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研究生: 廖奕翔
Liao, Yi-Hsiang
論文名稱: 單晶 EuCo2Al9 之磁性與輸運性質研究:三角晶格磁體中的場誘導相變
Magnetic and Transport Properties of Single Crystal EuCo2Al9: Field-Induced Phase Transition in a Triangular-Lattice Magnet
指導教授: 黃建龍
Huang, Chien-Lung
學位類別: 碩士
Master
系所名稱: 理學院 - 物理學系
Department of Physics
論文出版年: 2026
畢業學年度: 114
語文別: 英文
論文頁數: 89
中文關鍵詞: 幾何阻挫反鐵磁性三角晶格1/3 磁化平台自旋超固體
外文關鍵詞: geometrical frustration, antiferromagnetism, triangular lattice, 1/3 magnetization plateau, spin supersolid
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  • 我們針對金屬三角晶格反鐵磁體EuCo2Al9 單晶的磁性、熱力學與輸運性質,進行了全面的研究。該化合物結晶於六方空間群P6/mmm,其中Eu2+ 離子形成堆疊的三角晶格。高溫磁化率遵循居禮—外斯定律(Curie–Weiss law),得出的有效磁矩與Eu2+ 自由離子的理論值(S =7/2)一致。此外,負的居禮—外斯溫度(θCW ≈−12.5 K)指出反鐵磁交互作用佔主導地位。長程磁有序在TN ≈3.6K以下形成。於1.8 K測量的等溫磁化強度具有強烈的各向異性。當H⊥c時,磁化強度平滑上升至飽和值≈7µB/f.u.,且未出現任何磁化平台。相反地,當H ∥c時,在1–2 T 附近出現了明顯的1/3磁化平台。該平台是幾何阻挫易軸反鐵磁體中,共線「上-上-下」(up-up-down, UUD)態的標誌性特徵。透過結合磁化強度、磁阻與熱容量測量,我們建構了兩種磁場方向的磁場—溫度相圖。此外,完整磁熵Rln8的恢復證實了整個S =7/2的多重態(multiplet)皆參與了磁有序過程。我們的H ∥c 結果獨立驗證了近期關於該化合物金屬自旋超固體(spin-supersolid)相圖的報導。此外,本研究進一步將探討延伸至過去未被探索的H⊥c方向。綜合而言,這些全面的結果確立了EuCo2Al9 作為金屬系統中阻挫磁性研究的模型平台。

    We report a comprehensive study of the magnetic, thermodynamic, and transport properties of single crystals of the metallic triangular-lattice antiferromagnet EuCo2Al9. This compound crystallizes in the hexagonal space group P6/mmm, where the Eu2+ ions form a stacked triangular lattice. The high-temperature susceptibility follows the Curie–Weiss law, yielding an effective moment consistent with the free-ion value of Eu2+ (S = 7/2). Furthermore, a negative Curie–Weiss temperature (θCW ≈ −12.5 K) indicates dominant antiferromagnetic interactions. Long-range magnetic order devel ops below TN ≈ 3.6 K. The isothermal magnetization at 1.8 K is strongly anisotropic. For H ⊥ c, it rises smoothly to a saturation of ≈ 7 µB/f.u. without any plateau. In contrast, for H ∥ c, a clear 1/3 magnetization plateau appears near 1–2 T. This plateau is the hallmark of the collinear up-up-down (UUD) state in a geometrically frustrated easy-axis antiferromagnet. By combining magnetization, magnetoresistance, and heat capacity measurements, we construct the field–temperature phase diagrams for both field orientations. Additionally, the recovery of the full magnetic entropy Rln8 confirms that the entire S = 7/2 multiplet participates in the ordering. Our H ∥ c results provide an independent verification of the metallic spin-supersolid phase diagram recently reported for this compound. Moreover, our work extends the study to the previously unexplored H ⊥ c orientation. Together, these comprehensive results establish EuCo2Al9 as a model platform for frustrated magnetism in metallic systems.

