Exploring magnetic and topological complexity in MgMn 6 Sn 6 : From frustrated ground states to nontrivial Hall conductivity

We explore the intriguing topological itinerant magnet ${\mathrm{MgMn}}_{6}{\mathrm{Sn}}_{6}$, characterized by bilayer kagome Mn layers encasing a hexagonal Sn layer. Using ab initio density functional theory and dynamical mean-field theory calculations, we uncover the complex electronic properties and many-body configuration of its magnetic ground state. This frustrated many-body state stabilizes the ferromagnetic ground-state sector, providing the time-reversal--symmetry-broken background required for the nontrivial electronic structure. Consequently, the exchange-split topological bands and associated Berry-curvature response are intrinsically linked to the magnetic ground state. Our band dispersion calculations reveal a mirror symmetry-protected nodal line in the ${k}_{z}$ = 0 plane. When spin-orbit coupling is introduced, a gap is formed along the nodal line due to broken time-reversal symmetry with magnetic ordering, leading to substantial intrinsic Berry curvature. We identify Dirac fermions, van Hove singularities, and a flat band near the Fermi energy $({E}_{F})$, with spin-orbit coupling introducing a finite gap at key points. The unique proximity of the flat band to ${E}_{F}$ suggests potential instabilities. Spin-orbit coupling opens a 10 meV gap at the point of contact between the quadratic and flat bands, bestowing a nonzero ${\mathbb{Z}}_{2}$ invariant. This leads to a significant spin Hall conductivity. Despite the presence of large incoherent scattering due to electronic interactions, band crossings and flat band features persist at finite temperatures since the scattering does not impact these features near ${E}_{F}$. ${\mathrm{MgMn}}_{6}{\mathrm{Sn}}_{6}$ exhibits intriguing topological and magnetic properties, with promising applications in spintronics.