Table of contents

In 1966 Roger Cowley (together with Gerald Dolling) reported the first neutron inelastic scattering from the magnetic excitations from UO₂ below its antiferromagnetic ordering temperature of 30 K. They showed the strong magnon–phonon coupling in this material and that the excitations appeared to contain an additional mode that was not anticipated. Cowley never returned to UO₂, but showed a keen interest in the developments. Forty years after this pioneering work, unambiguous evidence was found (using resonance x-ray techniques) for the ordering below T_N of the electric quadrupoles involving the anisotropy of the 5f charge distribution around the uranium nuclei. A further 10 years later, now armed with a full theory for the excitation spectrum expected for phonons, magnons, and quadrupoles, we can identify the latter as the source of the 'extra' mode reported first in 1966. The story is a long winding one, with the expected serendipity and dead ends, but is now (almost) completed.

This article is dedicated to Roger A Cowley and his seminal contributions to our understanding of quantum liquids, both liquid ⁴He and ³He. Roger Cowley's neutron scattering measurements of the collective and independent particle response of liquid ⁴He were made at Chalk River Laboratories in 1965–74 chiefly with A D B (Dave) Woods. They measured the phonon–roton (P–R) mode energy, intensity and width with new precision. Particularly, they extended the measurements to higher wave vector and identified both collective and single particle response regimes. They showed that the P–R mode terminated at a finite energy as predicted by Pitaeskii rather than continuing as predicted by Feynman and Feynman and Cohen. They determined both the single P–R mode and multimode contributions to the dynamics. They made direct comparison with theory which Roger understood well. They observed the Bose–Einstein condensate (BEC) fraction in liquid ⁴He for the first time. This appears to be the first ever observation of BEC in any Bose gas or liquid. Roger Cowley's pioneering measurements of the density excitations of liquid ³He were made at the Institut Laue Langevin (ILL) in the period 1973–80. Roger, Reinhard Scherm, W G (Bill) Stirling and collaborators showed for the first time that the density response of this highly neutron absorbing liquid could indeed be observed with neutrons. They documented with others the dynamic response as a function of temperature and pressure stimulating extensive theoretical and experimental interest that continues today.

Neutron scattering has played a significant role in characterizing magnetic and structural correlations in Fe_1+yTe_1−xSe_x and their connections with superconductivity. Here we review several key aspects of the physics of iron chalcogenide superconductors where neutron studies played a key role. These topics include the phase diagram of Fe_1+yTe_1−xSe_x, where the doping-dependence of structural transitions can be understood from a mapping to the anisotropic random field Ising model. We then discuss orbital-selective Mott physics in the Fe chalcogenide series, where temperature-dependent magnetism in the parent material provided one of the earliest cases for orbital-selective correlation effects in a Hund's metal. Finally, we elaborate on the character of local magnetic correlations revealed by neutron scattering, its dependence on temperature and composition, and the connections to nematicity and superconductivity.

The early 1990s saw the first useful application of pulsed neutron spectroscopy to the study of excitations in low dimensional magnetic systems, with Roger Cowley as a key participant in important early experiments. Since that time the technique has blossomed as a powerful tool utilizing vastly improved neutron instrumentation coupled with more powerful pulsed sources. Here we review representative experiments illustrating some of the fascinating physics that has been revealed in quasi-one and two dimensional systems.

Charge order has recently been identified as a leading competitor of high-temperature superconductivity in moderately doped cuprates. We provide a survey of universal and materials-specific aspects of this phenomenon, with emphasis on results obtained by scattering methods. In particular, we discuss the structure, periodicity, and stability range of the charge-ordered state, its response to various external perturbations, the influence of disorder, the coexistence and competition with superconductivity, as well as collective charge dynamics. In the context of this journal issue which honors Roger Cowley's legacy, we also discuss the connection of charge ordering with lattice vibrations and the central-peak phenomenon. We end the review with an outlook on research opportunities offered by new synthesis methods and experimental platforms, including cuprate thin films and superlattices.

