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二维磁性材料的研究推动了现代纳米电子器件的发展. 寻找本征的具有磁性的层状材料, 为探索研究新的二维磁性材料、制备二维电子器件提供了重要的材料基础. 近来, 本征二维反铁磁拓扑材料的发现引起了人们的广泛关注和兴趣.
$ {\rm{EuIn}}_{2}{\rm{As}}_{2} $ 被预言是一种轴子拓扑绝缘材料, 它具有典型的反铁磁序和层状的晶体结构, 其潜在的多种拓扑量子效应可以为未来新型电子学器件提供新的发展思路. 实验结果表明$ {\rm{EuIn}}_{2}{\rm{As}}_{2} $ 处于金属态, 而非绝缘态. 本文通过掺杂Ca来调节体系的费米能级和磁性, 发现$ {\rm{E}}{{\rm{u}}_{1 - x}}{\rm{C}}{{\rm{a}}_x}{\rm{I}}{{\rm{n}}_2}{\rm{A}}{{\rm{s}}_2} $ 中仍然存在与母体类似的长程反铁磁的结果. 反铁磁矩沿面内方向, 符合理论预言的轴子态磁结构. 在反铁磁转变温度以上发现了铁磁极化子. 由此可见, 非磁性杂质掺杂对体系的磁性影响不大, 但是载流子浓度却降低了一个数量级, 费米能级沿电子型方向进行调制. 本文的研究为在二维磁性材料中探索和诱导非平庸拓扑态提供了重要信息.The study of two-dimensional (2D) magnetic materials has driven the development of modern nano-electronic devices. Exploration of novel intrinsic layered materials with 2D magnetic order will provide a material candidate pool for fabricating 2D devices and searching for new quantum phases. Recently the layered antiferromagnetic (AF) topological insulators have aroused the great interest of researchers. As one of the proposed axion insulators, EuIn2As2 exhibits a layered structure and 2D AF order. It is found that the parent compound EuIn2As2 exhibits metallic behavior instead of the predicted insulating feature. To pursuit the predicted non-trivial topological state and novel feature, in this paper, we use various elements to dope the system to adjust the Fermi level. It is found that only Ca is successfully doped into the EuIn2As2 system. The systematic transport and magnetization studies are performed on the single crystal of Eu1–xCaxIn2As2. The long-range AF order is revealed to be similar to the parent compound. Above the AF transition, the magnetization violated Curie-Weiss behavior and magnetoresistance keeps negative, indicating the ferromagnetic order. With doping nearly 20% non-magnetic Ca, the magnetic properties of the system barely change, which is favorable to keeping the former predicted nontrivial topological properties in EuIn2As2. Although Ca shares the same valence with Eu, the carrier density of Eu1–xCaxIn2As2 is one order lower than that of EuIn2As2. The Ca doping brings electrons in and lifts the Fermi level. The results enrich the 2D magnetic material candidate pool and provide useful information for realizing the nontrivial topological state in the 2D AF system.[1] Butler S Z, Hollen S M, Cao L, et al. 2013 ACS Nano 7 2898
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图 1 (a)
$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ 的晶体结构, 其中无磁的Ca元素替换掉部分磁性元素Eu; (b)体系材料能带结构示意图, 其中母体$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ 处于金属态, 通过掺杂提升费米能级, 可以实现可能的拓扑态; (c)母体$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ (上图)和$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ (下图)的X射线单面晶体衍射Fig. 1. (a) Crystal structure of
$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ . The atoms of non-magnetic element Ca replace some of the atoms of magnetic element Eu. (b) Schematic of band structure and Fermi level of$ {\rm{Eu}}_{1-x}{\rm{Ca}}_{x}{\rm{In}}_{2}{\rm{As}}_{2} $ . Fermi level can be lifted by doping. (c) X-ray diffraction pattern of single crystals of$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ (upper) and$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ (lower).
图 2 (a)温度依赖的
$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ 和$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ 的磁化率曲线$ \chi \left(T\right) $ , 蓝线来自于$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ 数据, 红线来自于${\rm{Eu}}_{0.81} $ $ {\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2}$ 数据. 测量以零场冷的方式在1000 Oe ($1~{\rm{O}}{\rm{e}}=\dfrac{{10}^{3}}{4{\text{π}}}{\rm{A}}/{\rm{m}})$ 下进行, 外加磁场的方向沿着ab面. 在20 K左右明显观察到一个磁化曲线的尖峰. 插图为温度依赖的$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ 的磁化率倒数$ 1/\chi ={{H}}/{{M}} $ 曲线, 其中H为外加磁场, M为样品的磁化强度, 虚线表示的是根据居里-外斯定律拟合的曲线. (b)$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ 的磁滞回线测量结果, 外加磁场分别沿着晶体的ab面和c轴. 插图为放大方框区域内的曲线, 其中黑色(右)对应磁化强度, 蓝色(左)对应磁化强度微分, 可以观察到微分曲线有一个明显的尖峰. (c)外加磁场沿晶体的ab面方向时, 样品在温度为2, 10, 15, 20和30 K时的磁化强度随磁场变化曲线. (d)外加磁场沿晶体的c方向时, 样品在温度为2, 5, 15, 20, 30, 35, 40, 60, 70和80 K时的磁化强度随磁场变化曲线Fig. 2. (a) Temperature dependent χ (where χ is the magnetic susceptlilty) of
$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ and$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ , the blue curve represents$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ , the red curve represents$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ . The inset is the temperature dependent$ 1/\chi $ of$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ and$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ in low temperature region. (b) The magnetic hysteresis loops at 2 K with the applied field within ab plane and along c axis. The inset is the$ {\rm{d}}{{M}}/{\rm{d}}{{H}} $ curve for the applied field within ab plane. (c) The magnetic hysteresis loops at 2, 10, 15, 20 and 30 K with the applied field within ab plane. (d) The magnetic hysteresis loops at 2, 5, 15, 20, 30, 35, 40, 60, 70 and 80 K with the applied field along c axis.
