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Novel effects induced by nonmagnetic impurities in frustrated magnets and quantum spin liquid represent a highly nontrivial and interesting problem. A theoretical proposal of extended modulated spin structures induced by doping of such magnets, distinct from the well-known skyrmions has attracted significant interest. Here, we demonstrate that nonmagnetic impurities can produce such extended spin structures in h-YMnO3, a triangular antiferromagnet with noncollinear magnetic order. Using inelastic neutron scattering (INS), we measured the full dynamical structure factor in Al-doped h-YMnO3 and confirmed the presence of magnon damping with a clear momentum dependence. Our theoretical calculations can reproduce the key features of the INS data, supporting the formation of the proposed spin textures. As such, our study provides the first experimental confirmation of the impurity-induced spin textures. It offers new insights and understanding of the impurity effects in a broad class of noncollinear magnetic systems., Comment: 18 pages, 4 figures and supplementary Information. Accepted for publication in Nature Communications

Non-collinear magnetic order arises for various reasons in several magnetic systems and exhibits interesting spin dynamics. Despite its ubiquitous presence, little is known of how magnons, otherwise stable quasiparticles, decay in these systems, particularly in metallic magnets. Using inelastic neutron scattering, we examine the magnetic excitation spectra in a metallic non-collinear antiferromagnet CrB$_{2}$, in which Cr atoms form a triangular lattice and display incommensurate magnetic order. Our data show intrinsic magnon damping and continuum-like excitations that cannot be explained by linear spin wave theory. The intrinsic magnon linewidth $\Gamma(q,E_{q})$ shows very unusual momentum dependence, which our analysis shows to originate from the combination of two-magnon decay and the Stoner continuum. By comparing the theoretical predictions with the experiments, we identify where in the momentum and energy space one of the two factors becomes more dominant. Our work constitutes a rare comprehensive study of the spin dynamics in metallic non-collinear antiferromagnets. It reveals, for the first time, definite experimental evidence of the higher-order effects in metallic antiferromagnets., Comment: 6 pages, 4 figures, accepted for publication in PRL

Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles$^1$. Theories typically define such states using gauge fields and deconfined quasiparticle excitations that emerge from a simple rule governing the local ground state of a frustrated magnet. For example, the '2-in-2-out' ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice in rare-earth pyrochlores - a state described by a lattice gauge theory of quantum electrodynamics$^{2-4}$. However, f-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and 'hidden' orders$^{5-6}$. Here we show that the correlated ground state of a Ce$^{3+}$-based pyrochlore, Ce$_2$Sn$_2$O$_7$, is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with the formation of a fluid-like state of matter, but the intensity distribution is weighted to larger scattering vectors, which indicates that the correlated degrees of freedom have a more complex magnetization density than that typical of magnetic dipoles in a spin liquid. The temperature evolution of the bulk properties in the correlated regime below 1 Kelvin is well reproduced using a model of dipole-octupole doublets on a pyrochlore lattice$^{7-8}$. The nature and strength of the octupole-octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a '2-plus-2-minus' rule. Our work identifies Ce$_2$Sn$_2$O$_7$ as a unique example of a material where frustrated multipoles form a 'hidden' topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations.

International audience; The compound La2−2xSr1+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, TC = 90–126 K, and are the layered analogues of the widely studied pseudo-cubic perovskite manganites, R1−xAxMnO3 (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 La2−2xSr1+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 TC, 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 La2−2xSr1+2xMn2O7 with ferromagnetic bilayers, and that there is a close connection between the antiferromagnetic fluctuations and polarons in these materials.

We use inelastic neutron scattering to study energy and wave vector dependence of spin fluctuations in SrCo_{2}As_{2}, derived from SrFe_{2-x}Co_{x}As_{2} iron pnictide superconductors. Our data reveal the coexistence of antiferromagnetic (AF) and ferromagnetic (FM) spin fluctuations at wave vectors Q_{AF}=(1,0) and Q_{FM}=(0,0)/(2,0), respectively. By comparing neutron scattering results with those of dynamic mean field theory calculation and angle-resolved photoemission spectroscopy experiments, we conclude that both AF and FM spin fluctuations in SrCo_{2}As_{2} are closely associated with a flatband of the e_{g} orbitals near the Fermi level, different from the t_{2g} orbitals in superconducting SrFe_{2-x}Co_{x}As_{2}. Therefore, Co substitution in SrFe_{2-x}Co_{x}As_{2} induces a t_{2g} to e_{g} orbital switching, and is responsible for FM spin fluctuations detrimental to the singlet pairing superconductivity.

