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

First-principles calculations demonstrate that isotropic strain and chemical potential tuning in the compensated ferrimagnet Mn $_3$ Al significantly enhance and modulate its anomalous Hall and Nernst conductivities by manipulating the distribution of Berry curvature associated with coexisting Weyl points, nodal lines, and gapped nodal lines.

Original authors: Guihyun Han, Minkyu Park, S. H. Rhim

Published 2026-02-05

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CC BY 4.0

Original authors: Guihyun Han, Minkyu Park, S. H. Rhim

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a tiny, invisible city built inside a crystal called Mn3Al. In this city, electrons (the tiny particles that carry electricity) don't just run in straight lines; they dance in complex patterns determined by the city's architecture and its magnetic rules.

This paper is like a mapmaker's report on how to change the "traffic flow" of these electrons by stretching the city or changing the "fuel" (chemical potential) available to them. Here is the story in simple terms:

1. The City and Its Rules

The crystal is made of Manganese and Aluminum atoms arranged in a specific 3D grid. It's a special kind of magnet called a compensated ferrimagnet.

The Analogy: Think of this city as having two groups of citizens: Group A (Manganese atoms) who want to run North, and Group B (Manganese atoms) who want to run South. They are equally strong, so the city as a whole doesn't pull in any one direction (zero net magnetism). However, because they are running in opposite directions, they create a hidden, swirling current inside the city that can be used for technology.

2. The "Traffic Hubs" (Topological Features)

The researchers found that at a specific energy level (like a specific time of day), the electrons encounter three special types of "traffic hubs" where their paths cross or loop in unique ways:

Weyl Points: Like a perfect, single intersection where two roads cross exactly.
Nodal Lines: Like a circular highway where the roads merge into a continuous loop.
Gapped Nodal Lines: Like a highway that is almost a loop but has a small bridge (gap) over it.

These hubs are protected by the city's symmetry rules. If you try to break the rules, the hubs disappear, but if you keep the rules, they stay.

3. Stretching the City (Strain)

The team tested what happens if you gently stretch or squeeze this crystal city (called "strain").

The Analogy: Imagine the city is made of a stretchy rubber sheet. If you pull it (tensile strain) or push it (compressive strain), the roads get longer or shorter, and the intersections move.
The Result: They found that stretching the city makes the "traffic" of electricity flow much more efficiently in a sideways direction (the Anomalous Hall Effect).
- Without stretching, the flow is good.
- With stretching, the flow becomes twice as strong (reaching a value of -1200). It's like widening a highway to allow twice as many cars to pass through at once.

4. The "Temperature" Switch (Nernst Effect)

They also looked at what happens when you heat the city slightly (the Anomalous Nernst Effect).

The Analogy: Imagine the electrons are like water. Usually, if you heat one side of a pipe, the water flows one way. But in this crystal, depending on how much you stretch it and where the "fuel" level is, the water can suddenly reverse direction and flow the other way.
The Result: At a specific energy level, stretching the crystal changes the direction of this heat-driven flow and makes it much stronger. It's like a switch that flips the direction of the current just by pulling on the material.

5. The Secret Ingredient: Berry Curvature

Why does this happen? The paper explains it using a concept called Berry Curvature.

The Analogy: Imagine the road map isn't flat; it's actually a bumpy, curved surface (like a saddle or a bowl). Even if the cars (electrons) try to drive straight, the shape of the road forces them to drift sideways.
The Discovery: The researchers found that while the roads (the electron paths) stay mostly the same when you stretch the crystal, the shape of the bumps (the Berry curvature) changes dramatically.
- When they stretch the crystal, the "bumps" get steeper and more concentrated in certain areas (specifically on the side walls of the city, the kykz plane).
- These steeper bumps are what force the electrons to move sideways with much greater force.

Summary

The paper claims that by taking a specific crystal (Mn3Al) and simply stretching it, you can:

Create a super-efficient sideways electric current.
Flip the direction of heat-driven currents.
Do this without needing any external magnets.

The "magic" isn't in building new roads, but in reshaping the invisible hills and valleys (Berry curvature) that guide the electrons, turning a standard material into a highly tunable tool for future electronics.

