Exploring magnetic and topological complexity in MgMn$_6$Sn$_6$: from frustrated ground states to nontrivial Hall conductivity

TL;DR

This study investigates the complex magnetic and topological electronic properties of MgMn$_6$Sn$_6$, revealing frustrated magnetic states, topological band features, and significant spin Hall effects with potential spintronics applications.

Contribution

It provides a comprehensive theoretical analysis of MgMn$_6$Sn$_6$, uncovering its frustrated magnetic ground state, topological band structures, and the impact of spin-orbit coupling on its electronic properties.

Findings

Identification of a mirror symmetry-protected nodal line in the band structure.

Discovery of a SOC-induced gap leading to nontrivial topological invariants.

Prediction of significant spin Hall conductivity in MgMn$_6$Sn$_6$.

Abstract

We explore the intriguing topological itinerant magnet MgMn$_6$Sn$_6$, characterized by bilayer kagome Mn layers encasing a hexagonal Sn layer. Using \textit{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. Mn d-orbital electrons form a frustrated many-body ground state with significant quantum fluctuations, resulting in competing antiferromagnetic and ferromagnetic spin exchanges. Our band dispersion calculations reveal a mirror symmetry-protected nodal line in the \textit{k}$_z$ = 0 plane. When spin-orbit coupling (SOC) is introduced, the gap is formed along the nodal line lifted due to broken time-reversal symmetry with magnetic ordering, leading to substantial intrinsic Berry curvature. We identify Dirac fermions, van Hove singularities, and flat band near the Fermi energy (\textit{E}$_F$), with SOC introducing a finite gap at key points. The unique proximity of the flat band to \textit{E}$_F$ suggests potential instabilities. Spin-orbit coupling opens a 20 meV gap at the quadratic touching point between the Dirac and flat band, bestowing a nonzero 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. MgMn$_6$Sn$_6$ exhibits intriguing topological and magnetic properties, with promising applications in spintronics.