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    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. We propose that CoSn and RhPb deserve the community's attention for exploring flat-band physics.

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    • Received 28 May 2020
    • Accepted 10 August 2020

    DOI:https://doi.org/10.1103/PhysRevB.102.075148

    ©2020 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    AntiferromagnetismCrystal growthElectronic structure
    1. Physical Systems
    Kagome latticeStrongly correlated systems
    1. Techniques
    AnnealingCrystal structuresDensity functional theoryMagnetization measurementsResistivity measurementsSpecific heat measurementsX-ray powder diffraction
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    William R. Meier1, Mao-Hua Du1, Satoshi Okamoto1, Narayan Mohanta1, Andrew F. May1, Michael A. McGuire1, Craig A. Bridges2, German D. Samolyuk1, and Brian C. Sales1

    • 1Materials Science & Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
    • 2Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

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    Issue

    Vol. 102, Iss. 7 — 15 August 2020

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    Images

    • Figure 1
      Figure 1

      (a) Kagome lattice with shaded CoSn unit cell. (b) The CoSn structure with labeled sites drawn in vesta [8]. (c) Tight-binding dispersion of kagome lattice from Ref. [9]. (d) CoSn Brillouin zones with labeled high-symmetry points.

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    • Figure 2
      Figure 2

      A photo of the CoSn-type samples with steel scale. The pale-blue metallic luster of CoSn is evident but the pale-pink hue of NiIn does not show up well.

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    • Figure 3
      Figure 3

      Thermal expansion of 23 electron kagome metals. The lattice parameters are normalized by dividing by the 15 K value of each compound. These four compounds show larger thermal expansion along the c axis than a but NiIn is nearly isotropic.

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    • Figure 4
      Figure 4

      The thermal expansion of FeGe, FeSn, and CoSn. Note that FeGe and FeSn show the opposite thermal expansion anisotropy to CoSn (and the other compounds without magnetic order). The moment reorientation in FeGe generates feature around 100 K. The inset shows the thermal expansion of FeSn up to 725 K. Antiferromagnetism appears to suppress c-axis expansion below TN.

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    • Figure 5
      Figure 5

      Heat capacity of the six kagome metals. The inset presents low-temperature fits used to estimate the Sommerfeld parameter γ and estimate the Debye temperature (θD) presented in Table 2. The moment reorientation transition in FeGe is evident as a change in slope around 100 K.

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    • Figure 6
      Figure 6

      Anisotropic magnetic susceptibility of the four kagome metals without magnetic order. The data for NiIn are from the annealed polycrystalline powder. The other three show a lower susceptibility with field along the c axis. CoSn shows a pronounced increase in χ with temperature.

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    • Figure 7
      Figure 7

      FeGe and FeSn show a dramatically larger magnetic response than CoSn and the other metals without magnetic order. The FeGe data were obtained with an annealed polycrystalline sample.

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    • Figure 8
      Figure 8

      Anisotropic electrical resistivity of the kagome metals.

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    • Figure 9
      Figure 9

      Band structures of the CoSn-type compounds without magnetic order calculated by DFT. Energy is measured with respect to the Fermi energy. The width of the colored lines on each band indicates the d-orbital character. The density of states D of each compound is plotted on the right of each panel. The red and green bars mark the approximate extent of the dxy,dx2−y2 and dxz,dyz flat bands, respectively. They are accompanied by the bandwidth in eV.

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    • Figure 10
      Figure 10

      Simple density of states model for the magnetic susceptibility of CoSn. (a) The step function model for density of states at T=0K shaded to show the filled states. (b) When kBT≥ɛS/4 states below ɛS begin to thermally depopulate. This allows more electrons to participate in spin polarization and the Pauli susceptibility is enhanced. In addition, the chemical potential μ shifts. (c) Plots of the relative change in Pauli susceptibility with temperature based on the density of states model (with ɛS=20 meV and R=5) including the shifting chemical potential. The dashed line represents the temperature corresponding to the energy scale of ɛS.

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    • Figure 11
      Figure 11

      Anisotropic magnetic susceptibility of the CoSn up to 750 K.

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