Magnetic structure of the topological semimetal ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$

Magnetic structure of the topological semimetal ${Co}_{3} {Sn}_{2} S_{2}$

Jian-Rui Soh, ChangJiang Yi, Ivica Zivkovic, Navid Qureshi, Anne Stunault, Bachir Ouladdiaf, J. Alberto Rodríguez-Velamazán, YouGuo Shi, Henrik M. Rønnow, and Andrew T. Boothroyd

Phys. Rev. B 105, 094435 – Published 28 March 2022

Abstract

${Co}_{3} {Sn}_{2} S_{2}$ has recently been predicted to be a Weyl semimetal in which magnetic order is key to its behavior as a topological material. Here, we report unpolarized neutron diffraction and spherical neutron polarimetry measurements, supported by magnetization and transport data, which probe the magnetic order in ${Co}_{3} {Sn}_{2} S_{2}$ below $T_{C} = 177$ K. The results are fully consistent with ferromagnetic order in which the spins on the Co atoms point along the crystal $c$ axis, although we cannot rule out some canting of the spins. We find no evidence for a type of long-ranged $(k = 0)$ in-plane $120^{\circ}$ antiferromagnetic order which had previously been considered as a secondary phase present at temperatures between $\sim$ 90 K and $T_{C}$ . A discontinuous change in bulk properties and neutron polarization observed at $T = 125$ K when samples are cooled in a field and measured on warming is found to be due to a sudden reduction in ferromagnetic domain size. Our results lend support to the theoretical predictions that ${Co}_{3} {Sn}_{2} S_{2}$ is a magnetic Weyl semimetal.

Received 1 October 2021
Accepted 21 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.094435

Physics Subject Headings (PhySH)

Weyl fermions

Topological materials

Neutron diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jian-Rui Soh ¹, ChangJiang Yi², Ivica Zivkovic¹, Navid Qureshi³, Anne Stunault ³, Bachir Ouladdiaf³, J. Alberto Rodríguez-Velamazán ³, YouGuo Shi^2,4,5,6, Henrik M. Rønnow¹, and Andrew T. Boothroyd ⁷

¹Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
²Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
³Institut Laue-Langevin, 71 Avenue des Martyrs, 38042 Grenoble Cedex 9, France
⁴School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
⁵Songshan Lake Materials Laboratory, Dongguan 523808, China
⁶Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101400, China
⁷Department of Physics, University of Oxford, Clarendon Laboratory, Oxford OX1 3PU, United Kingdom

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Vol. 105, Iss. 9 — 1 March 2022

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Figure 1
(a) ${Co}_{3} {Sn}_{2} S_{2}$ crystallizes in the $R \bar{3} m$ space group, with the Co atoms arranged on kagome planes stacked along the crystal $c$ axis at $z = \frac{1}{6}$ , $\frac{3}{6}$ , and $\frac{5}{6}$ . In this paper we adopt the hexagonal setting to describe the unit cell, as shown. (b) and (c) Depiction of three symmetry-allowed spin configurations ( $ψ_{i}$ ) of the Co moments compatible with the $k = 0$ magnetic propagation vector. (b) The $Γ_{1}^{+}$ irreducible representation (irrep) has one basis vector, $ψ_{1}$ , which corresponds to an in-plane $120^{\circ}$ AFM order. (c) The $Γ_{2}^{+}$ irrep has two basis vectors which describe a different in-plane $120^{\circ}$ AFM order ( $ψ_{2}$ ) and a FM order along the crystal $c$ axis ( $ψ_{3}$ ).
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Figure 2
(a) Magnetization $M$ , (b) Hall resistivity $ρ_{y x}$ , and (c) $P_{z z}$ neutron polarization ( $\bar{1} 02$ reflection) of ${Co}_{3} {Sn}_{2} S_{2}$ as a function of temperature. Three different measurement protocols were used: red squares, the sample was cooled in a field of 0.5 T along the crystal $c$ axis and measured on warming in zero field (FC-ZFW); blue circles, the sample was cooled in zero field and measured on warming in zero field (ZFC-ZFW); and green triangles, measurements were made while cooling in a field (FC).
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Figure 3
(a)–(c) Comparison of measured ( $I_{obs}$ ) and calculated ( $I_{calc}$ ) integrated intensities from the structural and magnetic refinement in the magnetically ordered phases ( $T = 15$ and 150 K) and the paramagnetic phase ( $T = 200$ K) of ${Co}_{3} {Sn}_{2} S_{2}$ , respectively.
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Figure 4
Polarization matrices $P_{i j}$ measured at the 110 reflection of ${Co}_{3} {Sn}_{2} S_{2}$ as a function of temperature. (a) and (b) correspond to measurements performed with the ZFC-ZFW and FC-ZFW protocols, respectively. For each temperature, the nine matrix elements are arranged in the following order (from left to right): $P_{x x}$ , $P_{x y}$ , $P_{x z}$ , $P_{y x}$ , $P_{y y}$ , $P_{y z}$ , $P_{z x}$ , $P_{z y}$ , and $P_{z z}$ .
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Figure 5
Polarization matrix components $P_{i j}$ for the 101 reflection with the $b$ axis vertical. The $P_{i j}$ are arranged in the same order on the horizontal axes as in Fig. 4. The data are the vertical gray bars, and the filled red circles are calculations for the $ψ_{3}$ FM structure with an ordered moment of 0.39 $μ_{B}$ /Co. (a) $T = 10$ K. The $\times$ symbols are calculated for the $ψ_{1}$ AFM structure with an ordered moment of 0.1 $μ_{B}$ /Co. (b) $T = 160$ K. (c) $T = 200$ K.
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Figure 6
Temperature dependence of the $P_{z z}$ matrix element of ${Co}_{3} {Sn}_{2} S_{2}$ measured at the 101 reflection with the ZFC-ZFW protocol. The dashed black, solid blue, and dotted red lines denote the calculated $P_{z z}$ assuming $100 %$ in-plane $ψ_{1}$ AFM order, $ψ_{3} 100 %$ FM order, and a coexistence of $ψ_{1}$ and $ψ_{3}$ in the ratio inferred by $μ SR$ in Ref. [13], respectively. Details of the calculation of $P_{z z}$ can be found in the Supplemental Material [25]. Here, vol. frac., volume fraction.
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Magnetic structure of the topological semimetal ${Co}_{3} {Sn}_{2} S_{2}$

Jian-Rui Soh, ChangJiang Yi, Ivica Zivkovic, Navid Qureshi, Anne Stunault, Bachir Ouladdiaf, J. Alberto Rodríguez-Velamazán, YouGuo Shi, Henrik M. Rønnow, and Andrew T. Boothroyd

Phys. Rev. B 105, 094435 – Published 28 March 2022

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Physical Review B

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Magnetic structure of the topological semimetal Co3Sn2S2

Jian-Rui Soh, ChangJiang Yi, Ivica Zivkovic, Navid Qureshi, Anne Stunault, Bachir Ouladdiaf, J. Alberto Rodríguez-Velamazán, YouGuo Shi, Henrik M. Rønnow, and Andrew T. Boothroyd

Phys. Rev. B 105, 094435 – Published 28 March 2022

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Magnetic structure of the topological semimetal ${Co}_{3} {Sn}_{2} S_{2}$