Linear spin wave theory for single-Q incommensurate magnetic structures

Entropy driven incommensurate structures in the frustrated kagome staircase Co3V2O8

Co3V2O8features spin-3/2 moments arrayed on a kagome staircase lattice. A spin density wave with a continuously evolving propagation vector ofk⃗=(0,δ,0), showing both incommensurate states and multiple commensurate lock-ins, is observed at temperatures above the ferromagnetic ground state. Previous work has suggested that this changing propagation vector could be driven by changes in exchange interactions due to Co atom displacements. We present a straightforward model showing that a Hamiltonian with competing (but temperature independent) interactions can semi-quantitatively reproduce this behavior using a mean field approximation. The simulated spin density wave magnetic structures feature buckled kagome planes that are either ferromagnetically or antiferromagnetically ordered. Propagation vectors that differ fromδ=1/2will have multiple different ways of arranging these ferromagnetic layers that have very similar energies. This classical stacking entropy appears to be crucial in stabilizing the temperature-dependent propagation vector.

Evidence of Strong Orbital-Selective Spin-Orbital-Phonon Coupling in CrVO_{4}

Coupling of orbital degree of freedom with a spin exchange, i.e., Kugel-Khomskii-type interaction (KK), governs a host of material properties, including colossal magnetoresistance, enhanced magnetoelectric response, and photoinduced high-temperature magnetism. In general, KK-type interactions lead to deviation in experimental observables of coupled Hamiltonian near or below the magnetic transition. Using diffraction and spectroscopy experiments, here we report anomalous changes in lattice parameters, electronic states, spin dynamics, and phonons at four times the Néel transition temperature (T_{N}) in CrVO_{4}. The temperature is significantly higher than other d-orbital compounds such as manganites and vanadates, where effects are limited to near or below T_{N}. The experimental observations are rationalized using first-principles and Green's function-based phonon and spin simulations that show unprecedentedly strong KK-type interactions via a superexchange process and an orbital-selective spin-phonon coupling coefficient at least double the magnitude previously reported for strongly coupled spin-phonon systems. Our results present an opportunity to explore the effect of KK-type interactions and spin-phonon coupling well above T_{N} and possibly bring various properties closer to application, for example, strong room-temperature magnetoelectric coupling.

Tetrahedral triple-Q magnetic ordering and large spontaneous Hall conductivity in the metallic triangular antiferromagnet Co1/3TaS2

The triangular lattice antiferromagnet (TLAF) has been the standard paradigm of frustrated magnetism for several decades. The most common magnetic ordering in insulating TLAFs is the 120° structure. However, a new triple-Q chiral ordering can emerge in metallic TLAFs, representing the short wavelength limit of magnetic skyrmion crystals. We report the metallic TLAF Co1/3TaS2 as the first example of tetrahedral triple-Q magnetic ordering with the associated topological Hall effect (non-zero σxy(H = 0)). We also present a theoretical framework that describes the emergence of this magnetic ground state, which is further supported by the electronic structure measured by angle-resolved photoemission spectroscopy. Additionally, our measurements of the inelastic neutron scattering cross section are consistent with the calculated dynamical structure factor of the tetrahedral triple-Q state.

Continuous Spin Excitations in the Three-Dimensional Frustrated Magnet K_{2}Ni_{2}(SO_{4})_{3}

Continuous spin excitations are widely recognized as one of the hallmarks of novel spin states in quantum magnets, such as quantum spin liquids (QSLs). Here, we report the observation of such kind of excitations in K_{2}Ni_{2}(SO_{4})_{3}, which consists of two sets of intersected spin-1 (Ni^{2+}) trillium lattices. Our inelastic neutron scattering measurement on single crystals clearly shows a dominant excitation continuum, which exhibits a distinct temperature-dependent behavior from that of spin waves, and is rooted in strong quantum spin fluctuations. Further using the self-consistent-Gaussian-approximation method, we determine that the fourth- and fifth-nearest-neighbor exchange interactions are dominant. These two bonds together form a unique three-dimensional network of corner-sharing tetrahedra, which we name as a "hypertrillium" lattice. Our results provide direct evidence for the existence of QSL features in K_{2}Ni_{2}(SO_{4})_{3} and highlight the potential for the hypertrillium lattice to host frustrated quantum magnetism.

