Harnessing disorder to tune, tailor and design classical and quantum spin liquids

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Entanglement underpins many of the defining non-classical properties of quantum mechanics, and long-range entanglement engenders exotic phenomena such as fractional quantum numbers and emergent topological excitations. The next generation quantum technologies will rely on our understanding and exploitation of coherence and entanglement, and this proposal directly tackles these issues. Exemplars of massive long-range entangled phases are quantum spin liquids -- states of quantum magnets in which electronic spins reside in macroscopic superpositions of infinitely many disordered, liquid-like microstates. Frustrated pyrochlore magnets often exhibit liquid-like short-range correlations down to the lowest temperatures and are therefore ideal candidate materials to look for classical and quantum spin liquid behaviour. The presence of disorder in any of its forms -- fluctuations, strain, structural defects -- is usually regarded as a nuisance that has the potential to obscure or disrupt the sought-after spin liquid phase. However, it has also been recently shown that the presence of structural disorder can sometimes stabilise classical and quantum spin liquids, and it can even lead to new magnetic degrees of freedom, the formation of topological spin glasses and the formation of entirely novel quantum spin liquids. Inspired by these results, we here take the view of disorder as a resource to tailor, tune and control spin liquid behaviour and quantum entanglement. Specifically, we propose to introduce structural disorder in pyrochlore materials in a controlled manner via doping, and to determine the defect structures using single-crystal diffuse neutron scattering. The results from these measurements will allow us to develop theoretical models and simulations to understand how the defects change the magnetic properties of the ions and their collective behaviour. In parallel to candidate materials for quantum spin liquid behaviour, we will also study related materials in the so-called `classical' regime, where the properties without disorder are better understood and where modelling and simulation capabilities are generally greater; in doing this we shall provide insight and support to the analysis of the more challenging quantum regime. In our concerted theory-experiment approach, we expect the insight from modelling to feed back into deciding which further samples to grow and which measurements to perform to test our predictions, ranging from thermodynamic measurements to dynamical structure factors using polarized neutrons. We will investigate questions about the stability of quantum spin liquid phases; the promotion of quantum fluctuation due to effective transverse fields introduced by disorder; the scattering and trapping of emergent excitations, and in general questions about localisation and glassiness, in response to the disorder produced by structural distortions. Our overarching aim is to investigate the relationship between topology, glassiness and liquidity, and to obtain unambiguous evidence for long-range entanglement in quantum spin liquids.