🔬 materials science

Modulation of the Nernst Thermoelectrics by Regulating the Anomalous Hall and Nernst Angles

This study proposes and experimentally validates a strategy to optimize the anomalous Nernst conductivity in magnetic topological materials by regulating the interplay between the tunable anomalous Nernst angle and the stable anomalous Hall angle, as demonstrated in iron-doped Co3Sn2S2.

Original authors: Meng Lyu, Junyan Liu, Jianlei Shen, Shen Zhang, Yang Liu, Jinying Yang, Yibo Wang, Yiting Feng, Binbin Wang, Hongxiang Wei, Enke Liu

Published 2026-07-02

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CC BY 4.0

Original authors: Meng Lyu, Junyan Liu, Jianlei Shen, Shen Zhang, Yang Liu, Jinying Yang, Yibo Wang, Yiting Feng, Binbin Wang, Hongxiang Wei, Enke Liu

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

The Big Picture: Turning Heat into Electricity (Sideways)

Imagine you have a block of metal. If you heat one side and cool the other, electricity usually flows straight from the hot side to the cold side. This is the standard way we make thermoelectric power.

But in certain special "magnetic" materials, something cooler happens: the electricity doesn't just flow straight; it flows sideways, perpendicular to the heat flow. This is called the Nernst Effect.

The scientists in this paper wanted to make this "sideways electricity" much stronger. They discovered a clever trick to do it by tuning two invisible "angles" inside the material so they work together instead of fighting each other.

The Material: A Magnetic "Kagome" Lattice

The material they studied is called Co3Sn2S2. Think of this material as a complex, 3D sandwich:

The "bread" is made of Sulfur atoms.
The "filling" is layers of Cobalt and Tin atoms.
The Cobalt atoms are arranged in a specific pattern called a Kagome lattice (named after a Japanese woven basket pattern).

This specific pattern creates a "topological" environment, which is like a highway for electrons where they can move very efficiently. In this highway, the electrons behave like they are in a magnetic field even when there isn't one, creating a huge "sideways" push.

The Problem: The "Tug-of-War"

To understand what the scientists fixed, imagine two teams of people pushing a heavy cart:

Team A (The Hall Team): They always push the cart to the Right. Their direction is very stable and doesn't change easily.
Team B (The Nernst Team): They push the cart either to the Right or the Left, depending on the temperature and the material's internal settings.

In the original, pure material (without any extra ingredients), Team B was pushing Left while Team A pushed Right. Because they were pushing in opposite directions, they canceled each other out. The cart (the electricity) barely moved. This is called "cancellation."

The Solution: Adding a "Flavor" Ingredient

The scientists decided to add a tiny amount of Iron (Fe) into the material, replacing some of the Cobalt atoms. Think of this like adding a pinch of salt to a soup to change its flavor profile.

Here is what happened when they added the Iron:

Shifting the Chemical Potential: Adding the Iron changed the "chemical potential" of the material. In our analogy, this is like shifting the starting line of the race.
The Sign Flip: This shift caused Team B (The Nernst Team) to suddenly change their mind. Instead of pushing Left, they started pushing Right.
Working Together: Now, both Team A and Team B were pushing the cart to the Right. Instead of canceling each other out, they added their strength together.

The Result: A Massive Boost

Because the two teams were finally working in the same direction, the "sideways electricity" (the Anomalous Nernst Conductivity) became 82.4% stronger at a specific amount of Iron doping.

The scientists also found that:

It's Intrinsic: This boost wasn't just a fluke or a surface effect; it came from the deep, fundamental physics of the material's structure (specifically the "Berry curvature," which is like the shape of the road the electrons travel on).
A Universal Rule: They noticed a specific mathematical pattern (a "TlnT" law) that appears in many magnetic materials, suggesting this is a common rule of nature for these types of materials.

The Takeaway

The paper doesn't claim to have built a new power plant yet. Instead, it offers a blueprint for how to fix these materials.

The main lesson is: If you have a material where two effects are fighting each other (canceling out), you can tune the material (by adding small amounts of other elements) to flip the direction of one effect so that both effects help each other.

This gives scientists a new "recipe" to make better thermoelectric materials in the future, simply by making sure the internal "angles" of the material are aligned to push in the same direction.

Technical Summary: Modulation of the Nernst Thermoelectrics by Regulating the Anomalous Hall and Nernst Angles

Problem Statement
While magnetic Weyl semimetals exhibit large anomalous Nernst conductivity (ANC) due to significant intrinsic Berry curvature, experimental strategies to optimize Nernst thermoelectric performance remain limited. Although substantial ANC values have been reported in materials like Co3Sn2S2, the mechanisms for enhancing these values through chemical tuning are not fully understood. Furthermore, while extrinsic scattering effects are known to influence the anomalous Hall conductivity (AHC), their specific impact on the ANC and the interplay between different transport angles in these systems require further investigation.

