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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 高英哲(Ying-Jer Kao) | |
| dc.contributor.author | Yuan-Chi Yang | en |
| dc.contributor.author | 楊淵棨 | zh_TW |
| dc.date.accessioned | 2021-06-16T08:07:17Z | - |
| dc.date.available | 2016-07-16 | |
| dc.date.copyright | 2014-07-16 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-06-11 | |
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B, vol. 64, p. 224416, Nov 2001. [21] J. Zhang, K. Fritsch, Z. Hao, B. V. Bagheri, M. J. P. Gingras, G. E. Granroth, P. Jiramongkolchai, R. J. Cava, and B. D. Gaulin, ``Neutron spectroscopic study of crystal field excitations in Tb2Ti2O7 and Tb2Sn2O7,' eprint arXiv:cond-mat/1310.3264, Oct. 2013. [22] S. H. Curnoe, ``Effective spin-1/2 exchange model for Tb2Ti2O7,' Phys. Rev. B, vol. 88, p. 014429, Jul 2013. [23] K. Fritsch, K. A. Ross, Y. Qiu, J. R. D. Copley, T. Guidi, R. I. Bewley, H. A. Dabkowska, and B. D. Gaulin, ``Antiferromagnetic spin ice correlations at (12 , 1 2 , 1 2 ) in the ground state of the pyrochlore magnet Tb2Ti2O7,' Phys. Rev. B, vol. 87, p. 094410, Mar 2013. [24] K. Fritsch, E. Kermarrec, K. A. Ross, Y. Qiu, J. R. D. Copley, D. Pomaranski, J. B. Kycia, H. A. Dabkowska, and B. D. Gaulin, ``Temperature and Magnetic Field Dependence of Spin Ice Correlations in the Pyrochlore Magnet Tb2Ti2O7,' eprint arXiv:cond-mat/1312.0847, Dec. 2013. [25] T. Taniguchi, H. Kadowaki, H. Takatsu, B. Fak, J. Ollivier, T. Yamazaki, T. J. Sato, H. Yoshizawa, Y. Shimura, T. Sakakibara, T. Hong, K. Goto, L. R. Yaraskavitch, and J. B. Kycia, ``Long-range order and spin-liquid states of polycrystalline Tb2Ti2O7,' Phys. Rev. B, vol. 87, p. 060408, Feb 2013. [26] R. Pynn, Neutron Scattering A Primer. Los Alamos Neutron Science Center, 1990. [27] J. Jensen and A. R. Mackintosh, Rare Earth Magnetism: Structures and Excitations. Clarendon Press Oxford, 1991. [28] K. A. Ross, L. Savary, B. D. Gaulin, and L. Balents, ``Quantum Excitations in Quantum Spin Ice,' Phys. Rev. X, vol. 1, p. 021002, Oct 2011. [29] Private Conumication with S. Onoda. [30] H. R. Molavian, P. A. McClarty, and M. J. P. Gingras, ``Towards an Effective Spin Hamiltonian of the Pyrochlore Spin Liquid Tb2Ti2O7,' eprint arXiv:cond-mat/ 0912.2957, Dec. 2009. [31] S. H. Curnoe, ``Quantum spin configurations in Tb2Ti2O7,' Phys. Rev. B, vol. 75, p. 212404, Jun 2007. [32] S. H. Curnoe, ``Structural distortion and the spin liquid state in Tb2Ti2O7,' Phys. Rev. B, vol. 78, p. 094418, Sep 2008. [33] P. M. Chaikin and T. C. Lubensky, Principle of condensed matter physics. Cambridge, 1995. [34] J. N. Reimers, A. J. Berlinsky, and A.-C. Shi, ``Mean-field approach to magnetic ordering in highly frustrated pyrochlores,' Phys. Rev. B, vol. 43, pp. 865--878, Jan 1991. [35] M. Enjalran and M. J. P. Gingras, ``Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of the Tb2Ti2O7 pyrochlore antiferromagnet,' Phys. Rev. B, vol. 70, p. 174426, Nov 2004. [36] M. Enjalran and M. J. P. Gingras, ``Theory of Two-Step Magnetic Ordering Phenomena in a Geometrically Frustrated Heisenberg Pyrochlore Antiferromagnet with Long Range Dipolar Interactions,' eprint arXiv:cond-mat/0307152, July 2003. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58165 | - |
| dc.description.abstract | 在本論文中，我們研究一種磁性的pyrochlore 氧化物，Tb2Ti2O7。
我們從一個微觀漢米爾頓出發，並對鋱離子4f 電子和氧離子2p 電子 之間的想像躍遷進行強相關微擾展開，而建立一個在一種量子自旋冰 材料上的等效模型。我們也考慮鋱離子晶格場基態及第一激發態之間 的量子波動。在這個模型中，除了二次交互作用之外，也包括一種三 體作用。我們提出可以解釋中子散射實驗中 Q = (1/2, 1/2, 1/2)次序的參數。 本論文的內容適合下列兩類型的讀者閱讀 • 對量子自旋冰系統有興趣，尤其是鋱鈦酸Tb2Ti2O7。 • 熟悉超交換作用和微擾理論，並對於其在挫折系統中的應用有興 趣的人。 | zh_TW |