Superconductivity in FeSe emerges from a nematic phase that breaks four-fold rotational symmetry in the iron plane. This phase may arise from orbital ordering, spin fluctuations, or hidden magnetic quadrupolar order. Here we use inelastic neutron scattering on a mosaic of single crystals of FeSe detwinned by mounting on a BaFe2As2 substrate to demonstrate that spin excitations are most intense at the antiferromagnetic wave vectors QAF = (1, 0) at low energies E = 6-11 meV in the normal state. This two-fold (C2) anisotropy is reduced at lower energies 3-5 meV, indicating a gapped four-fold (C4) mode. In the superconducting state, however, the strong nematic anisotropy is again reflected in the spin resonance (E = 3.7 meV) at QAF with incommensurate scattering around 5-6 meV. Our results highlight the extreme electronic anisotropy of the nematic phase of FeSe and are consistent with a highly anisotropic superconducting gap driven by spin fluctuations., Comment: accepted for Nature Materials

Deep neural networks (NNs) provide flexible frameworks for learning data representations and functions relating data to other properties and are often claimed to achieve ‘super-human’ performance in inferring relationships between input data and desired property. In the context of inelastic neutron scattering experiments, however, as in many other scientific scenarios, a number of issues arise: (i) scarcity of labelled experimental data, (ii) lack of uncertainty quantification on results, and (iii) lack of interpretability of the deep NNs. In this work we examine approaches to all three issues. We use simulated data to train a deep NN to distinguish between two possible magnetic exchange models of a half-doped manganite. We apply the recently developed deterministic uncertainty quantification method to provide error estimates for the classification, demonstrating in the process how important realistic representations of instrument resolution in the training data are for reliable estimates on experimental data. Finally we use class activation maps to determine which regions of the spectra are most important for the final classification result reached by the network.

We report a neutron scattering study of the metallic triangular lattice antiferromagnet PdCrO$_2$. Powder neutron diffraction measurements confirm that the crystalline space group symmetry remains $R\bar{3}m$ below $T_N$. This implies that magnetic interactions consistent with the crystal symmetry do not stabilise the non-coplanar magnetic structure which was one of two structures previously proposed on the basis of single crystal neutron diffraction measurements. Inelastic neutron scattering measurements find two gaps at low energies which can be explained as arising from a dipolar-type exchange interaction. This symmetric anisotropic interaction also stabilises a magnetic structure very similar to the coplanar magnetic structure which was also suggested by the single crystal diffraction study. The higher energy magnon dispersion can be modelled by linear spin wave theory with exchange interactions up to sixth nearest-neighbors, but discrepancies remain which hint at additional effects unexplained by the linear theory., Comment: 10 pages, 5 figures, submitted to Phys. Rev. B

Clustered quantum materials provide a new platform for the experimental study of many-body entanglement. Here we address a simple model of a single-molecule nano-magnet featuring N interacting spins in a transverse field. The field can induce an entanglement transition (ET). We calculate the magnetisation, low-energy gap and neutron-scattering cross-section and find that the ET has distinct signatures, detectable at temperatures as high as 5% of the interaction strength. The signatures are stronger for smaller clusters., 14 pages, 11 Figures; minor changes; Phys. Rev. B (accepted)

Magnons and phonons are fundamental quasiparticles in a solid and can be coupled together to form a hybrid quasi-particle. However, detailed experimental studies on the underlying Hamiltonian of this particle are rare for actual materials. Moreover, the anharmonicity of such magnetoelastic excitations remains largely unexplored, although it is essential for a proper understanding of their diverse thermodynamic behaviour and intrinsic zero-temperature decay. Here we show that in non-collinear antiferromagnets, a strong magnon–phonon coupling can significantly enhance the anharmonicity, resulting in the creation of magnetoelastic excitations and their spontaneous decay. By measuring the spin waves over the full Brillouin zone and carrying out anharmonic spin wave calculations using a Hamiltonian with an explicit magnon–phonon coupling, we have identified a hybrid magnetoelastic mode in (Y,Lu)MnO3 and quantified its decay rate and the exchange-striction coupling term required to produce it., The properties of magnetic, crystalline solids can be described in terms of quantum particles of spin-wave and lattice-vibration energy, known as magnons and phonons respectively. Here, the authors show that strong magnon-phonon coupling in a noncollinear antiferromagnet can create magnetoelastic excitations.

The soliton dynamics in the S = 1 2 quantum spin chain CsCoCl3 have been studied using inelastic neutron scattering techniques. A new theory is proposed on the basis of these results, which properly takes account of the mixing of crystal field levels.

We have used time-of-flight inelastic neutron scattering to measure the spin wave spectrum of the canonical half-doped manganite Pr$_{0.5}$Ca$_{0.5}$MnO$_{3}$, in its magnetic and orbitally ordered phase. Comparison of the data, which cover multiple Brillouin zones and the entire energy range of the excitations, with several different models shows that only the CE-type ordered state provides an adequate description of the magnetic ground state, provided interactions beyond nearest neighbor are included. We are able to rule out a ground state in which there exist pairs of dimerized spins which interact only with their nearest neighbors. The Zener polaron ground state, which comprises strongly bound magnetic dimers, can be ruled out on the basis of gross features of the observed spin wave spectrum. A model with weaker dimerization reproduces the observed dispersion but can be ruled out on the basis of subtle discrepancies between the calculated and observed structure factors at certain positions in reciprocal space. Adding further neighbor interactions results in almost no dimerization, i.e. interpolating back to the CE model. These results are consistent with theoretical analysis of the degenerate double exchange model for half-doping.

