Fullerene molecules are hollow cages of carbon atoms, for the discovery of which the British scientist Harry Kroto won the Nobel prize in 1996. Inside the cage is an empty space. Chemists and physicists have found many ingenious ways of trapping atoms or molecules inside the tiny fullerene cages. These encapsulated compounds are called endofullerenes. "Molecular surgery" is a remarkable synthetic method. First, a series of chemical reactions is used to open a hole in the fullerene cages. A small molecule such as water (H2O) is inserted into each fullerene cage by using high temperature and pressure. Finally, a further series of chemical reactions is used to "sew" the holes back up again. The result is the remarkable chemical compound called water-endofullerene, denoted H2O@C60. Our team has succeeded in developing new synthetic routes which have allowed the synthesis of endofullerenes containing a broader range of molecules, such as HF@C60 and CH4@C60. Larger fullerenes than C60 exist. The fullerene C70 consists of ellipsoidal carbon cages, surrounding a cavity which is larger than that of C60. The cavity of C70 may accommodate two atoms or small molecules. We propose to create such systems, and study the properties of the encapsulated molecules and atoms. One example is C70 containing two 3He atoms. The two 3He atoms are squeezed together by confinement inside the same cavity, and comprise an "artificial molecule" which cannot exist without confinement. We will synthesise such C70 endofullerenes, and study their quantised rotational, vibrational, and translational motions, using a variety of electromagnetic spectroscopic techniques as well as inelastic neutron scattering. The study of such systems will provide a wealth of experimental data on non-covalent interactions. Such information is very valuable since (1) non-covalent interactions are critically important for a wide range of materials and biomolecular properties, and (2) non-covalent interactions are hard to estimate for systems of reasonable size by current computational chemistry techniques. Some C70 endofullerenes will display spin isomerism, meaning that there are different varieties of the same compound, differing only by the way the nuclear magnetic moments are aligned with respect to each other. Such compounds will be particularly interesting if they also contain unpaired electron spins. For such systems, the energy splitting associated with the spin isomerism may be brought into coincidence with the energy splitting between the electron spin states, induced by an applied magnetic field. We expect to observe unique spectroscopic phenomena in such systems including highly selective magnetic-field-induced spin-isomer conversion. This conversion may be accompanied by enhancement of nuclear magnetic resonance signals. This phenomenon can eventually lead to new ways to enhance magnetic resonance imaging signals, with applications to the imaging of materials and in the clinical sciences.

Throwing a stone into water excites a wave that decays in distance and time. However, some wave-like phenomena, known as topological objects (TOs), don't behave like this. They are localised in space and trapped in existence for long periods of time. Many such TOs are found in magnetic materials (e.g. domain walls and, latterly, the more exotic skyrmions), but significantly more have been stabilised recently, including hopfions, blochions and merons. Topology provides the organising principle to understand the extraordinary properties of TOs, but also the classification of topological states (TS) of matter, including topological electronic structure and topological order. Magnetic phenomena in materials are some of the oldest discoveries of science and continue to be some of the technologically most useful. Despite this, an understanding of topological magnetism (TM) is relatively recent and is undergoing a rapid change, with key discoveries of new physics, materials and applications. TM systems have a wealth of potentially useful properties and excitations. However, the exploitation of topological magnetic effects in technology is in its infancy and is the long-term motivation of our project, with its combination of materials development and fundamental scientific investigation. The discovery of exotic TOs in magnetic materials and their potential for use as high-density, low-energy components in magnetic storage and in computation applications has made topological magnetism one of the hottest topics in worldwide physics research. The related investigation of TSs has also undergone rapid expansion, and the exploitation of topological states and excitations now holds promise for applications. What the field of TM lacks is the ability to control the topological properties of well-characterized magnetic materials. We will address this fundamental problem to achieve a step-change in the exploitation of topological magnetic states and excitations through the manipulation and elucidation of novel material systems. Our project is organised around two Work Package Clusters, whose key aims are: -Cluster 1 (C1): synthesise/characterize bulk topological-magnetic systems; -Cluster 2 (C2): using a host of techniques including x-ray, neutron and muon