First-principles study

Kagome lattice is a two-dimensional honeycomb structure network with triangular corner sharing. The band structure of kagome lattice has been theoretically predicted to possess both flat bands and Dirac states in the Brillouin zone. In addition, the band degeneracy will be lifted and present a topological nontrival gap as considering time-invariant intersite spin-orbit coupling. Recently, a new kagome family RMn₆Sn₆ has been found to provide a tunable magnetic configuration by replacing different rare earth elements R. For example, TbMn₆Sn₆ (R=Tb) shows a ferrimagnetic state with our-of-plane spin orientation. Based on first-principles calculations, we identify a highly orbital-selective massive Dirac state forming by Mn d_x2-y2/d_xy with 35 meV large energy gap at K point, which is well consistent with our tunneling measurement [1]. Remarkably, our calculation exhibits the strong Berry curvature in this gapped Dirac state, supporting TbMn₆Sn₆ may be an intrinsic Chern insulator. Besides TbMn₆Sn₆, we find an in-plane spin configuration in GdMn₆Sn₆. Our first-principles calculations demonstrate a magnetic nodal-line state resulted from the nearly gapless Dirac cone around K point in this easy-plane ferrimagnet spin structure. Our calculation reveals an orbital-selective and a tunable topological gap in kagome magnet RMn₆Sn₆ and provide a natural platform to investigate the interplay between topology and magnetism.