    中文摘要 i Abstract ii Acknowledgements iv Contents v List of Tables vii List of Figures viii 1 Introduction 1 1.1 Geometric Frustration in Triangular Lattices 1 1.2 The 1/3 Magnetization Plateau and the Up-Up-Down Phase 2 1.3 Metallic Spin Supersolid in EuCo2Al9 3 1.4 Motivation and Specific Contribution 8 2 Experimental Setup 9 2.1 X-ray Diffraction 9 2.1.1 Laboratory Powder X-ray Diffraction 9 2.1.2 Synchrotron Powder X-ray Diffraction 11 2.2 Magnetic Property Measurement System (MPMS) 14 2.2.1 Principle of a SQUID Sensor 16 2.2.2 Measurement Modes and Capabilities 16 2.3 Physical Property Measurement System 18 2.3.1 Heat Capacity Measurement 19 2.3.2 Electrical Resistivity Measurement 21 3 Experimental analysis method 24 3.1 Curie–Weiss Law 24 3.2 Expected Moment of Eu2+ 26 3.3 Two-Level Schottky Anomaly 27 3.4 Integrated Magnetic Entropy 29 3.5 Phase Transitions 31 3.5.1 Classification of Phase Transitions 31 3.5.2 Berezinskii–Kosterlitz–Thouless Transition 33 3.5.3 Three-State Potts Transition 34 3.5.4 Phase Diagram of the Triangular-Lattice XXZ Model 35 4 Experimental Results and Analysis 40 4.1 Single-Crystal Growth 40 4.2 Basic Properties 41 4.3 Magnetic Susceptibility 43 4.4 Isothermal Magnetization 45 4.5 Resistivity Measurement 47 4.6 Heat Capacity 52 4.7 Phase Diagram 60 4.7.1 H ∥ c Phase Diagram 60 4.7.2 H ⊥ c Phase Diagram 62 5 Conclusions and Future Works 64 References 66

    [1] M. F. Collins and O. A. Petrenko. Review/synthèse: Triangular antiferromagnets. Canadian Journal of Physics, 75(9):605–655, September 1997. doi:10.1139/p97-007.
    [2] V. Thanh Ngo and H. T. Diep. Phase transition in heisenberg stacked triangular antiferromagnets: End of a controversy. Phys. Rev. E, 78:031119, Sep 2008. doi:10.1103/PhysRevE.78.031119.
    [3] Hikaru Kawamura. Chiral criticality and multicriticality in triangular antiferromagnets. Journal of Magnetism and Magnetic Materials, 90-91:289–290, 1990. doi:10.1016/S0304-8853(10)80103-9.
    [4] A. V. Chubukov and D. I. Golosov. Quantum theory of an antiferromagnet on a triangular lattice in a magnetic field. Journal of Physics: Condensed Matter, 3(1):69–82, 1991.
    [5] Yutaka Shirata, Hidekazu Tanaka, Akira Matsuo, and Koichi Kindo. Experimental realization of a spin-1/2 triangular-lattice heisenberg antiferromagnet. Phys. Rev. Lett., 108:057205, Jan 2012. doi:10.1103/PhysRevLett.108.057205.
    [6] L. E. Svistov, A. I. Smirnov, L. A. Prozorova, O. A. Petrenko, L. N. Demianets, and A. Ya. Shapiro. Quasi-two-dimensional antiferromagnet on a triangular lattice RbFe(moo4)2. Phys. Rev. B, 67:094434, Mar 2003. doi:10.1103/PhysRevB.67.094434.
    [7] Junsen Xiang, Chuandi Zhang, Yuan Gao, Wolfgang Schmidt, Karin Schmalzl, Chin-Wei Wang, Bo Li, Ning Xi, Xin-Yang Liu, Hai Jin, Gang Li, Jun Shen, Ziyu Chen, Yang Qi, Yuan Wan, Wentao Jin, Wei Li, Peijie Sun, and Gang Su. Giant magnetocaloric effect in spin supersolid candidate Na2BaCo(PO4)2. Nature, 625(7994):270–275, January 2024. doi:10.1038/s41586-023-06885-w.
    [8] Mingfang Shu, Xitong Xu, Ning Xi, Miao He, Junsen Xiang, Gexing Qu, Dmitry Khalyavin, Pascal Manuel, Jumpei Nakamura, Jinlong Jiao, Yonglai Liu, Guoliang Wu, Kaizhen Guo, Haitian Zhao, Wei Xu, Qingchen Duan, Ruidan Zhong, Xinqing Wang, Yuyan Han, and Zhe Qu. Giant magnetocaloric effect and spin supersolid in a metallic dipolar magnet. Nature, 651:1–7, 02 2026. doi:10.1038/s41586-026-10144-z.
    [9] Wikipedia contributors. X-ray diffraction — Wikipedia, the free encyclopedia. https://en.wikipedia.org/wiki/X-ray_diffraction, 2026.
