臺灣博碩士論文加值系統

我們使用施溫格玻色子之平均場理論來分析在二或三維下具有螺旋自旋結構的布拉菲晶格系統。透過對此晶格系統的漢彌爾頓量做對角化計算，我們得到其平均場下的自由能和低激發態的色散關係，進而找出此系統的磁性序參量。除此之外，我們亦發現一條令人驚艷的關係式，其可說明(反)鐵磁序參量和自旋量之間的關連，且可減少在解此系統的熱力學量時所出現的變數。接著，我們把得到的結果應用在實際的系統上，像是磁電鈣鈦礦—RMnO3 (R為稀土族元素)，來計算其系統的尼爾相變溫度和其它的物理量。在低於尼爾溫度時會發生施溫格玻色子的玻色—愛因斯坦凝聚現象。我們發現其理論計算的數值結果和實驗量測的量很吻合。

We have analyzed the quantum Heisenberg model on the two and three dimensional Bravais lattice in the spiral spin state using the Schwinger boson mean-field theory. By diagonalizing the system’s Hamiltonian, we obtain the general form of the mean-field free energy and the low-lying excitation dispersion relation, and then can find its magnetic order parameters. We have also found the surprising relation between the (anti)ferromagnetic order parameters and the spin quantum order by this model. It can reduce the number of variables in the calculating process. Next, we apply this model to the real systems such as RMnO3 (R denoting rare-earth ions) lattice structure to calculate the Neel temperature and other physical quantities. Below this temperature Bose-Einstein condensation of Schwinger bosons can occur. We find that it has good agreement with the experiment results.

1. Introduction...........................................1
2. Heisenberg Model.......................................4
2.1 General Form..........................................4
2.2 Classical Approach....................................5
3. Theoretical Method.....................................7
3.1 Rotation..............................................7
3.2 Schwinger Boson Representation........................8
3.3 Mean-Field Approximation..............................11
3.4 Transformation and Diagonalization....................14
3.5 Mean-Field Free Energy and Thermodynamic Quantities...16
4. Bose-Einstein Condensation In The Spiral Spin State....19
4.1 Low Temperature Behavior..............................19
4.2 Application to RMnO3 Materials........................21
5. Conclusion.............................................24
Bibliography..............................................26

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