Grant: Discovery Grants Program - Individual

Frustration due to competing interactions is ubiquitous in nature - it acts among charge carriers in copper-oxide superconductors, is at play in the nuclear matter of neutron stars, and is at the heart of the protein folding problem. A high degree of frustration can lead to novel states of matter with exotic properties, often accompanied by substantial quantum mechanical fluctuations. The study of frustrated spin systems aimed as uncovering how the tussle between competing spin-spin interactions gets resolved, and how new physical phenomena or novel states of matter can emerge, is enhancing our broad understanding of condensed matter systems with strongly competing interactions. In this proposal, three objectives aim to advance our understanding of the phenomena showcased by highly frustrated magnetic systems. The first objective aims to understand the classical and quantum phenomena displayed by a novel frustrated "spin vorticity model". Each classical ground state of this model may be decomposed into collections of closed 2-dimensional "membranes of spins" and support fractionalized string excitations attached to the edges of open membranes. A number of analytical and numerical methods will be employed to uncover and understand the collective and exotic properties of this model. Frustrated spin systems often possess a large number of classical ground states that are energetically accidentally degenerate (i.e. all have the same energy). In such cases, thermal and quantum fluctuations can lift the degeneracy and select a subset of the degenerate states; a process called order-by-disorder (ObD). While ObD has been much studied theoretically, there is no known direct smoking-gun evidence of ObD in real materials. The second objective of this proposal will help address this conundrum by investigating the mechanisms via which ObD, when generated by thermal fluctuations, can produce a universal temperature dependence of the energy gap of the magnetic excitations in the system. Finding experimentally such a temperature dependence of the gap would help evincing ObD in real materials. A number of materials with magnetic rare-earth ions display a gamut of interesting magnetic phenomena. Most theoretical approaches used to describe the properties of these materials consider models in which individual magnetic moments are represented by a quantum spin-1/2 object, with each "spin" interacting with its nearest neighbours, such that the energy (Hamiltonian) of the system consist of a sum of pairwise spin-spin interactions. A number of puzzling experimental results suggest that such models need to be modified in two ways: (1) by including interactions that extend beyond nearest neighbour distance and (2) by including "many-body" interactions where trios, quartets, etc of spins interact together. The third objective will be to investigate whether such "upgrades" to pairwise models allow the puzzling experimental results to be understood.