The interplay between quantum magnetism and strong correlation in geometrically frustrated materials

推动新材料发展的一个重要研究目标是发现新现象背后的物理机制。在许多有趣的材料中，电子及其自旋的集体性质(与电子有关的固有角动量矢量)与单粒子物理的预期有很大的不同，导致了可观察到的涌现性质。这种材料被称为强关联材料，因为如果一个位置的自旋指向一个特定的方向，则邻近位置的自旋方向与第一个位置的自旋方向高度相关。静电相互作用有利于相邻自旋排列的材料被称为铁磁体(就像冰箱上的条形磁铁)。反铁磁体更为常见，并且有利于相邻自旋的反排列。如果自旋的晶格是由等边三角形或四面体组成的，并且晶格中的键具有反铁磁相互作用，那么自旋不可能都与它们的邻居对齐。这导致存在许多等能量或简并态，自旋结构不知道该选择哪种排列。具有角共享三角形和四面体的磁性晶格的材料被称为几何受挫材料。这个计划的目标是解释和预测新材料的奇异性质，这些性质可能是由于自旋之间的磁相互作用受挫而产生的，特别是那些可能由于量子效应而产生的性质。这项工作的动机是发现了新的低自旋(因此高度量子力学)磁阻材料，包括金属和绝缘材料。这项工作将考虑在非常低的温度下不有序的磁性系统，并询问这种材料的性质对所有受挫晶格都是通用的。这个项目将调查一些还没有被归类为受挫材料，也没有从理论上被理解的材料，可能会额外归入这一类材料。这些问题将通过使用各种数值和分析理论技术来解决。

An important goal of research, driving the development of new materials, is the discovery of the physical mechanisms behind novel phenomena. In many interesting materials, the collective properties of the electrons and their spins (intrinsic angular momentum vectors associated to the electron) vary greatly from the expectations of single particle physics, leading to observable emergent properties. Such materials are referred to as strongly correlated materials, as, if the spin at one site points in a particular direction, the direction of the spin at a neighbouring site is highly correlated with the first. Materials where the electrostatic interactions energetically favour the alignment of neighbouring spins are referred to as ferromagnets (like the bar magnet on a fridge). Antiferromagnets are more common, and favour the antialignment of neighbouring spins. If a lattice of spins is made of equilateral triangles or tetrahedra, and the bonds of the lattice have antiferromagnetic interactions, the spins cannot all antialign with their neighbours. This leads to there being many equal energy or degenerate states and the spin structure doesn't know which arrangement to choose. Materials with magnetic lattices built of corner-shared triangles and tetrahedra are referred to as geometrically frustrated materials. The goal of this program is to explain and predict exotic properties of new materials which may arise due to the frustration of the magnetic interactions between spins, particularly those which may arise due to quantum effects. This work is motivated by the discovery of new low spin (and therefore highly quantum mechanical) magnetically frustrated materials, both metallic and insulating. This work will consider magnetic systems which do not order to very low temperatures and ask what properties of such materials are generic to all frustrated lattices. This program will investigate the possibility that some materials that have not yet been classified as frustrated materials, yet have also not been understood theoretically, may additionally fall into this class of materials. These issues will be addressed through the use of a variety of numerical and analytic theoretical techniques.