Transverse transport effects such as anomalous Hall and Nernst effects are effective probes to topological texture in electronic band structures. In particular, large Berry curvature originating from Weyl nodes or nodal line structures is known to enhance these effects significantly. In contrast to the Hall conductivity σ_yx, which measures the summation of the Berry curvature below Fermi energy, the transverse thermoelectric conductivity α_yx sensitively captures the Berry curvature in the vicinity of the Fermi energy [1]. Therefore, the Nernst effect provides complementary information about the characteristics of the topological band structure. Moreover, scaling behavior α_yx ~ -T logT is recently reported in ferromagnet Co₂MnGa [2]. This anomaly is attributed to the Weyl semimetal state tuned close to the quantum Lifshitz critical point. However, the universality of this critical behavior is still yet to be confirmed experimentally.

Here, we report magnetic, transport, and thermoelectric properties of single crystals of ferromagnetic CoMnSb with a high Curie temperature of 470 K [3]. The actual experimental crystal structure of CoMnSb is a 2×2×2 superstructure of the previously predicted half-Heusler structure. Since theoretical understanding of the transverse transport phenomena in the superstructure CoMnSb is lacking, we performed first-principles calculation of superstructure CoMnSb to compare with experimental results.

Fig. 1. Temperature T dependence of (a) the Hall conductivity σ_yx, and (b) the transverse thermoelectric conductivity divided by T, α_yx / T in comparison with theoretical calculations (insets) for CoMnSb. Two different chemical potentials, E - E_F = -126 meV (black) and E - E_F = -130 meV (green), are selected for calculating σ_yx (T ) and α_yx (T ) / T .

We find a sizable anomalous Hall conductivity σ_yx and transverse thermoelectric conductivity α_yx experimentally. We observe substantial anomalous Hall conductivity σ_yx and transverse thermoelectric conductivity α_yx. The experimental σ_yx (T ) is well described by DFT calculation for the chemical potential E - E_F ≈ -130 meV (Fig. 1(a)), which is consistent with the valence electron count estimated from the sample composition measured by Inductively Coupled Plasma (ICP) method. Moreover, α_yx exhibits -T logT critical behavior instead of the conventional Fermi liquid behavior α_yx ~ T over a decade of temperature between 10 and 400 K (Fig. 1(b)). This behavior is similar to ferromagnetic Weyl semimetal Co2MnGa and nodal-line semimetals Fe₃X (X = Al, Ga) [2, 5]. Our theoretical calculation shows that in the vicinity of the chemical potential E - E_F ≈ -130 meV, the scaling behavior α_yx ~ -T logT arises from Weyl nodes in the band structure (Fig. 2).

Fig. 2. (a) Momentum-space distribution of Weyl nodes in CoMnSb on the k_x = 0 plane, which shows the Weyl node pair WP- (open blue circle) and WP⁺ (closed red circle). The coordinate of WP- and WP⁺ (k_y, k_z) are (0.21, -0.04) and (0.04, -0.21) in the unit of angstrom inverse, respectively. Black solid lines correspond to the boundary of the fcc Brillouin zone. (b) Band structure along A--A' (the black-dotted line) shown in (a).

In summary, we have successfully synthesized single-crystal samples of superstructure CoMnSb and explored their transverse transport properties. The observed critical scaling behavior in the transverse thermoelectric conductivity σ_yx ~ -T logT clearly deviates from the conventional Fermi liquid behavior, providing a hallmark of topological texture in the band structure. The comparison of experimental results with DFT calculations shows that this critical behavior results from Weyl nodes. This result indicates that the logarithmic criticality in the transverse thermoelectric conductivity provides a highly sensitive signature to reveal the topological band texture.

References

• [1] G. Sharma, P. Goswami, and S. Tewari, Phys. Rev. B 93, 035116 (2016).
• [2] A. Sakai et al., Nat. Phys. 14, 1119 (2018).
• [3] H. Nakamura et al., Phys. Rev. B 104, L161114 (2021).
• [4] S. Minami et al., Appl. Phys. Lett. 113, 032403 (2018).
• [5] A. Sakai et al., Nature 581, 53 (2020).

Authors

• H. Nakamura, S. Minami^a, T. Tomita, A. A. Nugroho^b, and S. Nakatsuji
• ^aThe University of Tokyo
• ^bInstitut Teknologi Bandung