Anomalous Nernst and Righi-Leduc effects in Mn$_{3}$Sn: Berry curvature and entropy flow

Abstract: We present a study of electric, thermal and thermoelectric response in noncollinear antiferromagnet Mn${3}$Sn, which hosts a large Anomalous Hall Effect (AHE). Berry curvature generates off-diagonal thermal(Righi-Leduc) and thermoelectric(Nernst) signals, which are detectable at room temperature and invertible with a small magnetic field. The thermal and electrical Hall conductivities respect the Wiedemann-Franz law, implying that the transverse currents induced by Berry curvature are carried by Fermi surface quasi-particles. In contrast to conventional ferromagnets, the anomalous Lorenz number remains close to the Sommerfeld number over the whole temperature range of study, excluding any contribution by inelastic scattering and pointing to Berry curvature as the unique source of AHE. The anomalous off-diagonal thermo-electric and Hall conductivities are strongly temperature-dependent and their ratio is close to k${B}$/e.

Anomalous Nernst and Righi-Leduc Effects in Mn(_{3})Sn: A Study of Berry Curvature and Entropy Flow

The paper in question provides a detailed examination of the anomalous Nernst and Righi-Leduc effects in the noncollinear antiferromagnet Mn({3})Sn, with a focus on the role of Berry curvature in generating these effects. The study highlights the strong anomalous transverse responses in the electric, thermal, and thermoelectric conductivity of Mn({3})Sn, revealing how Berry curvature at the Fermi surface is crucial to the observed phenomenon.

Key Findings and Numerical Results

1. Anomalous Transverse Conductivities: The research shows that Mn({3})Sn exhibits a significant Anomalous Hall Effect (AHE) which can be attributed to Berry curvature. The anomalous Hall conductivity (AHC) measured is significant, with a peak magnitude of approximately 70 S/cm at 200 K for (\sigma^{A}{xz}) and 90 S/cm for (\sigma^{A}_{zy}).

2. Validity of the Wiedemann-Franz Law: The study observes that the Wiedemann-Franz (WF) law holds for the anomalous transverse responses in Mn(_{3})Sn. The Lorenz number for the anomalous conductivities remains near the Sommerfeld constant, (L_0 = \frac{\pi^2}{3} \left( \frac{k_B}{e} \right)^2), across a wide temperature range. This underscores that the transverse currents are carried by Fermi surface quasi-particles without substantial inelastic scattering contributions.

3. Temperature Dependence: There is a marked strong temperature dependence of the anomalous conductivities, which diminish significantly as temperature rises from 200 K to 400 K. This dependency suggests that while AHE is fundamentally a topological property, the actual magnitude may be influenced by external parameters like temperature, potentially due to shifts in the Weyl nodes' energy levels.

4. Anomalous Nernst Effect (ANE): The paper quantifies the anomalous thermoelectric response, with (\alpha^{A}_{ij}) demonstrating a faster increase than (\sigma^{A}_{ij}) as the system cools, reaching a temperature-dependent (\alpha^{A}{ij}/\sigma^{A}{ij}) ratio close to (k_B/e). This large ANE is critical, considering the relatively low mobility and large Fermi energy, showing the ANE to be substantially larger than what can be attributed to quasiparticles alone.

Implications and Theoretical Considerations

The findings of this study have significant implications for understanding the intrinsic AHE and the associated Berry curvature effects in nontraditional magnetic materials such as noncollinear antiferromagnets. The persistence of the WF law in Mn(_{3})Sn implies a topological origin for the AHE that is constrained to states at the Fermi surface, contrasting with earlier conjectures about contributions from the entire Fermi sea.

The research supports the viewpoint that the wavefunctions associated with Bloch electrons and their Berry curvature play an essential role in determining various transport phenomena, further stimulating theoretical investigations into electronic properties deeply influenced by topological considerations.

Future Directions

The study opens several avenues for further research. Experimentally, exploring the influence of external perturbations such as strain could provide more insights into tuning Berry curvature effects. Theoretically, further calculations to better understand the temperature-dependent behavior of both AHE and ANE and confirm the topological origins across different material classes would be valuable. Moreover, expanding such studies to other candidate Weyl semimetals or topological insulators could significantly advance the field of topological quantum materials, potentially leading to novel applications in thermoelectric technologies.