We use time-of-flight (TOF) inelastic neutron scattering (INS) spectroscopy to investigate the doping dependence of magnetic excitations across the phase diagram of NaFe1-xCoxAs with x = 0, 0.0175, 0.0215, 0.05, and 0.11. The effect of electron-doping by partially substituting Fe by Co is to form resonances that couple with superconductivity, broaden and suppress low energy (E 80 meV) spin excitations compared with spin waves in undoped NaFeAs. However, high energy (E > 80 meV) spin excitations are weakly Co-doping dependent. Integration of the local spin dynamic susceptibility "(!) of NaFe1-xCoxAs reveals a total fluctuating moment of 3.6 μ2 B/Fe and a small but systematic reduction with electron doping. The presence of a large spin gap in the Cooverdoped nonsuperconducting NaFe0.89Co0.11As suggests that Fermi surface nesting is responsible for low-energy spin excitations. These results parallel Ni-doping evolution of spin excitations in BaFe2-xNixAs2, confirming the notion that low-energy spin excitations coupling with itinerant electrons are important for superconductivity, while weakly doping dependent high-energy spin excitations result from localized moments.

A systematic neutron-scattering study of large near-optimally doped single crystals of the cuprate superconductor, Bi2Sr2CaCu2O8+δ, indicates that its magnetic properties are governed by localized magnetic moments, and not by itinerant quasiparticles, as widely expected. Much of what we know about the electronic states of high-temperature superconductors is due to photoemission1,2,3 and scanning tunnelling spectroscopy4,5 studies of the compound Bi2Sr2CaCu2O8+δ. The demonstration of well-defined quasiparticles in the superconducting state has encouraged many theorists to apply the conventional theory of metals, Fermi-liquid theory, to the cuprates6,7,8,9. In particular, the spin excitations observed by neutron scattering at energies below twice the superconducting gap energy are commonly believed to correspond to an excitonic state involving itinerant electrons10,11,12,13,14. Here, we present the first measurements of the magnetic spectral weight of optimally doped Bi2Sr2CaCu2O8+δ in absolute units. The lack of temperature dependence of the local spin susceptibility across the superconducting transition temperature, Tc, is incompatible with the itinerant calculations. Alternatively, the magnetic excitations could be due to local moments, as the magnetic spectrum is similar to that in La1.875Ba0.125CuO4 (ref. 15), where quasiparticles16 and local moments17 coexist.

We have studied nanoscale diffusion of membrane hydration water in fluid-phase lipid bilayers made of 1,2-dimyristoyl-3-phosphocholine (DMPC) using incoherent quasi-elastic neutron scattering. Dynamics were fit directly in the energy domain using the Fourier transform of a stretched exponential. By using large, 2-dimensional detectors, lateral motions of water molecules and motions perpendicular to the membranes could be studied simultaneously, resulting in 2-dimensional maps of relaxation time, τ, and stretching exponent, β. We present experimental evidence for anomalous (sub-diffusive) and anisotropic diffusion of membrane hydration water molecules over nanometer distances. By combining molecular dynamics and Brownian dynamics simulations, the potential microscopic origins for the anomaly and anisotropy of hydration water were investigated. Bulk water was found to show intrinsic sub-diffusive motion at time scales of several picoseconds, likely related to caging effects. In membrane hydration water, however, the anisotropy of confinement and local dynamical environments leads to an anisotropy of relaxation times and stretched exponents, indicative of anomalous dynamics.

Author(s): Wang, M; Valdivia, P; Yi, M; Chen, JX; Zhang, WL; Ewings, RA; Perring, TG; Zhao, Y; Harriger, LW; Lynn, JW; Bourret-Courchesne, E; Dai, P; Lee, DH; Yao, DX; Birgeneau, RJ

An inelastic neutron scattering study of the spin waves corresponding to the stripe antiferromagnetic order in insulating ${\mathrm{Rb}}_{0.8}{\mathrm{Fe}}_{1.5}{\mathrm{S}}_{2}$ throughout the Brillouin zone is reported. The spin wave spectra are well described by a Heisenberg Hamiltonian with anisotropic in-plane exchange interactions. Integrating the ordered moment and the spin fluctuations results in a total moment squared of $27.6\ifmmode\pm\else\textpm\fi{}4.2{\ensuremath{\mu}}_{B}^{2}/\text{Fe}$, consistent with $S\ensuremath{\approx}2$. Unlike $X{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ ($X=\text{Ca}$, Sr, and Ba), where the itinerant electrons have a significant contribution, our data suggest that this stripe antiferromagnetically ordered phase in ${\mathrm{Rb}}_{0.8}{\mathrm{Fe}}_{1.5}{\mathrm{S}}_{2}$ is a Mott-like insulator with fully localized $3d$ electrons and a high-spin ground state configuration. Nevertheless, the anisotropic exchange couplings appear to be universal in the stripe phase of Fe pnictides and chalcogenides.

