Magnetic and electrical-thermal transport properties of Co3Sn2S2 single crystal

Zhu Xin-Qiang; Wang Jian; Zhu Can; Luo Feng; Chen Shu-Quan; Xu Jia-Hui; Xu Feng; Wang Jia-Fu; Zhang Yan; Sun Zhi-Gang

doi:10.7498/aps.72.20230621

Abstract

Co₃Sn₂S₂ is a magnetic Weyl semimetal with special magnetic and electronic structure. Its unique band structure makes it have many interesting physical properties such as abnormal Hall effect, negative magnetoresistance effect, and abnormal Nernst effect. In this work, high quality Co₃Sn₂S₂ single crystal with a dimension of 8 mm×7 mm×0.5 mm is synthesized by self-flux method. We measure its electrical transport properties (magnetoresistance effect, Hall effect, etc.) and thermal transport properties (Seebeck effect) at low temperature. The free surface of the single crystal exhibits obvious layered growth characteristics, indicating that the Co₃Sn₂S₂ crystal grows along the c-axis direction. The value of the normalized resistivity ρ_{3 K}/ρ_{300 K} for the single crystal sample at 3 K is only 0.08, indicating that the crystal quality of the sample is at a relatively high level. The thermomagnetic (M-T) curves show that a special magnetic structure near 140 K (T_A) below the Curie temperature point (T_C = 178 K). This special magnetic structure is a magnetic transition state in which ferromagnetic state and antiferromagnetic state coexist, making them appear as a local minimum point in the M-T curve. The Co₃Sn₂S₂ shows a negative anomalous “convex” magnetoresistance in a large range of 100—160 K, and there exists a maximum critical magnetic field B₀ (1.41 T), near T_A. The coercivity H_C drops to almost zero at T_A and the Hall resistivity ρ_yx also reaches a maximum value of about 20 μΩ·cm. This may be due to the competition between ferromagnetic state and antiferromagnetic state to form non-trivial spin texture, resulting in the unique electrical transport behavior near T_A. When the temperature rises to T_C, the Co₃Sn₂S₂ undergoes a ferromagnetic phase transition, with a saturation magnetization of M_S, anomalous Hall conductivity $ {\sigma }_{yx}^{\rm A} $, and Hall resistivity ρ_yx sharply decreasing. Large anomalous Hall conductance $ {\sigma }_{yx}^{A} $ and anomalous Hall angle $ {\sigma }_{yx}^{\rm A}/\sigma $ are also present in Co₃Sn₂S₂, with these values reaching 1.4×10³ Ω⁻¹·cm⁻¹ and 18%, respectively. The magnetoresistance measurements reveal that the variation of the magnetoresistance with the magnetic field is due to the combination of linear and parabolic contributions. The change in magnetoresistance with the angle θ between the magnetic field B and the current I has a reversal symmetry with C_2x symmetry, and the change in θ does not affect the contribution of its magnetoresistance source. In addition, positive magnetoresistance and negative magnetoresistance are found to be shifted at about 60 K. the shift in positive magnetoresistance and negative magnetoresistance are mainly attributed to the competing positive contribution of the Lorentz force to the magnetoresistance and the negative contribution of the spin disorder. The scattering mechanism of Co₃Sn₂S₂ at low temperature is a combination of acoustic wave scattering and electron– phonon scattering. At 60–140 K, the enhancement of spin disorder causes enhanced electron–phonon scattering, resulting in a plateau characteristic of the Seebeck coefficient S. The research shows that the special magnetic structure and electron spin of Co₃Sn₂S₂ at low temperatures have an important influence on its electrothermal transport behavior.

Keywords:

Authors and contacts

1.
State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China
2.
College of Science, Wuhan University of Technology, Wuhan 430070, China
3.
College of Material Science and Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China

Corresponding author: Sun Zhi-Gang, sun_zg@whut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12174297, 12204342) and the National Key Research and Development Program of China (Grant No. 2018YFE0111500).

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Cited By

图 1 (a) Co₃Sn₂S₂的粉末XRD结果, 黑×表示测量的衍射峰强度, 红线为计算的衍射峰强度, 蓝色的线条表示计算计算数据与测量数据之差, 绿色的线条表示Bragg衍射峰的位置; (b) Co₃Sn₂S₂的晶体表面XRD结果, XRD的峰对应于六方晶格的ab平面, 插图为Co₃Sn₂S₂晶体的光学影像

Figure 1. (a) Powder XRD results of Co₃Sn₂S₂, black × represents the measured diffraction peak intensity, the red line represents the calculated diffraction peak intensity, the blue line represents the difference between the calculated data and the measured data, and the green line represents the position of the Bragg diffraction peak; (b) XRD results of the crystal surface of Co₃Sn₂S₂. The peak of XRD corresponds to the ab plane of the hexagonal lattice. The insert shows the optical image of Co₃Sn₂S₂ crystal.

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图 2 (a) Co₃Sn₂S₂样品在2000倍下的表面SEM结果; (b) EDS面扫区域形貌; (c)—(e) Co₃Sn₂S₂样品的EDS面扫描结果

Figure 2. (a) Surface SEM results of Co₃Sn₂S₂ sample at 2000 times; (b) EDS surface scanning area morphology; (c)–(e) EDS surface scan results of Co₃Sn₂S₂ sample.

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图 3 (a) 零场下Co₃Sn₂S₂的电阻率ρ随温度变化的曲线, 插图为电阻率测量原理图; (b) 以 300 K 下的电阻率为基准的归一化电阻率 ρ/ρ_{300 K}随温度的变化曲线, 虚线是文献[6, 7, 15, 31]中报道的样品的归一化电阻率

Figure 3. (a) Temperature dependence of resistivity ρ of Co₃Sn₂S₂ at zero field, the insert is diagram of resistivity measurement; (b) temperature dependence of normalized resistivity ρ/ρ_{300 K} based on resistivity at 300 K. The dotted line is the normalized resistivity of the sample reported in Ref.[6, 7, 15, 31].

