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Co3Sn2S2是一种磁性外尔半金属, 具有特殊的磁性和电子结构, 其独特的能带结构使其拥有反常霍尔效应、负磁阻效应和反常能斯特效应等多种物理性质. 本文采用自熔剂法合成了高质量的Co3Sn2S2单晶, 并研究了Co3Sn2S2低温下的电输运行为(磁阻效应与霍尔效应等)和热输运行为(塞贝克效应). 热磁曲线表明, 在居里温度点(TC = 178 K)以下140 K(TA)处存在特殊的磁结构, 为铁磁态与反铁磁态共存的磁性过渡态. 研究发现, 在100—160 K出现负的反常“凸形”磁阻, 且在TA附近出现最大临界磁场B0, 为1.41 T, 同时霍尔电阻率ρyx也在TA处取得最大值约20 μΩ·cm. 这可能是由于铁磁态与反铁磁态之间会相互竞争形成非平凡的自旋织构, 导致TA附近独特的电输运行为. Co3Sn2S2在低温下的散射机制为声学波散射和电子-声子散射的共同作用, 在60—140 K时, 自旋无序的增强会引起电子-声子散射增强, 使得的塞贝克系数S出现平台特征. 研究表明, Co3Sn2S2在低温下的特殊磁结构和电子自旋对其电-热输运行为有着重要影响.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 ρ3 K/ρ300 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 (TA) below the Curie temperature point (TC = 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 TA. The coercivity HC drops to almost zero at TA and the Hall resistivity ρyx 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 TA. When the temperature rises to TC, the Co3Sn2S2 undergoes a ferromagnetic phase transition, with a saturation magnetization of MS, anomalous Hall conductivity
$ {\sigma }_{yx}^{\rm A} $ , and Hall resistivity ρyx 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 C2x 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:
- Co3Sn2S2 /
- anomalous Hall effect /
- magnetoresistance /
- Seebeck effect
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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
Fig. 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.
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
Fig. 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.
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/ρ300 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
Fig. 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/ρ300 K based on resistivity at 300 K. The dotted line is the normalized resistivity of the sample reported in Ref.[6, 7, 15, 31].
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MS和矫顽力HC随温度的变化曲线
Fig. 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 MS and coercivity HC.
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 = aB 2+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
Fig. 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 = aB 2+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.
图 6 (a) 不同温度下Co3Sn2S2的霍尔电阻率ρyx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ρyx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Fig. 6. (a) Hall resistivity ρyx versus 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 ρyx; (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.
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
Fig. 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.
图 8 (a) Co3Sn2S2的归一化饱和磁化强度MS, 归一化矫顽力HC, 归一化反常霍尔电导
$ {\sigma }_{yx}^{{\rm{A}}} $ , 归一化霍尔电阻率ρyx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Fig. 8. (a) Temperature-dependent normalized saturation magnetization MS, normalized coercivity HC, normalized anomalous Hall conductivity
$ {\sigma }_{yx}^{{\rm{A}}} $ , normalized Hall resistivity ρyx 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表 1 使用公式MR = aB 2+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 = aB 2+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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[1] Yan M H, Jin Y C, Hou X F, Guo Y F, Tsaturyan A, Makarova A, Smirnov D, Dedkov Y, Voloshina E 2021 J. Phys. Chem. Lett. 12 9807
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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