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Supporting information of JUSTC-2022-0182
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Figures of the Article
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Three possible crystal structures of LaRu3Si2 with a Kagome plane consisting of pure Ru atoms. (a), (c) Perfect Kagome structure. (b), (d), and (e) Two possible distorted Kagome structures with a doubling of the c -axis. (c)–(e) Top view of the Kagome planes. The anglesα,β and side lengthsl1,l2 of the hexagon, the fractional coordinates of Ru atomsx,y , and the space group are shown, respectively. The crystal structures are constructed by VESTA[36]. -
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Electronic correlation effects on stabilizing a perfect Kagome lattice. (a), (d) Fractional coordinates x of Ru (Fe) relaxed by LDA+U and GGA+U as functions of Hubbard U, for different lattice parameter ratio c/a with the fixed crystal volume of experiment. c = 7.12 Å is the experimental value. x = 0.5 for a perfect Kagome lattice. (b), (e) x relaxed by LDA+DMFT as functions of U. The yellow area mark that LaRu3Si2 is on the verge of becoming a perfect Kagome lattice. (c), (f) LDA+DMFT calculated mass-enhancement of Ru-4d (Fe-3d) orbitals due to electronic correlations, as functions of U. (a)–(c) for LaRu3Si2 and (d)–(f) for LaFe3Si2.
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Electronic correlation induced magnetism. (a), (d) Local magnetic susceptibilities calculated by LDA+DMFT as functions of temperate T for differentU values. (b), (e) The energies (per unit cell) of FM and AFM orders with respect to the non-magnetic state as functions ofU , calculated by GGA+U . (c), (f) Ordered magnetic moment in the FM and AFM states. (a)–(c) for LaRu3Si2, the crystal structures relaxed at the correspondingU are used. (d)–(f) for LaFe3Si2. The experimental lattice parameters,a=5.676 Å andc=7.12 Å, are used for both compounds. -
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Flat band near Fermi level. (a), (d) LDA calculated band structures. The flat bands (FB) with dx2−y2 character are shown in red. (b), (e) LDA+DMFT calculated spectrum functionA(k,ω) atU=4 eV,JH=0.782 eV andT=290 K. (c), (f) The corresponding density of states. (a)–(c) for LaRu3Si2, the crystal structure relaxed by LDA+DMFT atU=4 eV,JH=0.782 eV is used. (d)–(f) for LaFe3Si2. The experimental lattice parameters,a=5.676 Å andc=7.12 Å, are used for both compounds.
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