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研究生： 郭家農
Kuo, Chia-Nung
論文名稱： 核磁共振研究自旋能隙系統: Cu2Sc2Ge4O13, Cu2PO4OH, and BiCu2VO6
NMR Study of Spin Gap Systems: Cu2Sc2Ge4O13, Cu2PO4OH, and BiCu2VO6
指導教授： 呂欽山
Lue, Chin-Shan
學位類別： 博士
Doctor
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2010
畢業學年度： 98
語文別： 英文
論文頁數： 101
中文關鍵詞： 自旋能隙 、核磁共振
外文關鍵詞： Spin Gap, NMR
相關次數： 點閱：65  下載：7 
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    • 低維度磁性系統近年來在實驗及理論方面都已被廣泛的研究，由低維數引起的量子漲落會壓抑長程磁有序並可能造成一個有限的自旋能隙的開啟。在本篇論文中我們對三個不同的自旋能隙化合物Cu2Sc2Ge4O13, Cu2PO4OH, 及 BiCu2VO6以核磁共振技術進行了詳細的研究。三個樣品隨溫度變化的共振譜線位移與譜線寬度都顯示了低維磁性的特徵以及缺乏長程磁有序。超精細偶合常數可以從共振譜線位移對磁化率的變化求出。我們更進一步研究了變溫下的自旋晶格鬆弛率。變溫譜線位移與自旋晶格鬆弛率都表現出熱活化的反應，並且確認了自旋能隙的存在。其自旋能隙大小可個別由二聚體模型，四聚體模型，以及自旋梯的經驗公式推導出來。

    The low-dimensional magnetic systems have been widely investigated theoretically and experimentally in recent years. Strong quantum fluctuations due to low dimensionality may suppress the long-range magnetic ordering, resulting in an opening of a finite spin gap. In this thesis, we presented a detailed NMR study on the three spin gap compounds: Cu2Sc2Ge4O13, Cu2PO4OH, and BiCu2VO6. All the temperature dependence of NMR shifts and spectral line widths exhibit a character of low-dimensional magnetism and the absence of long-range ordering. The hyperfine coupling constants of those compounds can be extracted from the variation of NMR shift against magnetic susceptibility.
    We investigated the temperature dependence of spin-lattice relaxation rates further. Both NMR shifts and spin-lattice relaxation rates revealed the thermal activated behavior, confirming the existence of spin gap in those compounds. The values of spin gap can be deduced from the dimer model, tetramer model, and empirical formula, respectively.

    中文摘要………………………………………………………………………6 ABSTRACT…………………………………………………………………7 致謝…………………………………………………………………………8 Table of Content 1 Introduction……………………………………………………………9 1.1 Spin-Peierls compounds…………………………………10 1.2 Dimerized systems…………………………………………12 1.3 Two-dimensional frustrated systems…………………13 1.4 Spin ladder systems………………………………………14 1.5 Haldane gap systems………………………………………16 1.6 References…………………………………………………18 2 Fundamental principles of NMR…………………………21 2.1 Zeeman effect………………………………………………21 2.2 Hyperfine interaction……………………………………23 2.3 NMR line shape……………………………………………24 2.4 Quadrupole effect…………………………………………25 2.5 Magnetic ordering…………………………………………27 2.6 Other effects ……………………………………………28 2.7 Knight Shift………………………………………………29 2.8 Spin-lattice relaxation…………………………………31 2.9 References…………………………………………………34 3 Experiment methods of NMR………………………………35 3.1 Equations of motion………………………………………35 3.2 FID and Spin-Echo…………………………………………36 3.3 Magnetization Recovery of T1……………………………38 3.4 References……………………………………………………41 4 Theoretical models for spin gap systems……………42 4.1 Superexchange………………………………………………42 4.2 Curie-Weiss law……………………………………………43 4.3 Frustrated spin-1/2 chain………………………………44 4.4 Dimer model…………………………………………………45 4.5 Tetramer model………………………………………………48 4.6 Empirical formula for two-leg Heisenberg spin ladder……………………………………………………………………50 4.7 References…………………………………………………52 5 Experiment apparatus………………………………………53 5.1 NMR spectrometer……………………………………………54 5.2 NMR probe……………………………………………………55 5.3 Superconducting magnet……………………………………56 5.4 Temperature controller and cryostat…………………57 5.5 References……………………………………………………59 6 Cu2Sc2Ge4O13 : Isolated dimer chain system…………60 6.1 Introduction…………………………………………………60 6.2 Sample preparation…………………………………………60 6.3 Structure……………………………………………………61 6.4 NMR line shape and NMR shift……………………………63 6.5 Spin-lattice relaxation rate……………………………66 6.6 Conclusion……………………………………………………70 6.7 References……………………………………………………71 7 Cu2PO4OH: Square spin tetramer system………………72 7.1 Introduction…………………………………………………72 7.2 Sample preparation…………………………………………72 7.3 Structure……………………………………………………74 7.4 Magnetic susceptibility…………………………………75 7.5 NMR line shape and NMR shift……………………………77 7.6 Spin-lattice relaxation rate……………………………81 7.7 Conclusion……………………………………………………83 7.8 References……………………………………………………84 8 BiCu2VO6 : Two-leg spin ladder system………………86 8.1 Introduction…………………………………………………86 8.2 Sample preparation…………………………………………86 8.3 Structure……………………………………………………87 8.4 Magnetic susceptibility…………………………………89 8.5 NMR line shape and NMR shift……………………………92 8.6 Spin-lattice relaxation rate……………………………95 8.7 Conclusion………………………………………………………97 8.8 References……………………………………………………99 9 Conclusion…………………………………………………100 List of publications………………………………………………101

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