spectroscopy, determine the topological properties of novel magnetic TSs and TOs, especially where TOs and TSs coincide/interact, and develop methods to control them. The specific objectives are: C1: -Identify candidate materials exhibiting unconventional spin textures and topological and magnetic states; produce high-quality single crystals. -Optimise their structural, magnetic and electrical properties through chemical and physical manipulation, to promote contol over the topological elements. -This cluster will initially target a number of materials classes for investigation, before concentrating on the most promising. Our target materials classes include: -Frustrated kagome systems hosting magnetic topological phases such as Fe3Sn2 and RMn6Sn6. -Weyl semimetals/Dirac materials of the type RAlX (R=Ce, Pr; X=Si, Ge) -Intermetallics with the ThCr2Si2 structure proposed as hosts of topological structures, such as GdRu2Si2, REMn2Ge2 (RE=rare earth). -Spin liquid candidate materials Na3Co2SbO6 and Na2Co3TeO6. C2: -Determine which novel TOs, previously only stabilized in artificial structures, can be found intrinsically in bulk single-crystal systems; -Elucidate the role of three-dimensional magnetic structure in the stability and properties of those TOs usually treated as purely two-dimensional; -Characterize and control the dynamic processes that dominate the responses of TOs and TS; -Determine and control the ground states, TOs, and TSs occurring in exotic TM systems.

Dimensionality is hugely important in low-temperature physics, the study of materials and the behaviour of electrons and other excitations in solid crystals. The underlying mathematics and the resulting observed behaviour of a material or system is hugely and fundamentally different and exotic if its character becomes two-dimensional rather than the familiar 3D. Even more fascinating and elusive is the fuzzy halfway ground of how a system behaves as it is pushed from one regime to the other - '2.5D'. A nascent revolution in alternatives to silicon-based electronics is increasingly turning to the physics of 2D materials to design new devices to overcome the challenges of ever-increasing miniaturisation and an ever-mounting drive to become more energy efficient. 2D layered crystals have unique advantages in this regard, as they can be cleanly and easily thinned down to single layers of atoms (as with the famous example of graphene), then stacked together in nigh-unlimited complex configurations to combine their exotic properties. To design and use these systems at an application level, it is essential that the underlying physics, and with it both the limitations and possibilities intrinsic to the materials are fundamentally understood and tested. Furthermore, this research can inform potential new avenues to explore and the synthesis of new designer materials to fulfil established criteria. A large volume of recent work on low-dimensional physics has focused on thickness control, to tune towards the `true 2D' limit of the atomic monolayer. A complementary approach is to tune the interactions from 2D to 3D by applying hydrostatic pressure - an extremely clean and powerful tuning parameter in a van-der-Waals (vdW) material. These materials are formed of strongly-bonded flat planes of atoms, linked only by the extremely weak van-der-Waals chemical bond - akin to static electric attraction. Applying pressure to such a system overwhelmingly has the effect of pushing the crystal planes together, strengthening bonds between them and allowing ever-increasing crosstalk. This will often have profound effects on the conductivity and magnetism seen in the system, including the discovery of exotic new states of matter. I will use extremes of low temperature, high pressure, magnetic and electric fields to search for new functional and multifunctional quantum materials and tune existing systems into novel states, focussing on fundamental properties of transport and of magnetic and charge order in 2D materials. I will focus on fundamental properties of transport and magnetism in low-dimensional van-der-Waals materials, and then to nanoscale devices built from stacking individual atomic layers of different 2D materials together. Extreme-conditions tuning of these nanodevices is a completely new and exciting research direction that brings together two very different fields of research with essentially no overlap - my unique background across these two areas, and quantum computing, will allow me to build a new interdisciplinary programme to explore exciting new physics. These devices additionally harbour great potential for new technologies as well as blue-skies science interest. I am partnering with industry, and academic collaborators in electrical engineering, chemistry and materials science, to explore pathways to practical applications of the new materials, behaviours and architectures to be discovered. Potential uses are in new times of electronics and memory such as spintronics or low-power transistors, flexible electronics and precision sensors. I will also look to harness the exotic 'topological' properties of new 2D materials to build fault-tolerant new qubits for quantum computing, drawing on my expertise and contacts in this field.