We report neutron inelastic-scattering measurements and analysis of the spectrum of magnons propagating within the Fe2O4 bilayers of LuFe2O4. The observed spectrum is consistent with six magnetic modes and a single prominent gap, which is compatible with a single bilayer magnetic unit cell containing six spins. We model the magnon dispersion by linear spin-wave theory and find very good agreement with the domain-averaged spectrum of a spin-charge bilayer superstructure comprising one Fe3+-rich monolayer and one Fe2+-rich monolayer. These findings indicate the existence of polar bilayers in LuFe2O4. We also discuss a model of charge-segregated nonpolar bilayer order which we argue is not consistent with our data but which we cannot exclude definitively. Weak scattering observed below the magnon gap suggests that a fraction of the bilayers contain other combinations of charged monolayers not included in the model. Refined values for the dominant exchange interactions are reported.

Understanding the magnetic excitations in high-temperature (high-T(c)) copper-oxide superconductors is important because they may mediate the electron pairing for superconductivity(1,2). By determining the wavevector (Q) and energy ((h) over bar omega) dependence of the magnetic excitations, it is possible to calculate the change in the exchange energy available to the superconducting condensation energy(3-5). For the high-T(c) superconductor YBa(2)Cu(3)O(6+x), the most prominent feature in the magnetic excitations is the resonance(6-12). Suggestions that the resonance contributes a major part of the superconducting condensation(4,13) have not gained acceptance because the resonance is only a small portion of the total magnetic scattering(12-14). Here, we report an extensive mapping of magnetic excitations for YBa(2)Cu(3)O(6.95) (T(c) similar to 93 K). Absolute intensity measurements of the full spectra allow us to estimate the change in the magnetic exchange energy between the normal and superconducting states, which is about 15 times larger than the superconducting condensation energy(15,16) - more than enough to provide the driving force for high-T(c) superconductivity in YBa(2)Cu(3)O(6.95).

We have recently used inelastic neutron scattering to measure the magnetic excitation spectrum of La 1.875 Ba 0.125 CuO 4 up to 200 meV. This particular cuprate is of interest because it exhibits static charge and spin stripe order. The observed spectrum is remarkably similar to that found in superconducting YBa 2 Cu 3 O 6+ x and La 2− x Sr x CuO 4 ; the main differences are associated with the spin gap. We suggest that essentially all observed features of the magnetic scattering from cuprate superconductors can be described by a universal magnetic excitation spectrum multiplied by a spin gap function with a material-dependent spin-gap energy.

Experimental realizations of model magnetic systems--ones in which the interactions between the magnetic ions have a particularly simple form--are test-beds for our fundamental understanding of magnetic phenomena. If we are to understand the unusual properties of complex and potentially useful materials in which magnetism plays an important role, such as colossal magnetoresistive oxides or high temperature superconductors, we must also understand the properties of simple systems. SrCuO{sub 2} is an example of a one-dimensional magnetic system in which the characteristic energy of excitations from the magnetic ground state is comparable to that of charge motion along the chains. Our results show that the spectrum of magnetic excitations is nevertheless well described by that for the limiting case when charge and spin dynamics are separable.

The complex structure and magnetism of Pr$_{2-x}$Bi$_x$Ru$_2$O$_7$ was investigated by neutron scattering and EXAFS. Pr has an approximate doublet ground-state and the first excited state is a singlet. This overall crystal field level scheme is similar to metallic Pr$_2$Ir$_2$O$_7$, which is also reported here. While the B-site (Ru) is well ordered throughout, this is not the case for the A-site (Pr/Bi). A distribution of the Pr-O2 bond length indicates the Pr environment is not uniform even for $x=0$. The Bi environment is highly disordered ostensibly due to the 6s lone pairs on Bi$^{3+}$. Correspondingly we find the non-Kramers doublet ground state degeneracy otherwise anticipated for Pr in the pyrochlore structure is lifted so as to produce a quadrupolar singlet ground state with a spatially varying energy gap. For $x=0$, below T$_N$, the Ru sublattice orders antiferromagnetically, with propagation vector \textbf{k}= (0,0,0), as for Y$_2$Ru$_2$O$_7$. No ordering associated with the Pr sublattice is observed down to 100 mK. The low energy magnetic response of Pr$_{2-x}$Bi$_x$Ru$_2$O$_7$ features a broad spectrum of magnetic excitations associated with inhomogeneous splitting of the Pr quasi-doublet ground state. For $x=0$ ($x=0.97$) the spectrum is temperature dependent (independent). It appears disorder associated with Bi alloying enhances the inhomogeneous Pr crystal field level splitting so that inter-site interactions become irrelevant for $x=0.97$. The structural complexity for the A-site may be reflected in the hysteretic uniform magnetization of B-site ruthenium in the N\'{e}el phase., Comment: 20 pages, 21 figures, submitted to PRB

The magnetic excitations of the square-lattice spin-1/2 antiferromagnet and high- T(c) parent compound La2CuO4 are determined using high-resolution inelastic neutron scattering. Sharp spin waves with absolute intensities in agreement with theory including quantum corrections are found throughout the Brillouin zone. The observed dispersion relation shows evidence for substantial interactions beyond the nearest-neighbor Heisenberg term which can be understood in terms of a cyclic or ring exchange due to the strong hybridization path around the Cu4O4 square plaquettes.

