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

点击翻译按钮获取中文摘要

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.