Methodology
The study focuses on the magnetic Weyl semimetal Co3Sn2S2, specifically investigating the effects of iron (Fe) doping on its transverse thermoelectric properties.

Sample Preparation: Single crystals of Co3-xFexSn2S2 were grown using a high-temperature Pb and Sn mixed flux method with Fe doping levels (x) of 0, 0.05, 0.10, 0.15, and 0.20.
Transport Measurements: Comprehensive electrical and thermoelectric measurements were conducted between 2 K and room temperature. This included longitudinal resistivity ( $\rho_{xx}$ ), Hall resistivity ( $\rho_{yx}$ ), Seebeck coefficient ( $S_{xx}$ ), and Nernst signal ( $S_{yx}$ ).
Data Analysis: The anomalous Nernst conductivity ( $\alpha_{yx}^A$ ) was calculated using measured parameters via the relation $\alpha_{yx}^A = (S_{yx}^A \rho_{xx} - S_{xx} \rho_{yx}^A) / (\rho_{xx}^2 + \rho_{yx}^{A2})$ . The study also decomposed $\alpha_{yx}^A$ into constituent terms involving the anomalous Hall angle ( $\tan \theta_H^A$ ) and the anomalous Nernst angle ( $\tan \theta_N^A$ ).
Theoretical Comparison: The experimental results were compared with Density Functional Theory (DFT) calculations and the Tian-Ye-Jin (TYJ) model to distinguish between intrinsic and extrinsic contributions. The temperature dependence of $\alpha_{yx}^A/T$ was analyzed against a $T \ln T$ scaling law.

Key Contributions and Results

Significant Enhancement of ANC: The study demonstrates that increasing the Fe content to $x = 0.15$ enhances the maximum ANC by 82.4%, rising from 1.59 A m $^{-1}$ K $^{-1}$ (pristine) to 2.9 A m $^{-1}$ K $^{-1}$ .
Mechanism of Optimization via Angle Regulation: A central finding is that the magnitude of ANC is directly related to the sum of the anomalous Nernst and Hall angles ( $\tan \theta_H^A + \tan \theta_N^A$ $tan θ_{H}^{A} + tan θ_{N}^{A}$ ).
- In pristine Co3Sn2S2, these two angles possess opposite signs, leading to a cancellation effect that suppresses the total ANC.
- Fe doping induces a sign change in the anomalous Nernst angle ( $\tan \theta_N^A$ ), shifting it from negative to positive, while the anomalous Hall angle ( $\tan \theta_H^A$ ) remains positive.
- This alignment allows the two terms to work in concert rather than canceling each other, significantly boosting the total conductivity.
Intrinsic Origin and Chemical Potential Tuning:
- The study identifies a robust $T \ln T$ scaling law for $\alpha_{yx}^A/T$ in the 40–140 K range across all samples, consistent with intrinsic Berry curvature contributions found in other magnetic topological materials.
- Comparison with DFT calculations and Mott relation analysis indicates that Fe-hole doping lowers the chemical potential. This shift moves the chemical potential relative to the Weyl nodes and van Hove singularities, causing the sign reversal of the Berry curvature contribution to the Nernst signal.
- Unlike the AHC, where extrinsic contributions become dominant at higher Fe doping levels, the ANC in this system is confirmed to be primarily derived from intrinsic topological bands.
General Applicability: The analysis of various magnetic topological materials (e.g., MnBi, Fe3GeTe2) suggests that the cancellation of $\tan \theta_H^A$ and $\tan \theta_N^A$ is a common feature. The study proposes that tuning these angles to share the same sign is a viable scheme for optimizing Nernst thermoelectrics in a broad class of materials.

Significance
The paper claims that its primary contribution is the identification of a practical method to optimize Nernst thermoelectrics by regulating the signs of the anomalous Hall and Nernst angles. By demonstrating that chemical doping can intrinsically tune the anomalous Nernst angle to align with the anomalous Hall angle, the research offers a specific pathway to overcome the "Sondheimer cancellation" often observed in these systems. Additionally, the work reinforces the utility of Nernst effect measurements as a probe for topological band structures and Berry curvature, particularly given the robustness of the intrinsic ANC against small chemical potential shifts compared to the AHC. The findings provide a theoretical and experimental framework for material scientists to enhance the transverse thermoelectric performance of magnetic Weyl semimetals.