    [10] Subramanian Research Group. Rigaku Miniflex Standard Operating Procedure (SOP). Department of Chemistry, Oregon State University. URL: https://photos.labwrench.com/equipmentManuals/7384-3827.pdf.
    [11] William Henry Bragg and William Lawrence Bragg. X Rays and Crystal Structure. G. Bell and Sons, Ltd., London, 1915.
    [12] Henry H. G. J. Moseley and Charles G. Darwin. The reflexion of the x-rays. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 26(151):210–232, 1913. doi:10.1080/14786441308634968.
    [13] Tim Cullinan. MAT E 214 x-ray generation - part 2: Bragg-brentano x-ray optics, beam conditioning. Lecture slides, Iowa State University, 2022. Spring 2022. URL: https://faculty.sites.iastate.edu/tec/files/inline-files/L17%20-%20X-ray%20Generation%20-%20Part%202%2C%20BB%20Optics%2C%20Beam%20Conditioning.pdf.
    [14] Hydrargyrum and Michael Hadmack. Bragg diffraction 2.svg. https://en.wikipedia.org/wiki/File:Bragg_diffraction_2.svg, 2011.
    [15] Saulius Gražulis, Daniel Chateigner, Robert T. Downs, A. F. T. Yokochi, Miguel Quirós, Luca Lutterotti, Elena Manakova, Justas Butkus, Peter Moeck, and Armel Le Bail. Crystallography Open Database – an open-access collection of crystal structures. Journal of Applied Crystallography, 42(4):726–729, Aug 2009. doi:10.1107/S0021889809016690.
    [16] Saulius Gražulis, Adriana Daškevič, Andrius Merkys, Daniel Chateigner, Luca Lutterotti, Miguel Quirós, Nadezhda R. Serebryanaya, Peter Moeck, Robert T. Downs, and Armel Le Bail. Crystallography open database (cod): an open-access collection of crystal structures and platform for world-wide collaboration. Nucleic Acids Research, 40(D1):D420–D427, 2012. doi:10.1093/nar/gkr900.
    [17] Patsnap Eureka. X-ray diffraction vs synchrotron radiation: Advantages. https://eureka.patsnap.com/report-x-ray-diffraction-vs-synchrotron-radiation-advantages, Feb 2026. Accessed: 2026-04-23.
    [18] National Synchrotron Radiation Research Center. TPS Technical Manual. National Synchrotron Radiation Research Center, Hsinchu, Taiwan, 2015. Available at NSRRC Public Brochure. URL: https://www.nsrrc.org.tw/NsrrcWebSystem/UPLOADS/CHINESE/PUBLISH_BROCHURE/%e6%96%87%e5%ae%a3%e8%88%87%e6%8a%80%e8%a1%93%e6%89%8b%e5%86%8a/3cf94d6ebd.pdf.
    [19] National Synchrotron Radiation Research Center. Conceptual Design Report of TPS 19A Beamline. Conceptual design report, National Synchrotron Radiation Research Center (NSRRC), Hsinchu, Taiwan, 2013. URL: https://tpsbl.nsrrc.org.tw/userdata/upload/19A/TPS19A-CDR_Final.pdf.
    [20] H. M. Rietveld. A profile refinement method for nuclear and magnetic structures. Journal of Applied Crystallography, 2:65–71, 1969. doi:10.1107/S0021889869006558.
    [21] A. A. Coelho. TOPAS and TOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C++. Journal of Applied Crystallography, 51:210–218, 2018. doi:10.1107/S1600576718000183.
    [22] Robert E. Dinnebier, Andreas Leineweber, and John S. O. Evans. Rietveld Refinement: Practical Powder Diffraction Pattern Analysis using TOPAS. De Gruyter, Berlin, Boston, 2018.
    [23] W. A. Dollase. Correction of intensities for preferred orientation in powder diffractometry: application of the March model. Journal of Applied Crystallography, 19:267–272, 1986. doi:10.1107/S0021889886089458.
    [24] L. B. McCusker, R. B. Von Dreele, D. E. Cox, D. Louër, and P. Scardi. Rietveld refinement guidelines. Journal of Applied Crystallography, 32(1):36–50, 1999. doi:10.1107/S002188989800983X.
    [25] Wei-Tin Chen. Data sheet for joining the joint instrument center: Superconducting quantum interference device. https://www.ntu-ccms.ntu.edu.tw/uploads/ckeditor/attachments/282/CP02___________________1140918__.pdf, 8 2025. Location: Room R902, CCMS; Model: Quantum Design MPMS3.