Technical Summary: Strain Tunable Anomalous Hall and Nernst Conductivities in Compensated Ferrimagnetic Mn3Al

Problem Statement
While compensated ferrimagnets and antiferromagnets are recognized as promising candidates for spintronic applications due to their vanishing net magnetization and robust Berry curvature, the specific evolution of their anomalous transport properties under external tuning remains insufficiently understood. Specifically, the coexistence of multiple topological features (such as Weyl points and nodal lines) and their impact on the anomalous Hall conductivity (AHC) and anomalous Nernst conductivity (ANC) in Mn3Al under isotropic strain and chemical potential variation has not been fully clarified. Previous studies identified symmetry-protected Berry curvature hot spots in Mn3Al but did not explore how these features and the resulting transport coefficients respond to strain or doping.

Methodology
The authors employed first-principles calculations using the Vienna ab initio simulation package (VASP) with spin-orbit coupling included. The exchange-correlation energy was treated using the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) parameterization. The optimized lattice constant was determined to be 5.78 Å. Following self-consistent calculations, maximally-localized Wannier functions (MLWFs) were constructed using Wannier90 to interpolate the electronic structure. Berry curvature was computed via Wannier interpolation using a dense $300 \times 300 \times 300$ k-grid with the WannierBerri package. The AHC and ANC were calculated by summing the Berry curvature over occupied states and incorporating the fermion entropy, respectively, within the framework of the magnetic space group $I4/mm'm'$ (No. 139.537).

Key Contributions and Results

Topological Features: At a chemical potential of $\mu = -0.3$ eV, the study reveals that Mn3Al simultaneously hosts three distinct topological features along high-symmetry directions of the magnetic Brillouin zone: Weyl points, nodal lines, and gapped nodal lines. These features arise from the specific magnetic symmetry ($I4/mm'm'$), which renders certain high-symmetry paths (e.g., $\Gamma-M$ ) four-fold rotationally symmetric while others (e.g., $\Gamma-X$ ) are not, leading to band crossings, Weyl points, or avoided crossings depending on the path.
Strain-Dependent AHC: The anomalous Hall conductivity is found to be predominantly governed by the Berry curvature in the $k_y k_z$ plane. Under tensile strain, the AHC is significantly enhanced. Specifically, at $\mu = -0.3$ eV, the magnitude of the AHC increases monotonically with tensile strain, reaching approximately $-1200 \, (\Omega\text{cm})^{-1}$ at $\eta = +5\%$ . In contrast, at the Fermi level ( $\mu = E_F$ ), the AHC exhibits a different strain dependence, peaking at compressive strain ( $\eta = -2\%$ ) with a value of $830 \, (\Omega\text{cm})^{-1}$ .
Strain-Dependent ANC: The anomalous Nernst conductivity displays a sign change near the Fermi level. At $\mu = E_F$ , the ANC transitions from negative to positive values under compressive strain before becoming negative again under high tensile strain. However, at $\mu = -0.3$ eV, the ANC exhibits a quasi-quadratic dependence on strain, reaching a local minimum of $-2.92 \, (\text{A/K m})$ near zero strain.
Fermiology and Robustness: Despite substantial variations in the magnitude and distribution of the Berry curvature under strain, the underlying band structures and Fermi surface topologies remain robust. The study details how Fermi surface sheets ( $\alpha, \beta, \gamma, \delta$ ) evolve with strain, noting that while the overall topology is retained, the specific connectivity and degeneracy of these sheets change, driving the variations in transport coefficients.

Significance
The paper concludes that Mn3Al, as a compensated ferrimagnet, serves as a viable platform for Berry curvature engineering through strain and doping. The findings demonstrate that the interplay between symmetry, topology, and tunable parameters like isotropic strain and chemical potential can be used to modulate transverse transport responses. The ability to simultaneously realize multiple topological features and significantly enhance the AHC (up to $-1200 \, (\Omega\text{cm})^{-1}$ ) without altering the fundamental robustness of the band structure highlights the potential of Mn3Al for strain-engineered spintronic applications.