| dc.description.abstract | In this thesis, we study a magnetic pyrhochlore oxide, Tb2Ti2O7, which shows quantum spin ice behavior. We construct an effective pseudospin-1/2 model for a quantum spin ice material, Tb2Ti2O7, starting from a microscopic
Hamiltonian of Tb3+ local moments, and performing a strong-coupling perturbation expansion of the virtual hopping between the Tb 4f and O 2p electrons. We consider also the quantum fluctuations between the ground state and the low-lying first excited doublets of the Tb3+ crystal field levels. In this model, in addition to the exchange interactions, a three-body interaction among three neighboring spins is generated. We study this model using both the variational and real-space mean field theories. We propose parameters which can explain the Q = (1/2, 1/2, 1/2) short-range order observed in the neutron scattering experiment of Tb2Ti2O7. This thesis is intended for the reader who: • is interested in quantum spin ice system, especially Tb2Ti2O7. • is familiar with superexchange interaction and perturbation theory, and interested in their application on frustrated systems. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T08:07:17Z (GMT). No. of bitstreams: 1 ntu-103-R01222074-1.pdf: 9263614 bytes, checksum: a8bc2060c3e649574fea827a277ee8eb (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 口試委員審定書 i
銘謝ii Acknowledgments iii 摘要iv Abstract v Contents vi List of Figures viii List of Tables x 1 Introduction 1 1.1 Geometrical Frustration . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Magnetic Pyrochlore Oxides . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Spin Ice and Quantum Spin Ice . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.1 Spin Ice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.2 Quantum Spin Ice . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2 Theory 17 2.1 Superexchange Interaction . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Second-order Perturbation in 1 Δ . . . . . . . . . . . . . . . . . . . . . . . 19 2.3 Effective Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4 Mean Field Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4.1 Real-Space Mean Field Theory(RSMFT) . . . . . . . . . . . . . 23 2.4.2 Landau Theory and Variational Mean Field Theory(VMFT) . . . 26 3 Results 28 3.1 Mean Field Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.1.1 RSMFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.1.2 VMFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Diffuse Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . 33 4 Summary 40 A Crystal Field Levels of Terbium Titanate 41 B Effective Hamiltonian 43 C Real-Space Mean Field Theory(RSMFT) 48 D Variational Mean Field Theory(VMFT) 52 E Diffuse Neutron Scattering on Tb2Ti2O7 57 Bibliography 65 | |
| dc.language.iso | en | |
| dc.subject | 鋱鈦酸 | zh_TW |
| dc.subject | 量子自旋冰 | zh_TW |
| dc.subject | 中子散射 | zh_TW |
| dc.subject | 平均場理論 | zh_TW |
| dc.subject | 強相關微擾展開 | zh_TW |
| dc.subject | quantum spin ice | en |
| dc.subject | neutron scattering | en |
| dc.subject | mean field theory | en |
| dc.subject | strong-coupling perturbation expansion | en |
| dc.subject | Terbium Titanate | en |
| dc.title | 量子自旋冰物質鋱鈦酸的等效模型 | zh_TW |
| dc.title | Effective Model on a Quantum Spin Ice Material Tb2Ti2O7 | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 胡崇德(Chong Der Hu),郭光宇(Guang-Yu Guo),張烈錚(Lieh-Jeng Chang) | |
| dc.subject.keyword | 鋱鈦酸,量子自旋冰,中子散射,平均場理論,強相關微擾展開, | zh_TW |
| dc.subject.keyword | Terbium Titanate,quantum spin ice,neutron scattering,mean field theory,strong-coupling perturbation expansion, | en |
| dc.relation.page | 68 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-06-11 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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