Grant: Discovery Grants Program - Individual

This proposal concerns magnetic and superconducting crystals with exotic, symmetry-derived properties. At high temperatures, an ordered, non-magnetic crystal possesses the following symmetries: time reversal (i.e. the crystal appears the same whether time runs forward or backwards); various discrete rotations (for example, a cubic crystal looks the same if turned by 90 degrees); and discrete translations (when viewed on an atomic scale, the crystal can be moved a tiny distance corresponding to the size of the crystal unit cell). Time reversal symmetry is broken in magnetic crystals, which means that the direction of the magnetisation depends on the direction of time. In addition to time reversal symmetry breaking, other symmetries may be broken as well. In superconductors, a more complicated kind of symmetry, called gauge symmetry, is broken. This may also be accompanied by other kinds of symmetry-breaking, including broken time reversal symmetry. This work has several components, covering a wide range of issues in magnetic and superconducting systems. The first part concerns the existence of magnetism in crystals known as pyrochlores, which possess a complicated but highly symmetric structure. These systems are described by simple theoretical models, but it turns out that the models are extremely difficult to analyse. Part of this work will study these models using computers. The second part concerns magneto-electric crystals: materials for which the magnetic properties can be controlled by electric fields (and vice versa). The rest of the proposal deals with superconductors. Experimental studies yield a great deal of information about the symmetry properties of superconductors, but the route is often indirect and heavily reliant on theoretical calculation, which this work aims to provide. In each of these topics, the fundamental properties of matter, namely quantum mechanical and collective behaviour, will be investigated. While magneto-electric materials have obvious technological applications as data storage media, the exploitation of other unusual properties of magnetic and superconducting materials is just beginning to be explored.