# Quantum materials under extreme conditions

### The Project

The exploration of new and exotic states of matter is as fundamental to our understanding of the universe as is the detection of elementary particles or the discovery of celestial objects. What is more, many of these states exhibit properties that could have significant impact upon future technologies.

States of particular current interest include unconventional superconductors, low-dimensional ordered magnets, spin liquids and ices, topological insulators, bosonic superfluids, shape memory phases and multiferroics. All of these examples emerge from a complex soup of many-body quantum interactions, making them difficult systems to understand. Nevertheless, finding out how the states arise is the first, but essential step towards fully harnessing their capacity for application.

This project seeks to advance our knowledge of these issues by using extreme conditions of magnetic field and pressure to enable a continuous, clean and reversible tuning of quantum interactions, thereby shedding light on the building blocks of exotic magnetism and unconventional superconductivity. The overall objective is to better understand how quantum interactions and fluctuations, topology and disorder can give rise to states of matter with novel and functional properties.

### Team members

The team working on this project are: Sam Curley, Paul Goddard, Kathrin Gotze, Matthew Pearce and Robert Williams.

### Project publications

Here are details of recent results that have emerged from this project.

##### Implications of bond disorder in a* S* = 1 kagome lattice

Scientific Reports, **8**, 4745 (2018)

Long-range magnetic order (LRO) in low-dimensional materials is often the result of a delicate balance of competing interactions. This balance can be perturbed in a number of ways. Typically, the effect of introducing random disorder into a system of interacting spins is to suppress the onset of an ordered state.

However, the inherent structural configuration of some magnetic lattices (e.g. triangular, hexagonal, kagome) gives rise to a geometric frustration of the dominant exchange interactions, which itself precludes LRO, leading to a large ground-state degeneracy and the possibility of spin-liquid behaviour. In general, introducing structural disorder into such a system will act to lift the frustration and restore LRO.

The complex interplay between these three phenomena (order, disorder and frustration) is an area of considerable current interest. In this paper we set out to synthesize an ideally frustrated kagome lattice of *S* = 1 spins in a tunable molecule-based crystal. Unexpectedly, the material that self-assembles exhibits an unusual randomized network in which one-in-three magnetic exchange pathways is slightly distorted. This random structural disorder lifts the effect of magnetic frustration and should promote the onset of LRO. However, the surprising additional consequence is that the small distortion acts to suppress the size of the effective exchange energies, impeding LRO down to milli-Kelvin temperatures. Only with a combination of detailed magnetic investigations and density-functions theory were we able to understand the properties of this material.

##### Combining microscopic and macroscopic probes to untangle the single-ion anisotropy and exchange energies in an *S *= 1 quantum antiferromagnet

Physical Review B, **95**, 134435 (2017)

Many of the newest and most exciting materials are frequently only available in powdered form. This can lead to difficulties in determining the energy scales and anisotropy of competing interactions, particularly when these energies are similar in magnitude.

For this paper, we synthesized a quasi-1D molecular antiferromagnet, [Ni(HF2)(pyrazine)2]SbF6, composed of Ni(II) moments and H···F hydrogen bridges. Further connectivity through pyrazine ligands affords a robust 3D structural network. Such *S* = 1 chains are of interest especially if the single-ion anisotropy *D* and magnetic exchange energy *J* can be controlled and tuned. We show that a combination of high magnetic fields and neutron scattering could reveal and untangle these parameters, an unprecedented feat in a powder considering *D*/*J* is approximately 1 for this material.

While *D*/*J* is close to the experimentally elusive quantum tricritical point where Haldane, *XY* and quantum paramagnetic phases coexist, the small interchain exchange energy is still sufficient to prompt long-range *XY* antiferromagnetic order near 12 K. This work can enable characterisation of polycrystalline samples of other low-dimensional magnets with competing energy scales. Future work involves tuning of the parameters of this material through metal-ion doping and high pressure in an effort to tip the delicate balance of interactions, pushing towards the nearby phase boundaries and into Haldane physics territory.

##### Adiabatic physics of a magnetic quantum fluid: magnetocaloric effect, zero-point fluctuations, and two-dimensional universal behavior

Physical Review B **95**, 024404 (2017)

A key goal of physicists, materials scientists and chemists is to develop materials to test the theoretical predictions of quantum mechanics in real systems. High impact research in this field includes a focus on magnetic quantum fluids that exhibit the Bose-Einstein condensation (BEC) of magnons.

Often the experimental investigations of these systems are reliant on the results of measurements in pulsed magnetic fields. One of the results of our work is that, without careful consideration of the sample temperature in these measurements, a magnetocaloric effect can arise undetected and a naïve interpretation of the resulting data can lead to erroneous physics. This conclusion has possible implications for several existing and ongoing studies in this area, where we suggest similar distortions of the phase diagram occur.

Our results derive from the application of several state-of-the-art experimental techniques, including measurements of the susceptibility (at radio frequencies) and the magnetocaloric effect in pulsed magnets. Given these experiments revealed new physics in our material, we hope the work will encourage others to consider the consequences of studying quantum materials with ultra-high magnetic fields. Our experimental results are explained with a simple and general theoretical model and is relevant to the wider investigation of spin-gapped and correlated materials. Furthermore, we show that quantum fluctuations play a role in determining the magnetic properties of our low-dimensional system and that the critical exponents on either side of the BEC phase may be different, the possibility of which is an ongoing debate in this field.

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 681260).