偏離 [111] 磁場中偶極自旋冰的相圖和動力學

Abstract

本論文以數值方法研究古典自旋冰材料二鈦酸鏑(Dysprosium Titanate)在偏離[111]磁場下的行為。古典自旋冰材料，如二鈦酸鏑和二鈦酸鈥(Holmium Titanate)，是一種幾何不穩定的材料，其中具磁性之稀土離子排列成共角四面體之結構。其晶場分裂造成之各異向性(aniostropy)導致四個頂點的自旋可以指向四面體或是遠離四面體，產生類似冰的 「兩進兩出」原則和餘熵(residual entropy)。其中餘熵的量可以透過外加磁場來控制。 在先前的數值研究中，研究者發現偶極自旋冰模型在稍微偏離[111]磁場下出現一特殊的基態自旋結構：q=X態，並指出此結構的穩定性來自於長程偶極作用。由於有研究指出，在材料二鈦酸鏑中有第二和第三鄰近自旋交互作用，本篇論文將偶極自旋冰模型擴展至包含第二和第三鄰近自旋交互作用，以古典蒙地卡羅方法研究此模型在偏離[111]磁場下之行為及第二和第三鄰近自旋交互作用的影響。另外，我們藉由量測交流磁化率來了解在此特殊磁場下自旋冰的動力學。 第一章將介紹自旋冰系統及過去研究的脈絡，包含自旋冰的動力學和其在外加磁場下之行為。 第二章將介紹本論文所使用之數值方法。我們以單自旋更新演算法(single-spin-flip algorithm)為基本架構，並使用平行回火(parallel tempering)幫助低溫系統達到平衡。另外，我們用Ewald求和法(Ewald Summation)來處理長程偶極作用。 研究結果將在第三章呈現。在對應到古典自旋冰材料二鈦酸鏑之參數下，q=X態仍存在於偏離[111]磁場下。其中額外的第三鄰近自旋交互作用會使此結構更穩定，但第二鄰近自旋交互作用會使其更不穩定。我們發現當有第二鄰近自旋交互作用很大時，會破壞q=X態結構之穩定性，使系統進入另一種基態自旋結構：fully-polarized態。至於動力學方面，在偏離[111]磁場下Kagome平面上兩種方向之交流磁化率呈現不一致的結果，尤其當溫度接近相變溫度時。

In this thesis, we study the behavior of Dysprosium Titanate (Dy_2Ti_2O_7) ,one of the well established spin ice materials, in the tilted magnetic field numerically. Spin ice has attracted much attention in frustrated systems because it is the magnetic analogue to the water ice system. The frustration leads to the degenerate ground states and the residual entropy which appears in both spin ice and water ice. The ground state degeneracy can be lifted by applying magnetic field. An ordered state, q=X state, was found previously when applying a magnetic field along [111] direction with slightly tilt toward [112] direction in a numerical study of dipolar spin ice model. In this thesis, we extended our model to generalized dipolar spin ice model by adding further-neighbor interactions. The extra second- and third-nearest neighbor exchange interactions also support the existence of q=X state but shift the boundary value of the magnetic field along [111] direction. Also, in certain parameter space of further-neighbor interactions, antiferromagnetic spin chain ordering of q=X state on Kagome plane is suppressed and fully polarized state appears instead. We also study the dynamics of spin ice in tilted [111] field near transition where ordering of spin chains on Kagome plane start to be broken by the thermal fluctuation. By numerically measuring the AC susceptibility, we find the dynamics along two perpendicular directions on Kagome plane are different.