Correlated topological band structures of the kagome altermagnets Mn$_3X$ ($X=$ Sn, Ge, Ga)

Abstract

The interplay of topological band structures and electronic correlations may lead to novel quantum phenomena with potential applications. First-principles calculations are critical for guiding experimental discoveries and interpretations, but often fail if electronic correlations cannot be properly treated. Here we show that this issue occurs also in the kagome altermagnets Mn$_3X$ ($X=$ Sn, Ge, Ga), which were believed to exhibit large anomalous Hall effect due to topological band structures with Weyl nodes near the Fermi energy. Our systematic investigations reveal critical importance of beyond-DFT treatments on three key aspects of their magnetic, electronic, and topological properties: (1) establishment of noncollinear altermagnetic orders, (2) weakly renormalized band structures in excellent agreement with angle-resolved photoemission spectroscopy experiment, and (3) sensitive tuning of the Weyl nodes. Our work provides a unified basis for understanding topological properties of the Mn$_3X$ family, which challenges previous experimental interpretations based on DFT band structures and predicts potentially higher anomalous Hall conductivity in Mn$_3$Ga under electron doping. This underscores the importance of a correlation-aware framework beyond DFT in understanding topological magnetic materials.

Figures (6)

• Figure 1: Crystal and magnetic properties.a Illustration of the crystal structure of Mn$_3X$ with inverse triangular AFM configurations showing inverse symmetry between two adjacent layers VESTA. b Symmetry of the inverse triangular AFM order for two spin configurations, AFM1 and AFM2. Three planes are shown for $M_zT$ (magenta), $M_x$ (yellow), and $M_xT$ (green), where $M_x$ and $M_z$ are mirror operations and $T$ is the time reversal operation. c The spin moment of a single Mn-ion in Mn$_3$Sn for different choices of $U$ and $J$ calculated using DFT+DMFT at 300 K.
• Figure 2: Effect of the Hund's rule coupling on the Mn-ionic states and band renormalization.a, b Probabilistic distribution of the DMFT state of Mn$_3$Sn on different Mn-ionic configurations with the electron occupancy $N=4$, 5, 6 with ($J=0.55\,$eV) and without the Hund's rule coupling at $U =6\,$eV. The horizontal axis denotes their respective energy difference with respect to the configuration of largest probability. The insets show the distribution of $N=5$ state on the local $z$-component of the total spin, $S_z$. c Illustration of the fourth-order polynomial fitting (solid and dashed lines) to the imaginary part of the orbital-averaged self-energy as a function of the Matsubara frequency for $U=6\,$eV and $J=0.55\,$eV for Mn$_3$Sn. d The renormalization factor $Z$ estimated from the DFT+DMFT self-energies with varying $U$ and $J$ for Mn$_3$Sn. e Comparison of the spin moment per Mn-ion in Mn$_3$Sn, Mn$_3$Ge, and Mn$_3$Ga as functions of the Hund's rule coupling $J$ calculated using DFT+DMFT for a fixed $U=6\,$eV at 300 K. f Comparison of their renormalization factor $Z$ extracted from the DFT+DMFT self-energies with varying $J$ for $U=6\,$eV at 300 K.
• Figure 3: Comparison of ARPES Kuroda2017NM and DFT+DMFT band structures in Mn$_3$Sn. Intensity map of the theoretical and experimental spectral functions along: a, b the high-symmetry $\Gamma$-K-M-K-$\Gamma$ line (cyan arrows in the inset of a); c the high-symmetry M-K-$\Gamma$-K-M line (magenta arrows in the inset of a); d-f the $k_x$ direction with $|\Delta k_{y}|=0.072\,(2\pi/a)$ slightly off the $\Gamma$-K-M-K-$\Gamma$ path; g the $k_x$ direction with $\Delta k_{y}=-0.144\,(2\pi/a)$ from $\Gamma$-K-M-K-$\Gamma$; h the high-symmetry H-K-H line. The arrows of different colors highlight some characteristic features of excellent agreement. i Comparison of the theoretical and experimental Fermi surface mapping in the $k_z=0$ plane. To mimic the low resolution of the ARPES data, we have intentionally chosen the DFT+DMFT results at 300 K. The calculated Fermi surfaces are qualitative the same at 60 K. The yellow line in the left one indicates the hexagonal Brillouin zone. The red curves show the DFT-predicted Fermi surfaces reproduced from Ref. Kuroda2017NM.
• Figure 4: Effect of the Hund's rule coupling on the Weyl points in Mn$_3$Sn.a Illustration of the selected $\mathbf{k}$-paths marked by dashed lines of different colors on the $k_z=0$ plane of the Brillouin zone. b The spectral function along the high-symmetry line L-A-$\Gamma$-K-M-K-M$'$-A, where $\Gamma$-K-M-K-M$'$ is denoted by the red dashed line in a. The solid (dashed) arrow marks the band crossing (gap). c Comparison of the spectral functions along $\Gamma$-K-M (orange dashed line) and the line shifted by $\Delta k_{y}=-0.072\,(2\pi/a)$ (green dashed line). Note that the orange $\Gamma$-K-M line is different from the red one because of the lack of six-fold rotational symmetry. d Comparison of the spectral function along K-M$'$-K (blue dashed line) and the line shifted by $\Delta k_{1}=-0.072\,(2\pi/a)$ (purple dashed line). e, f The band maps on the $k_z=0$ plane at $E=9\,$meV for $J=0.6\,$eV and $E=50\,$meV for $J=0.55\,$eV, illustrating the evolution of the band crossings with the Hund's rule coupling.
• Figure 5: DFT+DMFT electronic band structures of Mn$_3$Ge and Mn$_3$Ga.a, b The DFT+DMFT spectral function along the high-symmetry line L-A-$\Gamma$-K-M-K-M$'$-A for Mn$_3$Ge with the AFM2 order at $J=0.66\,$eV, $U=6\,$eV, $T=300\,$K and Mn$_3$Ga with the lower-symmetry configuration at $J=0.6\,$eV, $U=6\,$eV, $T=300\,$K. c Band crossings of Mn$_3$Ge along the path shifted by $\Delta k_y = -0.090$ and -0.126 (2$\pi$/a) away from $\Gamma$-K-M (orange dashed line in Fig. \ref{['fig4']}a) for $U=6\,$eV and $J = 0.66\,$eV. d Gap opening at $J=0.68\,$eV in Mn$_3$Ge, showing sensitive tuning by the Hund's rule coupling. e, f Comparison of the band structures of Mn$_3$Ga along $\Gamma$-K-M and that shifted by $\Delta k_y = -0.072$ (2$\pi$/a) (green dashed line in Fig. \ref{['fig4']}a) for $U=6\,$eV and $J = 0.6$ and 0.7 eV, respectively. The solid arrows mark the band crossing and the dashed arrows mark the gap.