Strain tunable anomalous Hall and Nernst conductivities in compensated ferrimagnetic Mn$_3$Al

TL;DR

This work addresses whether a compensated ferrimagnet can exhibit tunable Berry-curvature–driven transport under strain and doping. Using first-principles calculations with Wannier interpolation, the authors show that Mn$_3$Al at $μ≈−0.3$ eV simultaneously hosts Weyl points, nodal lines, and gapped nodal lines, leading to a Berry-curvature landscape that is highly sensitive to isotropic strain. The anomalous Hall conductivity is dominated by curvature in the $k_y k_z$ plane and can be enhanced to about $−1200$ (Ω cm)−1 under tensile strain, while the anomalous Nernst conductivity changes sign near the Fermi level and grows with doping. These results demonstrate Berry-curvature engineering in a compensated ferrimagnet and highlight Mn$_3$Al as a model system for strain- and doping-tuned topological transport with potential spintronic applications.

Abstract

The tunability of anomalous Hall and Nernst conductivities is investigated in the compensated ferrimagnet Mn$_3$Al under isotropic strain ($η$) and chemical potential variation using first-principles calculations. At a chemical potential of $μ= -0.3$ eV, three distinct topological features -- Weyl points, nodal lines, and gapped nodal lines -- are simultaneously realized along high-symmetry directions of the Brillouin zone in the framework of magnetic space group. The anomalous Hall conductivity (AHC) is found to be predominantly governed by the Berry curvature in the $k_y k_z$ plane and can be enhanced significantly under tensile strain, reaching $-1200$ $(Ω~\mathrm{cm})^{-1}$. On the other hand, the anomalous Nernst conductivity (ANC) shows a sign change near the Fermi level and whose magnitude increases at $μ= -0.3$ eV with quasi-quadratic strain dependence. Regardless of strain, the underlying bands and Fermi surface structures remain robust, while the distribution and magnitude of Berry curvature evolve substantially. These results underscore the potential of Mn$_3$Al, a compensated ferrimagnet, as a platform for Berry curvature engineering via strain and doping.

Figures (5)

• Figure 1: (a) Crystal structure of Mn$_3$Al with magnetization along [$001$]. Mn(I), Mn(II), and Al are in blue, red, and gray spheres, respectively, with magnetic moments shown in arrows. Green line denotes cube formed by Mn(I) and Al, where Mn(II) is at the center of the cube. (b) Brillouin zone of Mn$_3$Al of magnetic space group $I4/mm'm'$ (No. 139.537). High symmetry points, symmetrically equivalent in space group but distinct in magnetic space group, are distinguished by colors.
• Figure 2: (a) $k$ projected Berry curvature of Mn$_3$Al without strain. Symmetrically distinct $k$ points are distinguished by colors in black, blue, and red. Shade boxes denote: crossing (in yellow) and avoided crossing (in blue). Crossing are further classified into crossing and Weyl points (see text). (b) (001) plane in Brillouin zone containing $X-W$, where crossing is denoted in yellow box. (c) (100) plane in Brillouin zone containing $X-P$ and $G-M$, which are Weyl point and avoided crossing, respectively. In insets of (b) and (c), group of $k$ and representation of bands are shown, where color of bands are $k$ resolved Berry curvature.
• Figure 3: (a) Anomalous Hall conductivity ($\sigma_{xy}$) and (b) anomalous Nernst conductivity ($\alpha_{xy}$) as function of strain and chemical potential in color contour. Solid and dashed lines correspond to $\mu=E_F$ and $\mu=E_F - 0.3$ eV, respectively. (c) $\sigma_{xy}$ and (d) $\alpha_{xy}$ with respect to strain for $\mu=E_F$ (solid line with filled symbol) and $\mu=E_F - 0.3$ eV (dashed line with open symbols), respectively.
• Figure 4: Contour of Berry curvature when $\mu=E_F$ for $\eta=-5$, $0$, and $+5\%$ from left to right column. Upper panel: $\Omega_{xy}({\bf k})$ on $k_xk_y$ plane ($001$) and lower panel: contour on $k_yk_z$ plane ($100$). Red (blue) color denotes positive (negative) $\Omega_{xy}({\bf k})$. Yellow line is for Brillouin zone boundary. Fermi surface is shown in black lines, where individual Fermi sheets are labeled by $\alpha$, $\beta$, $\gamma$, and $\delta$. High symmetry point labeled in black, red, and blue are consistent with Fig. \ref{['fig:2']}.
• Figure 5: Contour of Berry curvature when $\mu=E_F-0.3$ eV for $\eta=-5$, $0$, and $+5\%$. Upper panel: $\Omega_{xy}({\bf k})$ near the $k_xk_y$ plane ($001$) and lower panel: contour on $k_yk_z$ plane ($100$). Red (blue) color denotes positive (negative) $\Omega_{xy}({\bf k})$. Yellow line is for Brillouin zone boundary. Fermi surface is shown in black lines, where individual Fermi sheets are labeled by $\alpha'$, $\beta'$, $\gamma'$, and $\delta'$. High symmetry point labelled in black, red, and blue are consistent with Fig. \ref{['fig:2']}.