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图 4 (a) H∥c轴, 磁场为50 Oe时, Co₃Sn₂S₂样品的磁化强度M随温度的变化曲线, 插图展示的是磁化强度的一阶微分dM/dT随温度变化曲线; (b) H∥c轴, H⊥c轴, 在50 K, 100 K, 150 K下磁化强度M随磁场H的变化曲线: (c) H∥c轴, 在50—300 K下的磁化强度M随磁场H的变化曲线; (d) H∥c轴, 饱和磁化强度M_S和矫顽力H_C随温度的变化曲线

Figure 4. (a) H∥c axis, the magnetic field is 50 Oe, the temperature dependence of the magnetization M of Co₃Sn₂S₂. The insert shows the dM/dT with T; (b) H∥c axis, H⊥c axis, magnetic field dependence of magnetization at 50 K, 100 K, 150 K; (c) H∥c axis, M-H at 50–300 K; (d) H∥c axis, the temperature dependence of the saturation magnetization M_S and coercivity H_C.

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图 5 (a)当B∥I时, 3—220 K的磁阻曲线; (b) 当B∥I时, B = 7 T下磁阻MR随温度变化曲线, 插图为100—160 K的“凸形”磁阻的临界磁场B₀随温度变化曲线; (c) 当B⊥I时, 3 K下磁阻MR随磁场的变化, 黑色的实线表示根据公式拟合的值(MR = aB²+cB), 插图为3 K下dMR/dB随磁场的变化; (d) 3 K下, 磁场B与电流I在不同夹角下的磁阻变化曲线, 插图为MR随夹角变化的曲线, 红色实线为使用正弦函数拟合的值

Figure 5. (a) B∥I, the magnetoresistance(MR) curve of 3–220 K; (b) B∥I, the curve of MR versus temperature at B = 7 T , the insert is the critical point B₀ of “convex” MR versus temperature at 100–160 K; (c) B⊥I, the MR versus the magnetic field at 3 K, the black solid line represents the value fitted according to the formula (MR = aB²+cB), and the insert shows the dMR/dB versus the magnetic field at 3 K; (d) the MR of different angle between the B and I versus the magnetic field B at 3 K, and the insert is the MR versus different angles, the red solid line represents the value fitted according to sine function.

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图 6 (a) 不同温度下Co₃Sn₂S₂的霍尔电阻率ρ_yx随磁场变化的曲线, 插图为霍尔电阻率测量原理图; (b) 反常霍尔电导率$ {\sigma }_{yx}^{{\rm{A}}} $与霍尔电阻率ρ_yx随温度变化的曲线; (c) 反常霍尔角$ {\sigma }_{yx}^{{\rm{A}}}/\sigma $与随温度变化的曲线; (d) 载流子浓度n随温度变化曲线; (e) 载流子迁移率μ随温度变化曲线, 插图为ln μ随ln T的变化曲线

Figure 6. (a) Hall resistivity ρ_yxversus the magnetic field of Co₃Sn₂S₂ at different temperatures, the insert is the diagram of Hall resistivity measurement; (b) the temperature dependence of abnormal Hall conductivity $ {\sigma }_{yx}^{{\rm{A}}} $ and Hall resistivity ρ_yx; (c) the temperature dependence of abnormal Hall angle $ {\sigma }_{yx}^{{\rm{A}}}/\sigma $; (d) the carrier concentration n versus the temperature; (e) the carrier mobility μ versus the temperature, the insert is the ln μ versus ln T.

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图 7 (a) Co₃Sn₂S₂的电导率σ随温度变化的曲线; (b) 塞贝克系数S随温度变化的曲线; (c) 功率因子PF随温度变化的曲线; (d) 使用载流子输运的能带模型计算获得的有效质量m^*随温度变化的曲线

Figure 7. Temperature-dependent (a) conductivity σ, (b) Seebeck coefficient S, (c) power factor PF of Co₃Sn₂S₂; (d) effective mass m^* calculated according to the energy band model of carrier transport.

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图 8 (a) Co₃Sn₂S₂的归一化饱和磁化强度M_S, 归一化矫顽力H_C, 归一化反常霍尔电导$ {\sigma }_{yx}^{{\rm{A}}} $, 归一化霍尔电阻率ρ_yx随温度的变化曲线及归一化ZFC与FC曲线; (b) 归一化塞贝克系数S, 归一化磁阻MR随温度的变化曲线, 插图为lnμ随lnT的变化曲线

Figure 8. (a) Temperature-dependent normalized saturation magnetization M_S, normalized coercivity H_C, normalized anomalous Hall conductivity $ {\sigma }_{yx}^{{\rm{A}}} $, normalized Hall resistivity ρ_yx and normalized ZFC and FC curves of Co₃Sn₂S₂; (b) temperature-dependent normalized Seebeck coefficient S and normalized magnetoresistance MR, the insert is the lnμ versus lnT

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表 1 使用公式MR = aB²+cB拟合B与I在不同夹角下的MR - B曲线得到的拟合值

Table 1. The fitting values of the MR-B curve according to the formula MR = aB²+cB at different angles between B and I.

Angle/(°) a c a/c

0 0.11125 0.39786 0.27962
15 0.20063 0.76517 0.26221
30 0.31282 1.09081 0.28678
60 0.37345 1.52122 0.24549
75 0.42358 1.66508 0.25439
90 0.42455 1.71172 0.24803

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Magnetic and electrical-thermal transport properties of Co₃Sn₂S₂ single crystal