First-principles investigation of magnetic and transport properties in hole-doped shandite compounds ${\mathrm{Co}}_{3}{\mathrm{In}}_{x}{\mathrm{Sn}}_{2\ensuremath{-}x}{\mathrm{S}}_{2}$

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First-principles investigation of magnetic and transport properties in hole-doped shandite compounds ${Co}_{3} {In}_{x} {Sn}_{2 - x} S_{2}$

Yuki Yanagi, Junya Ikeda, Kohei Fujiwara, Kentaro Nomura, Atsushi Tsukazaki, and Michi-To Suzuki

Phys. Rev. B 103, 205112 – Published 7 May 2021

Abstract

Co-based shandite ${Co}_{3} {Sn}_{2} S_{2}$ is a representative example of magnetic Weyl semimetals showing rich transport phenomena. We thoroughly investigate magnetic and transport properties of hole-doped shandites ${Co}_{3} {In}_{x} {Sn}_{2 - x} S_{2}$ by first-principles calculations. The calculations reproduce nonlinear reduction of anomalous Hall conductivity with doping In for ${Co}_{3} {Sn}_{2} S_{2}$ as reported in experiments against the linearly decreased ferromagnetic moment within virtual crystal approximation. We show that a drastic change in the band parity character of Fermi surfaces, attributed to the nodal rings lifted energetically with In doping, leads to strong enhancement of anomalous Nernst conductivity with reversing its sign in ${Co}_{3} {In}_{x} {Sn}_{2 - x} S_{2}$ .

Received 30 November 2020
Revised 31 March 2021
Accepted 14 April 2021

DOI:https://doi.org/10.1103/PhysRevB.103.205112

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Anomalous Hall effect Thermoelectric effects

Half-metals Topological materials

First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuki Yanagi¹, Junya Ikeda², Kohei Fujiwara ², Kentaro Nomura^2,3, Atsushi Tsukazaki^2,3,4, and Michi-To Suzuki ^1,5

¹Center for Computational Materials Science, Institute for Materials Research, Tohoku University, Sendai, Miyagi 950-8577, Japan
²Institute for Materials Research, Tohoku University, Sendai Miyagi 950-8577, Japan
³Center for Spintronics Research Network, Tohoku University, Sendai, Miyagi 980-8577, Japan
⁴Center for Science and Innovation in Spintronics (CSIS), Core Research Cluster, Tohoku University, Sendai, Miyagi 980-8577, Japan
⁵Center for Spintronics Research Network, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan

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Vol. 103, Iss. 20 — 15 May 2021

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Figure 1
(a) Crystal structure of ${Co}_{3} {In}_{x} {Sn}_{2 - x} S_{2}$ , and (b) that on the Co-kagome layer. The solid line represents the conventional unit cell which is three times larger than the primitive one. These figures are drawn by using vesta [34].
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Figure 2
(a) DOS for ${Co}_{3} {Sn}_{2} S_{2}$ in nonmagnetic and ferromagnetic states. The solid and dashed (dot-dashed) lines represent DOS per spin in the nonmagnetic state and that with spin-up (-down) in the ferromagnetic state, respectively. The chemical potential dependences of (b) AHC at $k_{B} T = 0$ and (c) ANC at $k_{B} T = 0.01 eV$ . In panel (c), the solid and dashed lines represent the ANCs calculated via the Berry phase formula in Eq. (3) and generalized Mott formula in Eq. (5), respectively.
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Figure 3
(a)–(f) Band structures for ${Co}_{3} {In}_{x} {Sn}_{2 - x} S_{2}$ with spin-orbit coupling along high-symmetry $k$ lines where the color map represents the spin density along the $z$ axis. (g) The $k$ path on which the band structures are plotted in panels (a)–(f). (h) In-doping dependence of the net magnetization.
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Figure 4
(a) Doping dependence of AHC $σ_{x y}^{A}$ at $k_{B} T = 0$ and (b) that of ANC $α_{x y}^{A}$ at finite temperatures. (c) Temperature dependence of $α_{x y}^{A}$ and (d) that of $α_{x y}^{A} / T$ at various In-doping concentrations. In panel (a), experimental data extracted from Refs. [32, 45] are plotted together with calculated results for comparison.
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Figure 5
(a) The chemical potential dependence of $α_{x y}^{A} / T$ for various values of temperature with $0.002 eV \leq k_{B} T \leq 0.01 eV$ in 0.001 eV steps and (b) temperature dependence of $α_{x y}^{A} / T$ for various values of the chemical potential with $- 0.05 eV \leq μ \leq 0.05 eV$ in 0.002 eV steps at $x = 0$ .
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Figure 6
(a) Fermi surfaces for ${Co}_{3} {In}_{x} {Sn}_{2 - x} S_{2}$ where the color map represents the intensity of $\frac{Ω_{n, x y} (k)}{| \nabla_{k} ɛ_{n k} |}$ through the logarithmic function $g (x) \equiv sgn (x) ln (1 + | x |)$ . (b) Those on the $k_{x} − k_{z}$ plane at $k_{y} = 0$ . The black solid line represents the nodal lines in the absence of spin-orbit coupling. The upper (lower) triangles on the nodal lines denote the Weyl nodes with topological charge $+ 1 (- 1)$ in the presence of spin-orbit coupling. The $k$ path along which band structures plotted in panel (c) is shown by red arrows in the leftmost panel. (c) Majority spin band structures in the absence of the spin-orbit coupling. The solid and dashed lines represent the energy bands with eigenvalues $+ 1$ and $- 1$ of the mirror symmetry operator on the $k_{x} − k_{z}$ plane, respectively. Band crossings corresponding to nodal lines are shown by arrows. (a) and (b) are created with the use of the fermisurfer code [53].
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Physical Review B

covering condensed matter and materials physics

First-principles investigation of magnetic and transport properties in hole-doped shandite compounds ${Co}_{3} {In}_{x} {Sn}_{2 - x} S_{2}$

Yuki Yanagi, Junya Ikeda, Kohei Fujiwara, Kentaro Nomura, Atsushi Tsukazaki, and Michi-To Suzuki

Phys. Rev. B 103, 205112 – Published 7 May 2021

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Physical Review B

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First-principles investigation of magnetic and transport properties in hole-doped shandite compounds Co3InxSn2−xS2

Yuki Yanagi, Junya Ikeda, Kohei Fujiwara, Kentaro Nomura, Atsushi Tsukazaki, and Michi-To Suzuki

Phys. Rev. B 103, 205112 – Published 7 May 2021

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First-principles investigation of magnetic and transport properties in hole-doped shandite compounds ${Co}_{3} {In}_{x} {Sn}_{2 - x} S_{2}$