During the 1990s, Roger Cowley had a strong interest in the crystal and magnetic structures of rare-earth superlattices as a means to understand the rich and exotic magnetic properties of the rare-earth metals. High-quality samples can be grown by molecular beam epitaxy on sapphire substrates by first depositing a thin epitaxial layer of niobium, then a layer of yttrium or lutetium as a seed. High-resolution x-ray scattering is an excellent probe to characterise the crystal quality and was used to study the structure of the niobium layer. However, relatively little attention was paid to the seed layer. This article summarises some of the x-ray experiments performed by the Cowley group to study the structure of epitaxial niobium on sapphire, and extends the work to report some results on the structure of thin yttrium seed layers. The structure of the yttrium films is shown to have a strong dependence on the thickness of the niobium buffer, with the buffer needing to be thicker than a critical value of  ∼80 for the formation of misfit dislocations at the Nb/Al₂O₃ interface before highly coherent Y films can be grown. Yttrium films grown on Nb buffers thinner than  ∼500 show a similar two-peak line shape in scans through their specular Bragg peaks to that seen in the specular Nb Bragg peaks, with a resolution-limited feature on a broader diffuse peak. The resolution-limited feature depends on the thickness of the yttrium film, becoming weaker and having a stronger decay with increasing as the film thickness increases, while the width of the yttrium broad peak evolves as the square root of the width of the niobium Bragg peak. The data are discussed within the context of theories describing the scattering from films with misfit dislocations.

It is well established that in the low-temperature limit, the two-dimensional quantum Heisenberg antiferromagnet on a square lattice (2DQHAFSL) exhibits an anomaly in its spectrum at short-wavelengths on the zone-boundary. In the vicinity of the point the pole in the one-magnon response exhibits a downward dispersion, is heavily damped and attenuated, giving way to an isotropic continuum of excitations extending to high energies. The origin of the anomaly and the presence of the continuum are of current theoretical interest, with suggestions focused around the idea that the latter evidences the existence of spinons in a two-dimensional system. Here we present the results of neutron inelastic scattering experiments and Quantum Monte Carlo calculations on the metallo-organic compound Cu(DCOO)D₂O (CFTD), an excellent physical realisation of the 2DQHAFSL, designed to investigate how the anomaly at evolves up to finite temperatures . Our data reveal that on warming the anomaly survives the loss of long-range, three-dimensional order, and that it is thus a robust feature of the two-dimensional system. With further increase of temperature the zone-boundary response gradually softens and broadens, washing out the anomaly. This is confirmed by a comparison of our data with the results of finite-temperature Quantum Monte Carlo simulations where the two are found to be in good accord. In the vicinity of the antiferromagnetic zone centre, there was no significant softening of the magnetic excitations over the range of temperatures investigated.

In this paper, we summarize briefly some of the future trends in synchrotron science as seen at the National Synchrotron Light Source II, a new, low emittance source recently commissioned at Brookhaven National Laboratory. We touch upon imaging techniques, the study of dynamics, the increasing use of multimodal approaches, the vital importance of data science, and other enabling technologies. Each are presently undergoing a time of rapid change, driving the field of synchrotron science forward at an ever increasing pace. It is truly an exciting time and one in which Roger Cowley, to whom this journal issue is dedicated, would surely be both invigorated by, and at the heart of.

This paper reviews neutron and x-ray diffraction studies of the magnetism of rare-earth thin films and superlattices grown using the LaMBE Facility in Oxford. Epitaxial strain is found to change the magnetic ordering and surface effects are shown to alter the critical exponents for phase transitions. The magnetic coherence across spacer layers is found to depend on the band structure of the superlattice as a whole, and the conduction-electron spin-density wave responsible for interlayer magnetic coupling is measured directly.

This review is a study of how the idea of spin ice has evolved over the years, with a focus on the scientific questions that have come to define the subject. Since our initial discovery of spin ice in 1997, there have been well over five thousand papers that discuss it, and in the face of such detail, it must be difficult for the curious observer to 'see the wood for the trees'. To help in this task, we go in search of the biggest insight to have emerged from the study of spin ice. On the way, we identify highlights and outstanding puzzles, and celebrate the inspirational role that Roger Cowley played in the early years.

Motivated by the presence of an unquenched orbital angular momentum in CoO, a team at Chalk River, including a recently hired research officer Roger Cowley, performed the first inelastic neutron scattering experiments on the classic Mott insulator [Sakurai et al 1968 Phys. Rev.167 510]. Despite identifying two magnon modes at the zone boundary, the team was unable to parameterise the low energy magnetic excitation spectrum below T_N using conventional pseudo-bosonic approaches, instead achieving only qualitative agreement. It would not be for another 40 years that Roger, now at Oxford and motivated by the discovery of the high-T_c cuprate superconductors [Bednorz and Muller 1986 Z. Phys. B64 189], would make another attempt at the parameterisation of the magnetic excitation spectrum that had previously alluded him at the start of his career. Upon his return to CoO, Roger found a system embroiled in controversy, with some of its most fundamental parameters still remaining undetermined. Faced with such a formidable task, Roger performed a series of inelastic neutron scattering experiments in the early 2010s on both CoO and a magnetically dilute structural analogue Mg_0.97Co_0.03O. These experiments would prove instrumental in the determination of both single-ion [Cowley et al 2013 Phys. Rev. B88 205117] and cooperative magnetic parameters [Sarte et al 2018 Phys. Rev. B98 024415] for CoO. Both these sets of parameters would eventually be used in a spin–orbit exciton model [Sarte et al 2019 Phys. Rev. B100 075143], developed by his longtime friend and collaborator Bill Buyers, to successfully parameterise the complex spectrum that both measured at Chalk River almost 50 years prior. The story of CoO is of one that has come full circle, one filled with both spectacular failures and intermittent, yet profound, little victories.