    [26] Quantum Design, Inc. MPMS 3 Platform Measurement Options. Quantum Design, Inc. Accessed: 2026-04-29. URL: https://qdusa.com/siteDocs/productBrochures/1500-103.pdf.
    [27] Quantum Design, Inc. MPMS 3 Platform Measurement Options. Quantum Design, Inc., San Diego, CA, 2023. URL: https://qdusa.com/siteDocs/productBrochures/1500-103.pdf.
    [28] A. J. Leggett. The josephson effect: Lecture 13. PHYS598 Lecture Notes, University of Illinois at Urbana-Champaign, 2015. URL: https://courses.physics.illinois.edu/phys598sc1/fa2015/Lectures/Lecture13.pdf.
    [29] Sartaj Khan, Amna Ajaz, Muhammad Irfan, Adnan Qaseem, Amaduddin Usama, Muhammad Asim Ismail, and Shahid Ali. Squid sensor technology: Fundamental principle and applications in asw operation and geophysical exploration. In 2023 20th International Bhurban Conference on Applied Sciences and Technology (IBCAST). IEEE, 2023. doi:10.1109/IBCAST59916.2023.10713008.
    [30] Stephen Tsui and Neil Dilley. Magnetism demonstrations: Magnetic signatures of some common states of materials (vibrating sample magnetometer option). Discovery Teaching Labs. California State University San Marcos and Birck Nanotechnology Center, Purdue University. URL: https://discoveryteachinglabs.com/siteDocs/EM_QD_303.pdf.
    [31] Michael McElfresh. Fundamentals of magnetism and magnetic measurements featuring quantum design’s magnetic property measurement system. Application note, Quantum Design, 1994.
    [32] Quantum Design. PPMS Property Measurement System. Quantum Design, San Diego, CA. URL: https://qdusa.com/siteDocs/productBrochures/1070-002.pdf.
    [33] Quantum Design. Dilution Refrigerator: DynaCool (D850) / PPMS (P850). Quantum Design, San Diego, CA. URL: https://qdusa.com/siteDocs/productBrochures/1084-500_PPMS_DR.pdf.
    [34] Quantum Design, Inc. Physical Property Measurement System® Heat Capacity Option User’s Manual. Quantum Design, Inc., San Diego, CA, USA, 2015. Part Number 1085-150, Rev. M7. URL: https://files.wmich.edu/s3fs-public/attachments/u1045/2019/07_1085-150%20Rev%20M7%20HEAT%20CAPACITY%20OPTION%20USER%27S%20MANUAL.pdf.
    [35] S Riegel and G Weber. A dual-slope method for specific heat measurements. Journal of Physics E: Scientific Instruments, 19:790, 11 2000. doi:10.1088/0022-3735/19/10/006.
    [36] Quantum Design. Electrical Transport Option (ETO) User’s Manual. Quantum Design, San Diego, CA, 2017. URL: https://www.nanophys.kth.se/nanolab/ppms/4307-004%20Dynacool%20Digital%20User%20Manual%20Set/10%201084-700%20Rev%20B2%20ETO%20Option%20User’s%20Manual.pdf.
    [37] Allan H. Morrish. The Physical Principle of Magnetism, volume -1. 12 2000. doi:10.1109/9780470546581.
    [38] Stephen Blundell. Magnetism in Condensed Matter. Number 4 in Oxford Master Series in Condensed Matter Physics. Oxford Univ. Press, Oxford, reprint edition, 2014.
    [39] Sam Mugiraneza and Alannah M. Hallas. Tutorial: a beginner’s guide to interpreting magnetic susceptibility data with the curie-weiss law. Communications Physics, 5(1), April 2022. doi:10.1038/s42005-022-00853-y.
    [40] Dylan Errulat, Katie Harriman, Diogo Gálico, Elvin Salerno, Johan Tol, Akseli Mansikkamäki, Mathieu Rouzières, Stephen Hill, Rodolphe Clérac, and Muralee Murugesu. Slow magnetic relaxation in a europium(ii) complex. Nature Communications, 15, 04 2024. doi:10.1038/s41467-024-46196-w.
    [41] Mariano de Souza, Ricardo Paupitz, Antonio Seridonio, and Roberto E. Lagos. Specific heat anomalies in solids described by a multilevel model. Brazilian Journal of Physics, 46(2):206–212, February 2016. doi:10.1007/s13538-016-0404-9.