Inelastic neutron scattering has been used to measure the high-energy, low-temperature magnetic excitations of the itinerant antiferromagnet FeGe2. The spin-wave excitations follow a Heisenberg dispersion with exchange constant along the c-axis SJFM = 68?1 meV an order of magnitude higher than the basal-plane antiferromagnetic constant SJAFM = -4.4?0.6 meV. The?c-axis spin waves are highly damped, even at temperatures small compared to SJFM. The damping is roughly quadratic in energy (as in the hydrodynamic model) up to ~250?meV, beyond which a continuum of excitations emerges.

Inelastic neutron scattering reveals strong spin fluctuations with energies as high as 0.4 eV in the nearly antiferromagnetic metal ${\mathrm{Cr}}_{0.95}{\mathrm{V}}_{0.05}$. The magnetic response is well described by a modified Millis-Monien-Pines function. From the low-energy response, we deduce a large exchange enhancement, more than an order of magnitude larger than the corresponding enhancement of the low-temperature electronic heat capacity $\ensuremath{\gamma}T$. A scaling relationship between $\ensuremath{\gamma}$ and the inverse of the wave vector--averaged spin relaxation rate ${\ensuremath{\Gamma}}_{\mathrm{ave}}$ is demonstrated for a number of magnetically correlated metals.

We review briefly the magnetic fluctuation spectra, obtained by neutron scattering, of the high temperature superconductor YBa2Cu3O6.6 (Tc = 62.7 K). The resonance at 34 meV is the most prominent spectral feature in the superconducting state. Even so, its net weight accounts for a mere 1% of the total squared moment expected for planar Cu2+ ions. For context, we also provide a discussion of the spectral weights associated with the magnetic order and spin waves in two-dimensional S = 1/2 Heisenberg antiferromagnets.

The spin dynamics in $S=3/2,$ one-dimensional (1D) Heisenberg antiferromagnets, ${\mathrm{CsVCl}}_{3}$ and ${\mathrm{CsVBr}}_{3},$ was investigated using inelastic neutron scattering. The magnetic excitations were measured at temperatures above the three-dimensional ordering temperature in order to discuss the 1D properties in the present systems. We report on the spin dynamics at low temperatures and its temperature (T) dependence. From the observed dispersion relation, using the renormalization constant calculated from the quantum Monte Carlo method, we obtained the exchange constant (J) in good agreement with those taken from bulk-susceptibility measurements. The observed structure factor was well described by that calculated from the parameters describing the dispersion relation. The energy width (\ensuremath{\Gamma}) was independent of the 1D momentum transfer (q) at large energy transfers, however, its q dependence exhibits the minimum at the magnetic zone center. The parameters describing the energy scale in the spin dynamics at low T were found to be scaled by J. We also investigated the T dependence of the spin dynamics: $\ensuremath{\Gamma}(T)$ can be scaled by J, $\ensuremath{\Gamma}(T)$ at $TgJ$ is proportional to T as predicted by classical theory but at $TgJ,$ \ensuremath{\Gamma} decreases with decreasing T and becomes finite. On the other hand, we found that $\ensuremath{\kappa}(T)$ is proportional to T at any T. The scaling by J in the dynamics at low T as well as $\ensuremath{\Gamma}(T)$ suggests that the observed spin dynamics is of 1D origin. We conclude that the spin dynamics at high temperatures $TgJ,$ is well described by classical theory, however, at low temperatures $TlJ,$ the finite width indicates some quantum fluctuations. Therefore, we observed the crossover from the quantum state at low T to the classical state at high T in $S=3/2$ systems.

Neutron scattering is a direct probe of mass and magnetization density in solids. We start with a brief review of experimental strategies for determining the mechanisms of superconductivity and how neutron scattering contributed towards our understanding of conventional superconductors. The remainder of the article gives examples of neutron results with impact on the search for the mechanism of superconductivity in more recently discovered, `exotic', materials, namely the heavy fermion compounds and the layered cuprates.

The layered compound La2-2xSr1+2xMn2O7 (x=0.3) consists of bilayers of metallic MnO2 sheets separated by insulating material. The compound exhibits markedly anisotropic magnetoresistance at temperatures well below the three-dimensional magnetic ordering temperature TC=90 K in addition to colossal magnetoresistance around TC. We present neutron diffraction data which show that the magnetic structure of this material switches from antiferromagnetic stacking of the (ferromagnetically ordered) sheets in zero field to ferromagnetic stacking in a field of 1.5 Tesla. The data are the first to be collected on any manganite as a function of applied field, exactly as the magnetoresistance data themselves are collected. They provide a natural explanation of the low-field magnetoresistance in the ordered phase in terms of spin-polarised tunnelling between the magnetic layers and suggest that the material is a bulk stack of spin-valve devices., 11 pages and 3 figures To be published in Phys. Rev. B Rapid Communications

