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 ($η$) 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.

💡 Research Summary

In this work, the authors investigate how the anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) of the compensated ferrimagnetic Heusler compound Mn₃Al can be tuned by applying isotropic strain (η) and by shifting the chemical potential (μ). Using density‑functional theory within the GGA‑PBE approximation, including spin‑orbit coupling, they first obtain self‑consistent electronic structures on a 15³ k‑grid. Maximally‑localized Wannier functions are then constructed for 38 orbitals spanning 72 bands, enabling a high‑resolution Berry‑curvature calculation on a 300³ k‑mesh via WannierBerri. The anomalous Hall conductivity (AHC) is evaluated by integrating the Berry curvature over all occupied states, while the anomalous Nernst conductivity (ANC) is obtained by weighting the same curvature with the entropy factor of the Fermi‑Dirac distribution (or, equivalently, via the Mott relation at low temperature).

A key finding is that at a chemical potential of μ = –0.3 eV the band structure hosts three distinct topological entities simultaneously: Weyl points, symmetry‑protected nodal lines, and gapped nodal lines. These features appear along high‑symmetry directions (Γ–M, X–W, X–P) of the magnetic Brillouin zone defined by the magnetic space group I4/mm′m′ (No. 139.537). The Weyl points arise where the four‑fold rotation about the z‑axis is broken (e.g., along X–P), while the nodal lines are protected on mirror planes (e.g., X–W). Spin‑orbit coupling opens gaps in some nodal lines, creating additional Berry‑curvature hot spots.

The Berry curvature is found to be highly anisotropic: the k_y–k_z plane dominates the contribution to the AHC, whereas the k_x–k_y plane plays a minor role. Under tensile strain (η > 0) the separation between Weyl nodes increases, the curvature hot spots become more intense, and the AHC reaches values as large as –1200 (Ω·cm)⁻¹ (negative sign reflecting the chosen coordinate convention). Compressive strain (η < 0) reduces the magnitude of the AHC and can even change its sign in certain μ windows. When μ is set to the pristine Fermi level, the AHC varies between –300 and –1200 (Ω·cm)⁻¹ as strain is swept from –5 % to +5 %.

The ANC exhibits an even richer strain dependence. At μ = E_F the ANC changes sign around η ≈ –2 % and again near η ≈ +3 %, reflecting the delicate balance between positive and negative Berry‑curvature contributions. At μ = –0.3 eV the ANC is strongly negative (≈ –2.9 A·K⁻¹·m⁻¹) for most strain values, with a quasi‑quadratic dependence on η and a shallow minimum near zero strain. This behavior is consistent with the Mott relation, which links the energy derivative of the AHC to the ANC; the steep μ‑dependence of the AHC around –0.3 eV amplifies the ANC.

Despite the pronounced changes in transport coefficients, the underlying electronic band structure and Fermi‑surface topology remain remarkably robust under the applied strains. Detailed Fermi‑surface analysis shows that the four main sheets (labeled α, β, γ, δ) retain their overall shape, while the distribution of Berry‑curvature hot spots on these sheets shifts dramatically. For example, under tensile strain the β and δ sheets in the k_y–k_z plane approach each other, creating large negative curvature regions that drive the enhanced AHC and ANC.

The authors conclude that Mn₃Al provides an ideal platform for Berry‑curvature engineering: its compensated magnetic order eliminates stray fields, its Heusler lattice allows facile strain application (e.g., via epitaxial growth or hydrostatic pressure), and modest chemical doping can shift μ to the optimal –0.3 eV region where multiple topological features coexist. The demonstrated strain‑induced amplification of AHE and the sign‑tunable ANE suggest promising routes toward low‑power spintronic devices that exploit transverse charge and heat currents without external magnetic fields. Future experimental work—such as strain‑controlled transport measurements, angle‑resolved photoemission to locate Weyl points, and doping studies—will be crucial to validate the predictions and to harness Mn₃Al’s topological transport phenomena in practical applications.