    [42] Allen Wasserman. Thermal Physics: Concepts and Practice. Cambridge University Press, 06 2012. doi:10.1017/CBO9780511902611.
    [43] Wikipedia contributors. Schottky anomaly — Wikipedia, the free encyclopedia, 2025. [Online; accessed 14-May-2026]. URL: https://en.wikipedia.org/w/index.php?title=Schottky_anomaly&oldid=1329544626.
    [44] Katarína Karľová, Jozef Strečka, and Tomáš Madaras. The schottky-type specific heat as an indicator of relative degeneracy between ground and first-excited states: The case study of regular ising polyhedra. Physica B: Condensed Matter, 488:49–56, May 2016. doi:10.1016/j.physb.2016.01.033.
    [45] Wikipedia contributors. Landau theory — Wikipedia, the free encyclopedia, 2026. [Online; accessed 4-June-2026]. URL: https://en.wikipedia.org/w/index.php?title=Landau_theory&oldid=1354790881.
    [46] Wikimedia Commons. File:second order phase transition.png — wikimedia commons, the free media repository, 2026. [Online; accessed 4-June-2026]. URL: https://commons.wikimedia.org/w/index.php?title=File:Second_order_phase_transition.png&oldid=1188714911.
    [47] Wikipedia contributors. Mermin–wagner theorem — Wikipedia, the free encyclopedia, 2026. [Online; accessed 4-June-2026]. URL: https://en.wikipedia.org/w/index.php?title=Mermin%E2%80%93Wagner_theorem&oldid=1330909211.
    [48] Wikipedia contributors. Berezinskii–kosterlitz–thouless transition — Wikipedia, the free encyclopedia, 2026. [Online; accessed 4-June-2026]. URL: https://en.wikipedia.org/w/index.php?title=Berezinskii%E2%80%93Kosterlitz%E2%80%93Thouless_transition&oldid=1348385026.
    [49] MomoTheSir. What is the kosterlitz-thouless transition? Physics Stack Exchange, 2016. Accessed: 2026-06-04. URL: https://physics.stackexchange.com/q/255909.
    [50] Yuan Da Liao, Han Li, Zheng Yan, Hao-Tian Wei, Wei Li, Yang Qi, and Zi Yang Meng. Phase diagram of the quantum ising model on a triangular lattice under external field. Phys. Rev. B, 103:104416, Mar 2021. doi:10.1103/PhysRevB.103.104416.
    [51] Daisuke Yamamoto, Giacomo Marmorini, and Ippei Danshita. Quantum phase diagram of the triangular-lattice xxz model in a magnetic field. Phys. Rev. Lett., 112:127203, Mar 2014. doi:10.1103/PhysRevLett.112.127203.
    [52] Yuan Gao, Yu-Chen Fan, Han Li, Fan Yang, Xu-Tao Zeng, Xianlei Sheng, Ruidan Zhong, Yang Qi, Yuan Wan, and Wei Li. Spin supersolidity in nearly ideal easy-axis triangular quantum antiferromagnet Na2BaCo(PO4)2. npj Quantum Materials, 7:89, 09 2022. doi:10.1038/s41535-022-00500-3.
    [53] A.M.B. Douglas. The structure of Co2Al9. Acta Crystallographica (1,1948-23,1967), 3:19–24, 1950.
    [54] V. Thiede and Wolfgang Jeitschko. Crystal structure of europium cobalt aluminide (1/2/9), EuCo2Al9. Zeitschrift für Kristallographie - New Crystal Structures, 214, 11 2014. doi:10.1515/ncrs-1999-0205.
    [55] OriginLab Corporation. Smooth Algorithm: The Adjacent-Averaging Method. OriginLab Corporation, Northampton, MA, USA, 2026. URL: https://www.originlab.com/doc/Origin-Help/Smooth-Algorithm#The_adjacent-averaging_method.
    [56] D. J. García, J. G. Sereni, and A. A. Aligia. Specific heat of Gd3+ and Eu2+ based magnetic compounds. Phys. Rev. B, 113:054410, Feb 2026. doi:10.1103/rp8s-n9yh.
    [57] D. Betancourth, V. F. Correa, Jorge I. Facio, J. Fernández, V. Vildosola, R. Lora-Serrano, J. M. Cadogan, A. A. Aligia, Pablo S. Cornaglia, and D. J. García. Magnetostriction reveals orthorhombic distortion in tetragonal gd compounds. Phys. Rev. B, 99:134406, Apr 2019. doi:10.1103/PhysRevB.99.134406.

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