[论文解读] Towards an Effective Spin Hamiltonian of the Pyrochlore Spin Liquid Tb2Ti2O7

Hamid R. Molavian, Paul McClarty+1 more|ArXiv.org|Dec 15, 2009

Advanced Condensed Matter Physics参考文献 4被引用 3

一句话总结

该论文通过引入虚晶场激发（VCFEs），为pyrochlore自旋液体Tb2Ti2O7构建了一个有效的自旋-1/2哈密顿量，揭示了VCFEs带来的量子修正可稳定一个q=0有序冰相，并在反铁磁性近邻交换作用下诱导出铁磁关联。VCFEs引起的三体相互作用和Ising耦合导致了超出偶极相互作用的几何阻挫，解释了在50 mK以下仍无长程有序的现象。

ABSTRACT

Tb2Ti2O7 is a pyrochlore antiferromagnet that has dynamical spins and only short-range correlations even at 50 mK; the lowest temperature explored so far, which is much smaller than the scale set by the Curie-Weiss temperature T_{CW}~14 K. The absence of long-range order in this material is not understood. Recently, virtual crystal field excitations (VCFEs) have been shown to be significant in Tb2Ti2O7. While previous work found that VCFEs-induced renormalization of the nearest neighbor Ising exchange leads to spin ice correlations on a single tetrahedron, their effect on spin correlations has not been fully explored. In this paper, we construct an effective spin-1/2 low-energy theory for Tb2Ti2O7 on the pyrochlore lattice. We determine semiclassical ground states on a lattice that allow us to see how the physics of spin ice is connected to the possible physics of Tb2Ti2O7. We observe a shift in the phase boundaries with respect to those of the dipolar spin ice model as the quantum corrections become more significant. In addition to the familiar classical dipolar spin ice model phases, we see a stabilization of a q = 0 ordered ice phase over a large part of the phase diagram; ferromagnetic correlations being preferred by quantum corrections in spite of an antiferromagnetic nearest neighbor exchange in the microscopic model. Frustration is hence seen to arise from virtual crystal field excitations over and above the effect of dipolar interactions in spin ice in inducing ice-like correlations.

研究动机与目标

• 构建一个包含虚晶场激发（VCFEs）的Tb2Ti2O7低能有效自旋-1/2哈密顿量。
• 理解VCFEs如何在该pyrochlore自旋液体中导致阻挫并抑制长程磁序。
• 确定量子修正在稳定非平凡自旋关联（包括q=0有序冰相）中的作用。
• 通过分析偶极相互作用与VCFE诱导项之间的相互作用，建立自旋冰物理与Tb2Ti2O7物理之间的联系。

提出的方法

• 利用二阶微扰论推导有效自旋哈密顿量，以描述Tb2Ti2O7中的虚晶场激发（VCFEs）。
• 使用泡利矩阵代数将微观自旋-1/2哈密顿量映射到pyrochlore晶格上的低能有效理论。
• 通过对激发的晶场态求和，计算VCFE诱导的相互作用，得到Ising和三体自旋相互作用。
• 通过数值计算矩阵元和迹分解，提取有效哈密顿量的耦合常数。
• 通过分析半经典基态来绘制相图边界并识别稳定相。
• 将结果与经典偶极自旋冰模型进行比较，以分离出VCFEs带来的量子修正效应。

实验结果

研究问题

• RQ1 虚晶场激发（VCFEs）如何在Tb2Ti2O7中修改有效自旋哈密顿量，使其超越标准偶极相互作用？
• RQ2 VCFEs带来的量子修正在无长程有序条件下稳定q=0有序冰相中起什么作用？
• RQ3 VCFE诱导的三体和Ising相互作用在Tb2Ti2O7中导致阻挫的程度如何？
• RQ4 由于VCFEs效应，Tb2Ti2O7的相图与经典偶极自旋冰模型有何不同？
• RQ5 VCFEs能否解释Tb2Ti2O7中短程自旋关联持续存在于50 mK以下的现象？

主要发现

• 虚晶场激发（VCFEs）在Tb2Ti2O7中诱导出有效Ising和三体自旋相互作用，使低能哈密顿量超出偶极项的修正。
• VCFEs带来的量子修正稳定了q=0有序冰相，该相在经典偶极自旋冰模型中并不存在。
• 尽管微观模型中近邻交换作用为反铁磁性，VCFEs在有效理论中仍倾向于形成铁磁关联。
• 随着量子修正的增强，相边界发生显著移动，表明VCFEs是超越几何和偶极效应的主导阻挫来源。
• q=0有序相的稳定表明，VCFEs的量子效应在任何晶场能隙约为100 K或更小的pyrochlore材料中均可能具有重要意义。