量子自旋冰物質鋱鈦酸的等效模型

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。

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.