Logarithmic criticality in transverse thermoelectric conductivity of the ferromagnetic topological semimetal CoMnSb

Letter

Logarithmic criticality in transverse thermoelectric conductivity of the ferromagnetic topological semimetal CoMnSb

Hiroto Nakamura, Susumu Minami, Takahiro Tomita, Agustinus Agung Nugroho, and Satoru Nakatsuji

Phys. Rev. B 104, L161114 – Published 25 October 2021

Abstract

We report the results of our experimental studies on the magnetic, transport, and thermoelectric properties of the ferromagnetic metal CoMnSb. A sizable anomalous Hall conductivity $σ_{y x}$ and transverse thermoelectric conductivity $α_{y x}$ are found experimentally and comparable in size to the values estimated from first-principles calculation. Our experiment further reveals that CoMnSb exhibits $- T log T$ critical behavior in $α_{y x} (T)$ , deviating from Fermi liquid behavior $α_{y x} \sim T$ over a decade of temperature between 10 and 400 K, similar to ferromagnetic Weyl and nodal-line semimetals. Our theoretical calculation for CoMnSb also predicts the $- T log T$ behavior when the Fermi energy locates near the Weyl nodes in momentum space.

Received 12 June 2021
Accepted 23 August 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L161114

Physics Subject Headings (PhySH)

Topological materials

Ferromagnets Thermoelectrics Weyl semimetal

First-principles calculations Wannier function methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Hiroto Nakamura^1,*, Susumu Minami ², Takahiro Tomita ^1,3, Agustinus Agung Nugroho ⁴, and Satoru Nakatsuji ^{1,2,3,5,6,†}

¹Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
²Department of Physics, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
³CREST, Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan
⁴Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, 40132 Bandung, Indonesia
⁵Trans-Scale Quantum Science Institute, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
⁶Institute for Quantum Matter and Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA

^*hnakamura@issp.u-tokyo.ac.jp
^†Author to whom correspondence should be addressed: satoru@phys.s.u-tokyo.ac.jp

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Vol. 104, Iss. 16 — 15 October 2021

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Images

Figure 1
(a) Superstructure of ferromagnet CoMnSb having eight unit cells of the half-Heusler one. Mn and Sb atoms are only shown in the single unit cell in this figure for simplicity. Our previous work finds that superstructure CoMnSb has the cubic space group $F m \bar{3} m$ (No. 225) [24]. The magnetic structure is a collinear ferromagnetism having magnetic moments at both Co and Mn sites [25]. Inset: Photograph of a single-crystalline sample of CoMnSb. The electric or heat current is applied along $Q | | [2 \bar{1} 1]$ , and a magnetic field is applied along $H | | [011]$ . (b) Temperature dependence of the longitudinal resistivities $ρ_{i i}$ ( $i = x, y$ ) (left axis) and the Seebeck coefficient $- S_{x x}$ (right axis). (c) Magnetic field dependence of the Nernst coefficient $- S_{y x}$ (left axis) and the magnetization $M$ (right axis) at 100 and 300 K. (d) Temperature dependence of the Nernst coefficient $- S_{y x}$ (left axis) and the normalized magnetization $M / M_{0}$ measured under a magnetic field of 1000 Oe (right axis). $M_{0}$ is defined as the maximum magnetization in the temperature dependence. The dashed line indicates the ferromagnetic transition temperature $T_{C} \sim 470$ K determined in this study
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Figure 2
Temperature $T$ dependence of (a) the Hall conductivity $σ_{y x}$ , and (b) the transverse thermoelectric conductivity divided by $T, α_{y x} / T$ obtained in experiment in comparison with those obtained in theoretical calculations for CoMnSb (insets). Two different chemical potentials $E - E_{F} = - 126 meV$ (black) and $E - E_{F} = - 130 meV$ (green), are selected to display both $σ_{y x} (T)$ and $α_{y x} (T) / T$ obtained by the theory in insets, respectively. The error bars are shown if they are larger than the symbol size.
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Figure 3
(a) Band structure of CoMnSb. Red and blue solid lines show up- and down-spin bands, respectively. Green dotted lines show bands including SOC. (b) Density of states of CoMnSb for up- and down-spin bands.
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Figure 4
(a) Distribution of Weyl nodes for CoMnSb in momentum space on the $k_{x} = 0$ plane. The two Weyl node pairs $W P^{-}$ (open blue circle) and $W P^{+}$ (solid red circle) are shown. The coordinates of $W P^{-}$ and $W P^{+}$ ( $k_{y}, k_{z}$ ) are $(0.21, - 0.04)$ and $(0.04, - 0.21)$ in the units 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). (c) Berry curvature contribution near the Weyl nodes. The contour shows the $x$ component of the Berry curvature ( $Ω_{x}$ ). The arrows indicate the $y$ and $z$ components of the Berry curvature ( $Ω_{y}, Ω_{z}$ ). Left and right panels correspond to $W P^{+}$ and $W P^{-}$ , respectively. Each axis range is $\pm 0.001$ in the units of angstrom inverse. The origins are set as the center of Weyl node. These Weyl nodes appear around $E - E_{F} = - 132$ meV.
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