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  • 學位論文

偶極自旋冰在偏離[111]方向的磁致相變

Phase Transitions of Dipolar Spin Ice in Tilted [111] Field

指導教授 : 高英哲

摘要


阻挫性磁性材料是凝態物理中一門有趣的課題。除了自旋液體(spin liquid)、自旋玻璃(spin glasses)以外,新興的自旋冰(spin ice)材料在過去二十年逐漸為人所熟知並且被廣泛研究。除實驗技術的演進使自旋冰在極低溫度下的性質能被研究外,數值模擬方法的發展與運算資源的突破亦提供理論學家可行的研究工具。在古典自旋冰材料如二鈦酸鏑(dysprosium titanate)與二鈦酸鈥(holmium titanate)中,磁性稀土離子是以頂點相接的正四面體單元所形成的特殊結構。由於其特殊的幾何結構和晶場分裂所造成的各向異性(anisotropy),產生磁阻挫性與低溫時冰法則(ice rule)的微觀態限制。最常見的理論模型是最鄰近自旋交互作用模型(nearest-neighbor model),大多數的自旋冰行為可以在此模型的理論研究中重現。但是,有越來越多的實驗現象無法以此模型描述,因此其他模型如遠程偶極交互作用模型(long-range dipolar model)被提出,並在數值模擬中確認其有效性。 在過去自旋冰的中子散射實驗中,研究者在稍微偏離[111]方向的外加磁場之下,觀察到特殊的臨界散射,其行為無法在最鄰近模型的模擬中重現。本篇論文使用古典蒙地卡羅模擬方法,研究遠程偶極交互作用模型在此特殊磁場方向之下的行為。並提出對實驗現象的可能解釋。 在第一章中將會介紹阻挫性自旋系統以及自旋冰材料過去的研究脈絡,尤其是不同理論模型的差異與在不同磁場方向下的行為。第二章將介紹本篇論文中使用到的數值工具與計算方法。本篇主要使用的演算法是單自旋更新演算法(single-spin-flip-update),輔以平行回火(parallel tempering)以幫助系統在低溫下達到熱平衡。另外,遠程交互作用在數值運算中難以直接計算,我們使用Ewald求和法(Ewald summation)去處理遠程的偶極交互作用。 第三章中,我們將呈現遠程偶極作用模型的模擬結果。我們發現,此模型可以重現前述中子散射實驗中的圖譜,因此比最鄰近作用模型更貼近實際的自旋冰材料行為。此外,我們發現此臨界散射乃是由於一個特殊的基態自旋結構:q = X態,由於此結構的穩定性是來自於遠程的偶極作用,因此無法在過去最鄰近作用模型當中被發現。此狀態在溫度變化下會經歷一個明顯的相變,因此實驗上可以在熱力學性質測量中確認此相變的存在。本篇論文的結論增加了理論研究者對偶極作用模型在模擬自旋冰材料的信心,並且提供實驗學家進一步研究q = X態的可能性。

並列摘要


Frustrated spin system is a popular and challenging field in condensed matter physics. The complicated interplay between interactions and special geometry of the lattice leads to macroscopically degenerate ground states even at the temperatures closed to absolute zero. Among frustrated magnets, the classical spin ice is very noticeable because it is the magnetic analogue to the water ice system. Ground state degeneracy, residual entropy, and the ice-rule configurations are found in both water ice and spin ice. In this thesis, we numerically study the dipolar spin ice model under slightly tilted magnetic field in [111] direction by classical Monte Carlo simulation. The Ewald summation and parallel tempering algorithm are applied for calculating the long-range interaction and equilibrating the system at low temperatures, respectively. The magnetic scattering maps are produced in our simulation and are comparable to the results of neutron scattering experiment. Also, we find a phase transition and a long-range ordered state which is responsible for the anomalous critical scattering observed in single crystal of Ho2Ti2O7. The order parameter is calculated to show that the origin of ordering comes from antiferromagnetic alignment of spins on the kagome plane. The recovery of thermal entropy indicates the broken degeneracy of kagome ice phase under the perturbation of tilted field. Finally, we plot the phase diagram in different magnetic fields and temperatures, and discuss several spin configurations accounted for different phase regions.

參考文獻


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