Flatbands and Emergent Ferromagnetic Ordering in ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$ Kagome Lattices

A flatband representing a highly degenerate and dispersionless manifold state of electrons may offer unique opportunities for the emergence of exotic quantum phases. To date, definitive experimental demonstrations of flatbands remain to be accomplished in realistic materials. Here, we present the first experimental observation of a striking flatband near the Fermi level in the layered ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$ crystal consisting of two Fe kagome lattices separated by a Sn spacing layer. The band flatness is attributed to the local destructive interferences of Bloch wave functions within the kagome lattices, as confirmed through theoretical calculations and modelings. We also establish high-temperature ferromagnetic ordering in the system and interpret the observed collective phenomenon as a consequence of the synergetic effect of electron correlation and the peculiar lattice geometry. Specifically, local spin moments formed by intramolecular exchange interaction are ferromagnetically coupled through a unique network of the hexagonal units in the kagome lattice. Our findings have important implications to exploit emergent flat-band physics in special lattice geometries.

Figure 1

Structural characterization of the ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$ bulk and surface. (a) Schematic diagram of the wave function self-localization on the hexagons in the kagome lattice: Because of the special structure of the kagome lattice, the wave function alternates its sign around the six vertices in each hexagon, leading to destructive interference outside of the hexagon and, therefore, electrons locally circulate around each hexagon. (b),(c) Top and perspective views of the optimized structure of bulk ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$. The bond lengths in the red and cyan colored triangles are 2.54 and 2.77 Å, respectively. Three different layers are denoted as Fe-Sn-1, Fe-Sn-2, and Sn, respectively. (d) Cross-sectional TEM image with the atomic resolution of three different layers. (e) Large-scale STM image of a cleaved ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$ surface with two different surface layers. The sample bias was $V_s=0.4\mathrm{V}$. (f)–(i) Atomic resolution STM images taken at $V_s=0.2$ and $-0.2\mathrm{V}$ on the two different surface layers. The scale bars in (f)–(i) are 1 nm. The corresponding simulated STM images for the two surface layers are also given in the insets.

Figure 2

Electronic band structure of the ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$ surface. (a),(b) (Top) ARPES results along the $\mathrm{\Gamma }\text{−}K$ and $\mathrm{\Gamma }\text{−}M$ lines, respectively. (Bottom) Calculated spin-polarized bands projected onto the top few layers of the Fe-Sn-1 surface structure. Here, the majority (minority) spin bands are drawn with the red (blue) circles whose sizes are proportional to the weights of the projected electrons. (c) Calculated spin-polarized band structure for the Fe-Sn-1 surface structure. Here, the Fermi level $E_F$ is set at zero energy, and the purple shaded stripe highlights the nearly flatbands close to $-0.2\mathrm{eV}$. (d) Photoemission intensity map at the Fermi level superimposed with the calculated Fermi surfaces for the Fe-Sn-1 (solid circles) and Sn (dashed circle) surfaces.

Figure 3

Scanning tunneling spectroscopy of the Fe-Sn-1 surface. (a) Differential conductance ($dI/dV$ spectra) scan (bottom) along the blue line on the STM image obtained at $V_s=-0.2\mathrm{V}$ (top). (b) (Top) Calculated charge character of the flat-band state at the $\mathrm{\Gamma }$ point obtained from the Fe-Sn-1 surface structure. Here, the charge density distribution is drawn with an isosurface of $0.004e/{\mathrm{bohr}}^3$. (Bottom) A cross-section view drawn parallel to the Fe-Sn layers.

Figure 4

Ferromagnetic order of ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$. (a),(b) Hysteresis loop (obtained at 2 K) and temperature-dependent magnetic moment (applied field of 100 Oe) of an ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$ single crystal, respectively. Here, the magnetic field is applied parallel to the Fe-Sn layers. (c) Calculated band structure, DOS, and partial DOS for the nonmagnetic state of bulk ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$. The ten flatbands with dispersion smaller than 0.2 eV are drawn by solid or heavy dashed lines. (d) Calculated DOS for the ferromagnetic state of bulk ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$. (e) Spin density distribution of the ferromagnetic state. The spin density distribution is drawn with an isosurface of $0.01e/{\mathrm{bohr}}^3$.