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.

Fullerenes are football-shaped cages of carbon atoms, for the discovery of which the British scientist Harry Kroto won the Nobel prize in 1996. Inside the cage is an empty space. Chemists and physicists have found many ingenious ways of trapping atoms or molecules inside the tiny fullerene cages. These encapsulated compounds are called endofullerenes and denoted A@C60. A remarkable method is called "molecular surgery" in which a series of chemical reactions is used to open a hole in the fullerene, a small molecule or atom is inserted into each fullerene cage, and a further series of chemical reactions is used to "sew" the holes back up again to reform the pristine cage with the atom or molecule inside. Initial examples were hydrogen (H2@C60) and water (H2O@C60). Our team greatly improved the reported method and extended it to HF@C60. Our team recently achieved a breakthrough in encapsulating methane to give CH4@C60 - the first time an organic molecule has been put inside C60. The route developed, using a larger hole than before, opens the way to encapsulating other interesting molecules such as ammonia (NH3), oxygen (O2) and formaldehyde (CH2O). In the gas phase, ammonia (NH3) displays an unusual resonance in the microwave region of the electromagnetic spectrum. This resonance is associated with the "inversion" of the pyramid-shaped ammonia molecule, similar to an umbrella being inverted in a strong wind. This ammonia resonance is of great historical significance, since it was used for the very first MASER experiment (microwave amplification by stimulated emission of radiation), which was the precursor of the laser. This MASER resonance is quenched for ammonia in ordinary experimental conditions, by the interaction of the ammonia with neighbouring molecules. However it may exist for ammonia trapped inside the closed cavity of a C60 molecule. We intend to find out. Many small symmetrical molecules display a phenomenon called spin-isomerism. This means that they exist in several forms distinguished by the configurations of their magnetic atomic nuclei, and which convert only slowly into each other. We will study the spin-isomerism of confined molecules such as methane, ammonia, and formaldehyde by using techniques such as nuclear magnetic resonance (NMR), which detects radio frequency emissions from the atomic nuclei in a strong magnetic field. In some circumstances, spin-isomerism may be exploited to give strongly enhanced NMR signals. This is potentially important since NMR is widely used throughout science for examining the structure and motion of matter - the most famous example being MRI (magnetic resonance imaging). Any technique that increases the strength of NMR signals is potentially of great importance. Oxygen (O2) is an unusual molecule since it has two unpaired electron spins in the ground state. For this reason, oxygen is slightly magnetic. We will study the behaviour of the unpaired electron spins in fullerene-encapsulated oxygen by using a technique called electron paramagnetic resonance (EPR) in which the unpaired electrons are monitored for microwave emission in a strong magnetic field. We have reason to believe that oxygen molecules in which one of the oxygen atoms has atomic mass number 16, and the other one has atomic mass number 18, will have very unusual and useful EPR properties at low temperature. The element Helium (He) has two stable isotopes, called helium-3 and helium-4. Helium-3 (3He) is a very favourable nucleus for NMR, giving a strong, narrow signal. However it is a very rare and expensive gas. We will encapsulate 3He inside fullerene cages and greatly enhance the 3He NMR signals of the helium-endofullerene by exposing the solid material to 3He gas which has been brought into a strongly polarized state by using lasers. The polarized 3He-endofullerene solid may have applications as a tracer substance, for example in magnetic resonance imaging.