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

The tunability of anomalous Hall and Nernst conductivities is investigated in the compensated ferrimagnet Mn${}_3$Al under isotropic strain ($\eta$) and chemical potential variation using first-principles calculations. At a chemical potential of $\mu =-0.3$ 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 $-1200$ $(\mathrm{\Omega }\mathrm{c}\mathrm{m}{)}^{-1}$. On the other hand, the anomalous Nernst conductivity (ANC) shows a sign change near the Fermi level and whose magnitude increases at $\mu =-0.3$ 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.