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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 高英哲 | |
| dc.contributor.author | Yang-Zhi Chou | en |
| dc.contributor.author | 周揚智 | zh_TW |
| dc.date.accessioned | 2021-06-15T01:42:39Z | - |
| dc.date.available | 2010-07-16 | |
| dc.date.copyright | 2009-07-16 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-07-13 | |
| dc.identifier.citation | [1] R. Moessner and J. Chalker, Phys. Rev. Lett. 80, 2929 (1998). 8
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43207 | - |
| dc.description.abstract | 自旋冰系統(spin ice)的最簡易模型可用一個非等向性(anisotropy)的Heisenberg 模型描述。過去的研究只著重在當此非等向性無限強的情況，此時可以得到一個Ising 模型來描述。 我們主要的研究在於有限非等向性的修正，嘗試更進一步的與真實物質比對。
首先在古典的Heisenbeg 模型裡，我們在強非等向性極限下使用微擾方法(perturbation)，得到了一個q=0 的有序態。 我們在量子的Heisenberg 模型裡，採用簡併態的微擾理論，於強非等向性極限下得到了一個半古典的等效Ising模型。 我們亦使用VMFT 來探索其有序態且計算中子繞射圖。 VMFT 的結果也支持q=0 的有序態。 我們也用Monte Carlo 與loop update 方法來求半古典的等效Ising 模型的基態。得到的結果和古典模型一致，q=0 的有序態。從自旋冰到q=0 有序態的相變為一階相變。我們也提供了相關的相圖。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2021-06-15T01:42:39Z (GMT). No. of bitstreams: 1 ntu-98-R96222057-1.pdf: 1782533 bytes, checksum: 8efc97015e378a8bfbeddebde02c7441 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | 1 Introduction 8
1.1 Geometrical Frustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Geometrical Frustrated Ferromagnet: Spin Ice . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Microscopic Models of Pyrochlore Spin Ice . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 Ice Rule: Strong Local Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5 Quantum Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.6 Low Temperature behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.7 Corrections of Finite Anisotropy in Spin Ice . . . . . . . . . . . . . . . . . . . . . . . 16 2 Classical Heisenberg Model 17 2.1 Classical Heisenberg Model in a single Tetrahedron . . . . . . . . . . . . . . . . . . . 18 2.2 Anisotropic Heisenberg Model in Pyrochlore . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Ferromagnetic Interaction in The Strong Anisotropic Limit . . . . . . . . . . . . . . 19 3 Eective Hamiltonian 23 3.1 Rayleigh-Schr�odinger Perturbation Theory . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1.1 An Example: A Pair of Spin-S Model with Collinear Anisotropy . . . . . . . 26 3.2 The Eective Hamiltonian For Finite The Anisotropic Spin Ice . . . . . . . . . . . . 28 3.3 A Digression: Eective Hamiltonian for Spin-1 Heisenberg Model . . . . . . . . . . . 32 3.4 Brief Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4 Variational Mean Field Theory 35 4.1 Review of VMFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.1.1 Landau Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.2 VMFT for Pyrochlore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.2.1 Anisotropic Classical Heisenberg Model . . . . . . . . . . . . . . . . . . . . . 39 4.2.2 Eective Ising Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.3 Elastic Neutron Scattering Cross Section in VMFT . . . . . . . . . . . . . . . . . . . 43 4.3.1 Elastic Neutron Scattering Cross Section in Dipolar Approximation . . . . . 43 4.3.2 Neutron Scattering in The Mean Field Approximation . . . . . . . . . . . . . 45 4.3.3 Neutron Scattering Patterns in VMFT . . . . . . . . . . . . . . . . . . . . . . 47 4.3.4 The Peak Shift And The Soft Mode . . . . . . . . . . . . . . . . . . . . . . . 49 4.4 Summary of VMFT Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5 Monte Carlo Simulation 53 5.1 Basic Ideas of Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.1.1 Markov Processes, Ergodicity, and Detailed Balance . . . . . . . . . . . . . . 54 5.2 Metropolis Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.3 Loop Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.3.1 Long Loop Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.3.2 Short Loop Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.4 Summary of Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 6 Simulation Results of Eective Ising Hamiltonian 61 6.1 Ground State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.2 Excited States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.2.1 Properties Between Two Phases . . . . . . . . . . . . . . . . . . . . . . . . . 66 6.3 Phase Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 6.4 Brief Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 7 Conclusion 69 A Positions and Displacements 72 A.1 Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 A.2 Local Frame Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 B Eective Hamiltonian 74 B.1 Detailed Calculations for Eective Hamiltonian . . . . . . . . . . . . . . . . . . . . . 74 B.1.1 Non-collinear Easy Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 B.1.2 Mapping to Ising Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 B.2 Lists of Coecients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 B.3 Lists of Interaction Pairs In Eective Hamiltonian . . . . . . . . . . . . . . . . . . . 78 B.4 Parameters in Spin-1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 C Interaction Matrices in VMFT 82 C.1 Construction of Interaction Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 C.2 Reduction from Heisenberg Model to Ising Model . . . . . . . . . . . . . . . . . . . . 83 Bibliography . . . . . . . . . .85 | |
| dc.language.iso | en | |
| dc.subject | 非等向性 | zh_TW |
| dc.subject | 自旋冰 | zh_TW |
| dc.subject | 幾合挫折 | zh_TW |
| dc.subject | anisotropy | en |
| dc.subject | geometrical frustration | en |
| dc.subject | spin ice | en |
| dc.title | 有限非等向性效應在自旋冰系統 | zh_TW |
| dc.title | Finite Anisotropy Effect in The Spin Ice System | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 郭光宇,胡崇德,陳智泓 | |
| dc.subject.keyword | 自旋冰,幾合挫折,非等向性, | zh_TW |
| dc.subject.keyword | spin ice,geometrical frustration,anisotropy, | en |
| dc.relation.page | 87 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-07-13 | |
| 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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