Triple-q Order in Na_{2}Co_{2}TeO_{6} from Proximity to Hidden-SU(2)-Symmetric Point

In extended Heisenberg-Kitaev-Gamma-type spin models, hidden-SU(2)-symmetric points are isolated points in parameter space that can be mapped to pure Heisenberg models via nontrivial duality transformations. Such points generically feature quantum degeneracy between conventional single-q and exotic multi-q states. We argue that recent single-crystal inelastic neutron scattering data place the honeycomb magnet Na_{2}Co_{2}TeO_{6} in proximity to such a hidden-SU(2)-symmetric point. The low-temperature order is identified as a triple-q state arising from the Néel antiferromagnet with staggered magnetization in the out-of-plane direction via a 4-sublattice duality transformation. This state naturally explains various distinctive features of the magnetic excitation spectrum, including its surprisingly high symmetry and the dispersive low-energy and flat high-energy bands. Our result demonstrates the importance of bond-dependent exchange interactions in cobaltates, and illustrates the intriguing magnetic behavior resulting from them.

Complete field-induced spectral response of the spin-1/2 triangular-lattice antiferromagnet CsYbSe2

Fifty years after Anderson's resonating valence-bond proposal, the spin-1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF) remains the ultimate platform to explore highly entangled quantum spin states in proximity to magnetic order. Yb-based delafossites are ideal candidate TLHAF materials, which allow experimental access to the full range of applied in-plane magnetic fields. We perform a systematic neutron scattering study of CsYbSe2, first proving the Heisenberg character of the interactions and quantifying the second-neighbor coupling. We then measure the complex evolution of the excitation spectrum, finding extensive continuum features near the 120°-ordered state, throughout the 1/3-magnetization plateau and beyond this up to saturation. We perform cylinder matrix-product-state (MPS) calculations to obtain an unbiased numerical benchmark for the TLHAF and spectacular agreement with the experimental spectra. The measured and calculated longitudinal spectral functions reflect the role of multi-magnon bound and scattering states. These results provide valuable insight into unconventional field-induced spin excitations in frustrated quantum materials.

Low-Dimensional Metal-Organic Magnets as a Route toward the S = 2 Haldane Phase

Metal-organic magnets (MOMs), modular magnetic materials where metal atoms are connected by organic linkers, are promising candidates for next-generation quantum technologies. MOMs readily form low-dimensional structures and so are ideal systems to realize physical examples of key quantum models, including the Haldane phase, where a topological excitation gap occurs in integer-spin antiferromagnetic (AFM) chains. Thus, far the Haldane phase has only been identified for S = 1, with S ≥ 2 still unrealized because the larger spin imposes more stringent requirements on the magnetic interactions. Here, we report the structure and magnetic properties of CrCl₂(pym) (pym = pyrimidine), a new quasi-1D S = 2 AFM MOM. We show, using X-ray and neutron diffraction, bulk property measurements, density-functional theory calculations, and inelastic neutron spectroscopy (INS), that CrCl₂(pym) consists of AFM CrCl₂ spin chains (J₁ = -1.13(4) meV) which are weakly ferromagnetically coupled through bridging pym (J₂ = 0.10(2) meV), with easy-axis anisotropy (D = -0.15(3) meV). We find that, although small compared to J₁, these additional interactions are sufficient to prevent observation of the Haldane phase in this material. Nevertheless, the proximity to the Haldane phase together with the modularity of MOMs suggests that layered Cr(II) MOMs are a promising family to search for the elusive S = 2 Haldane phase.

Magnetic molecular orbitals in MnSi

A large body of knowledge about magnetism is attained from models of interacting spins, which usually reside on magnetic ions. Proposals beyond the ionic picture are uncommon and seldom verified by direct observations in conjunction with microscopic theory. Here, using inelastic neutron scattering to study the itinerant near-ferromagnet MnSi, we find that the system's fundamental magnetic units are interconnected, extended molecular orbitals consisting of three Mn atoms each rather than individual Mn atoms. This result is further corroborated by magnetic Wannier orbitals obtained by ab initio calculations. It contrasts the ionic picture with a concrete example and presents an unexplored regime of the spin waves where the wavelength is comparable to the spatial extent of the molecular orbitals. Our discovery brings important insights into not only the magnetism of MnSi but also a broad range of magnetic quantum materials where structural symmetry, electron itinerancy, and correlations act in concert.

Plane wave implementation of the magnetic force theorem for magnetic exchange constants: application to bulk Fe, Co and Ni

We present a plane wave implementation of the magnetic force theorem, which provides a first principles framework for extracting exchange constants parameterizing a classical Heisenberg model description of magnetic materials. It is shown that the full microscopic exchange tensor may be expressed in terms of the static Kohn-Sham susceptibility tensor and the exchange-correlation magnetic field. This formulation allows one to define arbitrary magnetic sites localized to predefined spatial regions, hence rendering the problem of finding Heisenberg parameters independent of any orbital decomposition of the problem. The susceptibility is calculated in a plane wave basis, which allows for systematic convergence with respect to unoccupied bands and spatial representation. We then apply the method to the well-studied problem of calculating adiabatic spin wave spectra for bulk Fe, Co and Ni, finding good agreement with previous calculations. In particular, we utilize the freedom of defining magnetic sites to show that the calculated Heisenberg parameters are robust towards changes in the definition of magnetic sites. This demonstrates that the magnetic sites can be regarded as well-defined and thus asserts the relevance of the Heisenberg model description despite the itinerant nature of the magnetic state.