The magnetic critical scattering of the near-ideal three-dimensional Heisenberg antiferromagnet (AF) RbMnF3 has been remeasured using neutron scattering. The critical dynamics has been studied in detail in the temperature range 0.77T(N) < T < 1.11T(N), where T-N is the Neel temperature. In agreement with previous measurements, at T-N and for wave vectors away from the AF zone center, the scattering has a quasielastic component in addition to the inelastic response predicted by renormalization-group and mode-coupling theories. Both components scale with the dynamic exponent z = 1.43 +/- 0.04, in agreement with dynamic scaling. On cooling below T-N the inelastic peaks transform into the transverse spin waves and a crossover has been observed in the dispersion from a power-law relation omega(q) = Aq(z) at T-N to a linear behavior omega(q) = cq in the hydrodynamic region below T-N. The quasielastic component evolves below T-N into the longitudinal susceptibility identified in an earlier polarized neutron experiment. The intensity and energy width of the longitudinal scattering decrease on cooling below T-N. Down to the lowest temperatures where the longitudinal susceptibility could be measured the leading term in the scaling behavior of the energy width was gamma(q) approximate to q(1.58+/-0.03) (hydrodynamic theory predicts a q(2) law). Possible explanations for the observed behavior of the longitudinal susceptibility are discussed.

FeGe_2, and lightly doped compounds based on it, have a Fermi surface driven instability which drive them into an incommensurate spin density wave state. Studies of the temperature and magnetic field dependence of the resistivity have been used to determine the magnetic phase diagram of the pure material which displays an incommensurate phase at high temperatures and a commensurate structure below 263 K in zero field. Application of a magnetic field in the tetragonal basal plane decreases the range of temperatures over which the incommensurate phase is stable. We have used inelastic neutron scattering to measure the spin dynamics of FeGe_2. Despite the relatively isotropic transport the magnetic dynamics is quasi-one dimensional in nature. Measurements carried out on HET at ISIS have been used to map out the spin wave dispersion along the c-axis up the 400 meV, more than an order of magnitude higher than the zone boundary magnon for wavevectors in the basal plane., 6 pages, Latex2e uses epsfig and elsart, to appear in the Proceedings of the International Conference on the Physics of Transition Metals, Physica B

We review neutron scattering experiments which address the coherence of the ground states of four transition metal oxides. The states considered include some which, at the qualitative level, can be described classically and others which require a quantum mechanical understanding. In the former category are the antiferromagnetism of YBa2Cu3O6.15 and the peculiar ground state of the Kagome compound SrCr9pGa12−9pO19, which is neither an antiferromagnet nor a spin glass. The latter category contains the Haldane quantum spin liquid, seen very clearly in the linear-chain compound Y2BaNiO5, and the superconducting state of La1.86Sr0.14CuO4.

We review measurements of the high-frequency magnetic excitations in the paramagnetic alloy Cr0.95V0.05 made using pulsed spallation neutron techniques. Spatially coherent magnetic excitations are observed up the highest energy investigated, h ω = 400 meV . The wavevector-integrated or local susceptibility increases approximately linearly with frequency up to this energy. Our observations contrast strongly with those on pure Cr in its paramagnetic phase.

We have used inelastic neutron scattering to measure the spin wave dispersion througout the Brillouin zone of the double exchange ferromagnet La0.7Pb0.3MnO3. The dispersion is well described by that for the double exchange Hamiltonian. The Curie temperature calculated for a local moment ferromagnet with the observed dispersion agrees with experiment within 15%. In the paramagnetic phase of the two-dimensional analogue La1.2Sr1.8Mn2O7, we have observed long-lived antiferromagnetic cluster coexisting with ferromagnetic fluctuations. This effect must be included in theories that attempt to explain giant magnetoresistance in manganites, at least in two dimensions.

The bilayer manganite ${\mathrm{La}}_{1.2}{\mathrm{Sr}}_{1.8}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ exhibits a transition between nearly insulating paramagnetic and metallic ferromagnetic states at ${T}_{C}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}126\mathrm{K}$. We use magnetic neutron scattering to show that the paramagnetic state contains long-lived antiferromagnetic clusters coexisting with ferromagnetic critical fluctuations. The principal implication is that at least in two dimensions, Anderson localization effects must also be taken into account in attempts to explain giant magnetoresistance in manganites.

The breakdown of magnons, the quasiparticles of magnetic systems, has rarely been seen. By using an inelastic neutron scattering technique, we report the observation of spontaneous magnon decay in multiferroic ${\mathrm{LuMnO}}_{3}$, a simple two dimensional Heisenberg triangular lattice antiferromagnet, with large spin $S=2$. The origin of this rare phenomenon lies in the nonvanishing cubic interaction between magnons in the spin Hamiltonian arising from the noncollinear 120\ifmmode^\circ\else\textdegree\fi{} spin structure. We observed all three key features of the nonlinear effects as theoretically predicted: a rotonlike minimum, a flat mode, and a linewidth broadening, in our inelastic neutron scattering measurements of single crystal ${\mathrm{LuMnO}}_{3}$. Our results show that quasiparticles in a system hitherto thought of as ``classical'' can indeed break down.