Materials based on the cubic perovskite unit cell continue to provide the basis for technologically important materials with two notable recent examples being lead-based relaxor piezoelectrics and lead-based organic–inorganic halide photovoltaics. These materials carry considerable disorder, arising from site substitution in relaxors and molecular vibrations in the organic–inorganics, yet much of our understanding of these systems derives from the initial classic work of Prof. Roger A Cowley, who applied both theory and neutron scattering methods while at Chalk River Laboratories to the study of lattice vibrations in SrTiO₃. Neutron scattering continues to play a vital role in characterizing lattice vibrations in perovskites owing to the simple cross section and the wide range of energy resolutions achievable with current neutron instrumentation. We discuss the dynamics that drive the phase transitions in the relaxors and organic–inorganic lead-halides in terms of neutron scattering and compare them to those in phase transitions associated with a 'central peak' and also a soft mode. We review some of the past experimental work on these materials and present new data from high-resolution time-of-flight backscattering spectroscopy taken on organic–inorganic perovskites. We will show that the structural transitions in disordered lead-based perovskites are driven by a broad frequency band of excitations.

The compound La_2−2xSr_1+2xMn₂O₇, x = 0.30–0.40, consists of bilayers of ferromagnetic metallic MnO₂ sheets that are separated by insulating layers. The materials show colossal magnetoresistance—a reduction in resistivity of up to two orders of magnitude in a field of 7 T—at their three-dimensional ordering temperatures, T_C = 90–126 K, and are the layered analogues of the widely studied pseudo-cubic perovskite manganites, R_1−xA_xMnO₃ (R = rare earth, A = Ca, Sr, Ba, Pb). Two distinct short-range orderings—antiferromagnetic fluctuations and correlated polarons, which are related to the magnetic and the lattice degrees of freedom respectively—have previously been discovered in La_2−2xSr_1+2xMn₂O₇, x = 0.40, and have each been qualitatively connected to the resistivity. Here, in a comprehensive study as a function of both temperature and magnetic field for the different hole-concentrations per Mn site of x = 0.30 and 0.35, we show that antiferromagnetic fluctuations also appear at temperatures just above T_C, and that the intensities of both the antiferromagnetic fluctuations and polaron correlations closely track the resistivity. In particular, for x = 0.35 we show that there is a simple scaling relation between the intensities of the antiferromagnetic fluctuations and the in-plane resistivity that applies for the temperatures and magnetic fields used in the experiments. The results show that antiferromagnetic fluctuations are a common feature of

La_2−2xSr_1+2xMn₂O₇ with ferromagnetic bilayers, and that there is a close connection between the antiferromagnetic fluctuations and polarons in these materials.

Orientational disorder of the molecular ${\mathrm{C}\mathrm{O}}_{3}^{2-}$ anions in BaCO₃, which occurs naturally as the mineral witherite, has been studied using a combination of neutron total scattering analysed by the reverse Monte Carlo method and molecular dynamics simulations. The primary focus is on the phase transition to the cubic phase, which assumes a rocksalt structure (Strukturbericht type B1) with highly disordered orientations consistent with the mismatch between the site ($m\overline{3}m$) and molecular (3/m) symmetries. Both experiment and simulation show a high degree of disorder, with the C–O bond orientation distribution never exceeding 25% variation from that of a completely uniform distribution, although there are differences between the two methods regarding the nature of these variations. Molecular dynamics simulations are also reported for the analogous phase transitions in the very important mineral calcite, CaCO₃. The combination of the simulations and comparison with BaCO₃ shows that the properties of calcite at all temperatures within its stability field are affected mostly by the onset of orientational disorder associated with the high-temperature cubic phase, even though this lies outside the stability field of calcite. This is a new understanding of calcite, which previously had been interpreted purely in terms of the phase transition to an intermediate partially-disordered phase. Finally, we also found that witherite itself appears to support the development of orientational disorder on heating, with the simulations showing a sequence of phase transitions that explain the much larger thermal expansion of one axis.