Magnon mode transition in real space

Spin excitation of an ilmenite FeTiO₃ powder sample is measured by time-of-flight inelastic neutron scattering. The dynamic magnetic pair-density function D_M(r, E) is obtained from the dynamic magnetic structure factor S_M(Q, E) by the Fourier transformation. The real space spin dynamics exhibit magnon mode transitions in the spin-spin correlation with increasing energy from no-phase-shift to π-phase-shift. The mode transition is well reproduced by a simulation using the reciprocal space magnon dispersions. This analysis provides a novel opportunity to study the local spin dynamics of various magnetic systems.

Line-Graph Approach to Spiral Spin Liquids

Competition among exchange interactions is able to induce novel spin correlations on a bipartite lattice without geometrical frustration. A prototype example is the spiral spin liquid, which is a correlated paramagnetic state characterized by subdimensional degenerate propagation vectors. Here, using spectral graph theory, we show that spiral spin liquids on a bipartite lattice can be approximated by a further-neighbor model on the corresponding line-graph lattice that is nonbipartite, thus broadening the space of candidate materials that may support the spiral spin liquid phases. As illustrations, we examine neutron scattering experiments performed on two spinel compounds, ZnCr_{2}Se_{4} and CuInCr_{4}Se_{8}, to demonstrate the feasibility of this new approach and expose its possible limitations in experimental realizations.

Strong band renormalization and emergent ferromagnetism induced by electron-antiferromagnetic-magnon coupling

The interactions between electrons and antiferromagnetic magnons (AFMMs) are important for a large class of correlated materials. For example, they are the most plausible pairing glues in high-temperature superconductors, such as cuprates and iron-based superconductors. However, unlike electron-phonon interactions (EPIs), clear-cut observations regarding how electron-AFMM interactions (EAIs) affect the band structure are still lacking. Consequently, critical information on the EAIs, such as its strength and doping dependence, remains elusive. Here we directly observe that EAIs induce a kink structure in the band dispersion of Ba_1-xK_xMn₂As₂, and subsequently unveil several key characteristics of EAIs. We found that the coupling constant of EAIs can be as large as 5.4, and it shows strong doping dependence and temperature dependence, all in stark contrast to the behaviors of EPIs. The colossal renormalization of electron bands by EAIs enhances the density of states at Fermi energy, which is likely driving the emergent ferromagnetic state in Ba_1-xK_xMn₂As₂ through a Stoner-like mechanism with mixed itinerant-local character. Our results expand the current knowledge of EAIs, which may facilitate the further understanding of many correlated materials where EAIs play a critical role.

Excitations in the Ordered and Paramagnetic States of Honeycomb Magnet Na_{2}Co_{2}TeO_{6}

Na_{2}Co_{2}TeO_{6} is a proposed approximate Kitaev magnet, yet its actual magnetic interactions are elusive due to a lack of knowledge on the full excitation spectrum. Here, using inelastic neutron scattering and single crystals, we determine the system's temperature-dependent magnetic excitations over the entire Brillouin zone. Without committing to specific models, we unveil a distinct signature of the third-nearest-neighbor coupling in the spin waves, which signifies the associated distance as an emerging effective link in the ordered state. The presence of at least six nonoverlapping spin-wave branches is at odds with all models proposed to date. Above the ordering temperature, persisting dynamic correlations can be described by equal-time magnetic structure factors of a hexagonal cluster, which reveal the leading instabilities. Our result sets definitive constraints on theoretical models for Na_{2}Co_{2}TeO_{6} and provides new insight for the materialization of the Kitaev model.

Magnetic Interactions of the Centrosymmetric Skyrmion Material Gd_{2}PdSi_{3}

The experimental realization of magnetic skyrmion crystals in centrosymmetric materials has been driven by theoretical understanding of how a delicate balance of anisotropy and frustration can stabilize topological spin structures in applied magnetic fields. Recently, the centrosymmetric material Gd_{2}PdSi_{3} was shown to host a field-induced skyrmion crystal, but the skyrmion stabilization mechanism remains unclear. Here, we employ neutron-scattering measurements on an isotopically enriched polycrystalline Gd_{2}PdSi_{3} sample to quantify the interactions that drive skyrmion formation. Our analysis reveals spatially extended interactions in triangular planes, and large ferromagnetic interplanar magnetic interactions that are modulated by the Pd/Si superstructure. The skyrmion crystal emerges from a zero-field helical magnetic order with magnetic moments perpendicular to the magnetic propagation vector, indicating that the magnetic dipolar interaction plays a significant role. Our experimental results establish an interaction space that can promote skyrmion formation, facilitating identification and design of centrosymmetric skyrmion materials.