The S=1/2 spin chain material SrCuO2 doped with 1% S=1 Ni-impurities is studied by inelastic neutron scattering. At low temperatures, the spectrum shows a pseudogap \Delta ~ 8 meV, absent in the parent compound, and not related to any structural phase transition. The pseudogap is shown to be a generic feature of quantum spin chains with dilute defects. A simple model based on this idea quantitatively accounts for the exprimental data measured in the temperature range 2-300 K, and allows to represent the momentum-integrated dynamic structure factor in a universal scaling form., Comment: 5 pages, 3 figures

High-temperature superconductivity in iron pnictides occurs when electrons and holes are doped into their antiferromagnetic parent compounds. Since spin excitations may be responsible for electron pairing and superconductivity, it is important to determine their electron/hole-doping evolution and connection with superconductivity. Here we use inelastic neutron scattering to show that while electron doping to the antiferromagnetic BaFe2As2 parent compound modifies the low-energy spin excitations and their correlation with superconductivity (100 meV), hole-doping suppresses the high-energy spin excitations and shifts the magnetic spectral weight to low-energies. In addition, our absolute spin susceptibility measurements for the optimally hole-doped iron pnictide reveal that the change in magnetic exchange energy below and above Tc can account for the superconducting condensation energy. These results suggest that high-Tc superconductivity in iron pnictides is associated with both the presence of high-energy spin excitations and a coupling between low-energy spin excitations and itinerant electrons., Spin excitations are believed by many to play an important role in the emergence of superconductivity in the iron pnictides. Neutron scattering results collected by Wang et al. suggest that strong coupling between itinerant electrons and spin excitations is necessary for superconductivity in these materials.

Magnetic fluctuations in the molecular-intercalated FeSe superconductor Li{x}(ND2){y}(ND3){1-y}Fe2Se2 (Tc = 43K) have been measured by inelastic neutron scattering from a powder sample. The strongest magnetic scattering is observed at a wave vector Q ~ 1.4 A^{-1}, which is not consistent with the (pi,0) nesting wave vector that characterizes magnetic fluctuations in several other iron-based superconductors, but is close to the (pi, pi/2) position found for A{x}Fe{2-y}Se2 systems. At the energies probed (~ 5kB Tc), the magnetic scattering increases in intensity with decreasing temperature below Tc, consistent with the superconductivity-induced magnetic resonance found in other iron-based superconductors., Comment: 5 pages, 4 figures

Pulsed neutron spectroscopy is used to absolute measurements of the dynamic magnetic susceptibility of insulating YBa{sub 2}Cu{sub 3}O{sub 6.15}. Acoustic and optical modes, derived from in- and out-of-phase oscillation of spins in adjacent CuO{sub 2} planes, dominate the spectra and are observed up to 250 meV. The optical modes appear first at 74{plus_minus}5 meV. Linear-spin-wave theory gives an excellent description of the data and yields intralayer and interlayer exchange constants of {ital J}{sub {parallel}}=125{plus_minus}5 meV and {ital J}{sub {perpendicular}}=11{plus_minus}2 meV, respectively, and a spin-wave intensity renormalization {ital Z}{sub {chi}}=0.4{plus_minus}0.1. {copyright} {ital 1996 The American Physical Society.}

We use inelastic neutron scattering to measure the spin wave dispersion throughout the Brillouin zone of the double-exchange ferromagnet La0.7Pb0.3MnO3. Magnons with energies as high as 95 meV are directly observed and an unexpectedly simple Heisenberg Hamiltonian, with solely a nearest-neighbor coupling of 8.79 +/- 0.21 meV, accounts for the entire dispersion relation. The calculated Curie temperature for this local moment Hamiltonian overestimates the measured Curie point (355 K) by only 15%. Raising temperature yields unusual broadening of the high frequency spin waves, even within the ferromagnetic phase.

We show by inelastic neutron scattering that the frustrated magnet ${\mathrm{SrCr}}_{9p}{\mathrm{Ga}}_{12\ensuremath{-}9p}{\mathrm{O}}_{19}$ $[p\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.92(5)]$ has dispersionless magnetic excitations at energies 18.6(1) and 37.2(5) meV. The wave vector and temperature dependence of the excitations as well as the ratio 1:2 of excitation energies is perfectly accounted for by isolated antiferromagnetically exchange coupled pairs of spins $s\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2$. Consideration of the layered structure of magnetic chromium ions and the ligand environment indicates that these pairs are adjacent spins in neighboring triangular lattice planes which separate two-dimensional sublattices of interacting kagom\'e-triangle-kagom\'e layers.

We use neutron scattering to show that the low-temperature, short-range ordered spin configuration in the geometrically frustrated magnet SrCr9pGa12 − 9pO19 (p = 0.92(5)) is composed of small groups of spins whose dipole moments cancel. The local magnetic fluctuation spectrum, χ''(ω), vanishes approximately in proportion to ω for ω < 0.5 meV, distinguishing this magnet from conventional spin glasses which display a featureless continuum of excited states. We argue that this behavior results from the absence of local, low-energy excitations in the zero-spin clusters from which the frozen spin configuration is composed.