图 3 (a)温度依赖的
$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ 和$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ 的电阻率ρ数据. 蓝线代表$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ , 红线代表$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ . (b)温度依赖的$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ 和$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ 的霍尔系数数据. 蓝线代表$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ , 红线代表$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ . 测量时外加磁场沿着c轴. 插图为2 K下随磁场变化的$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ 和$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ 霍尔电阻率数据. 蓝线代表$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ , 红线代表${\rm{Eu}}_{0.81} $ $ {\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2}$ Fig. 3. (a) Temperature dependent resistivity of
$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ and$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ . The blue curve represents$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ , and the red curve represents$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ . (b) The temperature dependent Hall coefficients of of$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ and$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ . The blue curve represents$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ , and the red curve represents$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ . The field is exerted along c axis. The inset is the field dependent of Hall resistivity of$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ and$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ . The blue curve represents$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ , and the red curve represents${\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ .
图 4 (a)
$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ 在2, 5, 8, 10, 12, 14, 16, 30, 60和150 K时随磁场变化的磁阻数据; (b)根据Bethe-Ansatz模型在18, 20和30 K时归一化的磁阻数据; (c)根据Majumdar-Littlewood公式在20, 30和60 K时拟合的磁阻数据Fig. 4. (a) Field dependent MR of
$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $ at 2, 5, 8, 10, 12, 14, 16, 30, 60 and 150 K; (b) the scaled MR at 18, 20 and 30 K within Bethe-Ansatz model; (c) the fitting of MR data at 20, 30 and 60 K by using Majumdar-Littlewood formula.表 1
$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $ 体系不同元素掺杂材料的单晶制备实验结果Table 1. Summary of results of single crystal growth of doped EuIn2As2 compounds∶ Ag, Sm, Sb
掺杂的
元素被替换
的元素配比(助熔剂均为In)
(以下配比含助熔剂)结晶结果(XRD测量结果) 掺杂结果(SEM测量结果) Ga In Eu∶In∶Ga∶As = 1∶11.6∶0.4∶3 生长出$ {\rm{Eu}}{\rm{Ga}}_{2}{\rm{As}}_{2} $结构的单晶 Eu∶In∶Ga∶As = 19.24∶18.62∶21.01:41.13 Cd In Eu∶In∶Cd∶As = 1∶11.6∶0.4∶3 生长出$ {\rm{Eu}}{\rm{Cd}}_{2}{\rm{As}}_{2} $结构的单晶 Eu∶In∶Cd∶As = 20.09∶38.18∶0∶41.78 Zn In Eu∶In∶Zn∶As = 1∶11.6∶0.4∶3 生长出$ {\rm{Eu}}{\rm{Zn}}_{2}{\rm{As}}_{2} $结构的单晶 Eu∶In∶Zn∶As = 19.58∶39.41∶0∶41.01 Sn In Eu∶In∶Sn∶As = 1∶11.6∶0.4∶3 生长出$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $结构的单晶 Eu∶In∶Sn∶As = 19.09∶39.02∶1.36∶40.54 Ag In Eu∶In∶Ag∶As = 1∶11.6∶0.4∶3 生长出$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $结构的单晶 Eu∶In∶Ag∶As = 19.42∶37.83∶0.36∶42.40 Ca Eu Eu∶Ca∶In∶As = 0.8∶0.2∶12∶3 生长出$ {\rm{Eu}}_{0.81}{\rm{Ca}}_{0.19}{\rm{In}}_{2}{\rm{As}}_{2} $结构的单晶 Eu∶Ca∶In∶As = 16.23∶3.70∶38.08∶41.99 Sm Eu Eu∶Sm∶In∶As = 0.8∶0.2∶12∶3 生长出$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $结构的单晶 Eu∶Sm∶In∶As = 19.54∶0∶37.89∶42.56 Sb As Eu∶In∶As∶Sb = 1∶12∶2.4∶0.6 生长出$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $结构的单晶 Eu∶In∶As∶Sb = 19.37∶38.49∶42.14∶0 P As Eu∶In∶As∶P = 1∶12∶2.4∶0.6 生长出$ {\rm{Eu}}{\rm{In}}_{2}{\rm{As}}_{2} $结构的单晶 Eu∶In∶As∶P = 19.16∶39.08∶41.76∶0 
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