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

Xiaokang Li, Xu, Liangcai+6 more|arXiv (Cornell University)|Dec 19, 2016

Powder Metallurgy Techniques and MaterialsEngineering19 citations

TL;DR

This study investigates anomalous Nernst and Righi-Leduc effects in the noncollinear antiferromagnet Mn₃Sn, demonstrating that Berry curvature generates large transverse thermoelectric and thermal Hall responses detectable at room temperature. The anomalous conductivities obey the Wiedemann-Franz law, confirming that Berry curvature—rather than inelastic scattering—drives the anomalous Hall effect, with the ratio of anomalous Hall to thermoelectric conductivity closely matching k_B/e.

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.

Motivation & Objective

• To investigate the existence and magnitude of anomalous Nernst and Righi-Leduc effects in Mn₃Sn, a noncollinear antiferromagnet with a large anomalous Hall effect.
• To determine whether the anomalous transverse transport coefficients are governed by Berry curvature or inelastic scattering processes.
• To test the validity of the Wiedemann-Franz law in Mn₃Sn and compare it with conventional ferromagnets like Fe and Ni.
• To quantify the relationship between anomalous Hall conductivity and anomalous thermoelectric conductivity, linking it to the location of Weyl nodes.

Proposed method

• Measured longitudinal and transverse transport coefficients (resistivity, thermal conductivity, Seebeck coefficient) in Mn₃Sn single crystals under varying magnetic fields and temperatures.
• Used resistivity tensor and Seebeck-Nernst tensor data to compute off-diagonal anomalous conductivities via matrix inversion: α_xz ≈ (ρ_zz S_xz - ρ_xz S_zz)/(ρ_xx ρ_zz).
• Extracted anomalous Righi-Leduc thermal conductivity using the relation κ_xz ≈ -κ_xx(B)κ_zz(B)ΔT_x(B)t / (I²R), derived from thermal current balance under transverse temperature gradients.
• Applied field-cooling magnetization measurements to confirm magnetic ordering at T_N = 420 K and weak ferromagnetic remanence above T₁ = 200 K.
• Compared the anomalous Lorenz number (L^A = α^A² / (σ^A κ)) in Mn₃Sn with that in Fe and Ni to assess the role of inelastic scattering.
• Used theoretical models to interpret the ratio of anomalous Hall to thermoelectric conductivity as a probe of Weyl node positions.

Experimental results

Research questions

• RQ1 Does the anomalous Nernst effect in Mn₃Sn arise from Berry curvature, and is it measurable at room temperature?
• RQ2 To what extent do the anomalous thermal and thermoelectric conductivities in Mn₃Sn obey the Wiedemann-Franz law?
• RQ3 Is inelastic scattering a significant contributor to the anomalous Hall effect in Mn₃Sn, as it is in conventional ferromagnets?
• RQ4 What is the relationship between the anomalous Hall conductivity and the anomalous thermoelectric conductivity, and how does it inform the location of Weyl nodes?
• RQ5 Can the ratio of anomalous Hall to thermoelectric conductivity be used as a diagnostic tool for the underlying Berry curvature distribution?

Key findings

• The anomalous Righi-Leduc conductivity in Mn₃Sn is large and detectable at room temperature, with a magnitude consistent with the Wiedemann-Franz law over an extended temperature range.
• The anomalous Lorenz number remains close to the Sommerfeld value (k_B²/e²) across the entire temperature range studied, indicating that inelastic scattering does not contribute to the anomalous transport, thus confirming Berry curvature as the sole source of the anomalous Hall effect.
• The ratio of anomalous Hall conductivity (σ^A) to anomalous thermoelectric conductivity (α^A) is quantitatively close to k_B/e, supporting a direct link between Berry curvature and transverse transport.
• The anomalous off-diagonal conductivities are strongly temperature-dependent, with the anomalous Nernst effect showing a clear temperature evolution consistent with Berry curvature-driven transport.
• The Wiedemann-Franz law holds in Mn₃Sn, distinguishing the Fermi-surface picture of anomalous transport from the Fermi-sea picture, which does not necessarily obey this law.
• The measured transport coefficients are consistent with a magnetic structure involving a triangular spin arrangement stabilized by Dzyaloshinskii-Moriya interaction, with possible chiral spin reorientation under magnetic field.