Neutron scattering measurements have been made of the high-energy excitonic excitations of Co2+ ions in CoF2 and CsCoCl3. The measurements were performed with the HET direct geometry time-of-flight spectrometer on the ISIS pulsed neutron source at the Rutherford Appleton Laboratory. In the case of CoF2 the results are consistent with previous estimates of the crystal-field and spin-orbit parameters, but for CsCoCl3 there are marked discrepancies. The results can be fitted by adjusting the crystal-field parameters, but this has the consequence that the exchange interactions between the spins in CsCoCl3 are anisotropic.

We have measured the spin-wave spectrum of the half-doped bilayer manganite Pr(Ca,Sr)2Mn2O7 in its spin, charge, and orbital ordered phase. The measurements, which extend throughout the Brillouin zone and cover the entire one-magnon spectrum, are compared critically with spin-wave calculations for different models of the electronic ground state. The data are described very well by the Goodenough model, which has weakly interacting ferromagnetic zig-zag chains in the CE-type arrangement. A model that allows ferromagnetic dimers to form within the zigzags is inconsistent with the data. The analysis conclusively rules out the strongly bound dimer (Zener polaron) model., Comment: Published in Physical Review Letters. Supplementary material is available from the corresponding authors

Systematic inelastic neutron scattering studies have been performed on La${}_{1.85}$Sr${}_{0.15}$Cu${}_{1\ensuremath{-}y}$Ni${}_{y}$O${}_{4}$ in order to elucidate the microscopic mechanism of magnetic Ni impurity doping effects on spin dynamics and superconductivity. In contrast to Zn doping, which precipitates static or quasistatic spin correlations around dopant, Ni doping remarkably reduces ${E}_{\mathrm{comme}}$, the minimum energy of the upward branch of the hourglass-shaped magnetic dispersion where a commensurate magnetic peak is observed. Ni doping at $y\ensuremath{\sim}0.04$ further reduces ${E}_{\mathrm{comme}}$ to zero energy and broadens the distribution of ${E}_{\mathrm{comme}}$, corresponding to the appearance of the normal state at base temperature ($T\ensuremath{\sim}4$ K) as well as the broadening of the superconducting transition.

We use inelastic neutron scattering to study temperature dependence of the paramagnetic spin excitations in iron pnictide BaFe${}_{2}$As${}_{2}$ throughout the Brillouin zone. In contrast to a conventional local moment Heisenberg system, where paramagnetic spin excitations are expected to have a Lorentzian function centered at zero energy transfer, the high-energy ($\ensuremath{\hbar}\ensuremath{\omega}g100$ meV) paramagnetic spin excitations in BaFe${}_{2}$As${}_{2}$ exhibit spin-wave-like features up to at least 290 K ($T=2.1{T}_{N}$). Furthermore, we find that the sizes of the fluctuating magnetic moments $\ensuremath{\langle}{m}^{2}\ensuremath{\rangle}\ensuremath{\approx}3.6{\ensuremath{\mu}}_{B}^{2}$ per Fe are essentially temperature independent from the antiferromagnetic ordered state at $0.05{T}_{N}$ to $2.1{T}_{N}$, which differs considerably from the temperature dependent fluctuating moment observed in the iron chalcogenide Fe${}_{1.1}$Te [Zaliznyak et al., Phys. Rev. Lett. 107, 216403 (2011)]. These results suggest unconventional magnetism and strong electron correlation effects in BaFe${}_{2}$As${}_{2}$.

We report neutron inelastic scattering measurements on the normal and superconducting states of single-crystalline Cs0.8Fe1.9Se2. Consistent with previous measurements on RbxFe2−ySe2, we observe two distinct spin excitation signals: (i) spin-wave excitations characteristic of the block antiferromagnetic order found in insulating AxFe2−ySe2 compounds, and (ii) a resonance-like magnetic peak localized in energy at 11 meV and at an in-plane wave-vector of (0.25,0.5). The resonance peak increases below Tc=27 K, and has a similar absolute intensity to the resonance peaks observed in other Fe-based superconductors. The existence of a magnetic resonance in the spectrum of RbxFe2−ySe2 and now of CsxFe2−ySe2 suggests that this is a common feature of superconductivity in this family. The low-energy spin-wave excitations in Cs0.8Fe1.9Se2 show no measurable response to superconductivity, consistent with the notion of spatially separate magnetic and superconducting phases.

We report inelastic neutron-scattering measurements of the magnetic excitations in SrFe${}_{2}$As${}_{2}$, the parent of a family of iron-based superconductors. The data extend throughout the Brillouin zone and up to energies of $~$$260$ meV. The spectrum calculated from a ${J}_{1}$-${J}_{2}$ model does not accurately describe our data, and we show that some of the qualitative features that the model fails to describe are readily explained by calculations from a five-band itinerant mean-field model. In particular, the high-energy part of the spectra recorded above ${T}_{\mathrm{N}}$ do not differ significantly from those at low temperature, which is explained by the itinerant model and which has implications for theories of electronic nematic and orbital ordering.