Thermal Evolution of Dirac Magnons in the Honeycomb Ferromagnet CrBr_{3}

CrBr_{3} is an excellent realization of the two-dimensional honeycomb ferromagnet, which offers a bosonic equivalent of graphene with Dirac magnons and topological character. We perform inelastic neutron scattering measurements using state-of-the-art instrumentation to update 50-year-old data, thereby enabling a definitive comparison both with recent experimental claims of a significant gap at the Dirac point and with theoretical predictions for thermal magnon renormalization. We demonstrate that CrBr_{3} has next-neighbor J_{2} and J_{3} interactions approximately 5% of J_{1}, an ideal Dirac magnon dispersion at the K point, and the associated signature of isospin winding. The magnon lifetime and the thermal band renormalization show the universal T^{2} evolution expected from an interacting spin-wave treatment, but the measured dispersion lacks the predicted van Hove features, pointing to the need for more sophisticated theoretical analysis.

Systematic electronic structure in the cuprate parent state from quantum many-body simulations

The quantitative description of correlated electron materials remains a modern computational challenge. We demonstrate a numerical strategy to simulate correlated materials at the fully ab initio level beyond the solution of effective low-energy models and apply it to gain a detailed microscopic understanding across a family of cuprate superconducting materials in their parent undoped states. We uncover microscopic trends in the electron correlations and reveal the link between the material composition and magnetic energy scales through a many-body picture of excitation processes involving the buffer layers. Our work illustrates a path toward a quantitative and reliable understanding of more complex states of correlated materials at the ab initio many-body level.

Exciton-coupled coherent magnons in a 2D semiconductor

The recent discoveries of two-dimensional (2D) magnets^1-6 and their stacking into van der Waals structures^7-11 have expanded the horizon of 2D phenomena. One exciting application is to exploit coherent magnons¹² as energy-efficient information carriers in spintronics and magnonics^13,14 or as interconnects in hybrid quantum systems^15-17. A particular opportunity arises when a 2D magnet is also a semiconductor, as reported recently for CrSBr (refs. ^18-20) and NiPS₃ (refs. ^21-23) that feature both tightly bound excitons with a large oscillator strength and potentially long-lived coherent magnons owing to the bandgap and spatial confinement. Although magnons and excitons are energetically mismatched by orders of magnitude, their coupling can lead to efficient optical access to spin information. Here we report strong magnon-exciton coupling in the 2D A-type antiferromagnetic semiconductor CrSBr. Coherent magnons launched by above-gap excitation modulate the exciton energies. Time-resolved exciton sensing reveals magnons that can coherently travel beyond seven micrometres, with a coherence time of above five nanoseconds. We observe these exciton-coupled coherent magnons in both even and odd numbers of layers, with and without compensated magnetization, down to the bilayer limit. Given the versatility of van der Waals heterostructures, these coherent 2D magnons may be a basis for optically accessible spintronics, magnonics and quantum interconnects.

Spin Waves and Magnetic Exchange Hamiltonian in CrSBr

CrSBr is an air-stable two-dimensional (2D) van der Waals semiconducting magnet with great technological promise, but its atomic-scale magnetic interactions-crucial information for high-frequency switching-are poorly understood. An experimental study is presented to determine the CrSBr magnetic exchange Hamiltonian and bulk magnon spectrum. The A-type antiferromagnetic order using single crystal neutron diffraction is confirmed here. The magnon dispersions are also measured using inelastic neutron scattering and rigorously fit the excitation modes to a spin wave model. The magnon spectrum is well described by an intra-plane ferromagnetic Heisenberg exchange model with seven nearest in-plane exchanges. This fitted exchange Hamiltonian enables theoretical predictions of CrSBr behavior: as one example, the fitted Hamiltonian is used to predict the presence of chiral magnon edge modes with a spin-orbit enhanced CrSBr heterostructure.

Spin Density Wave versus Fractional Magnetization Plateau in a Triangular Antiferromagnet

We report an excellent realization of the highly nonclassical incommensurate spin-density wave (SDW) state in the quantum frustrated antiferromagnetic insulator Cs_{2}CoBr_{4}. In contrast to the well-known Ising spin chain case, here the SDW is stabilized by virtue of competing planar in-chain anisotropies and frustrated interchain exchange. Adjacent to the SDW phase is a broad m=1/3 magnetization plateau that can be seen as a commensurate locking of the SDW state into the up-up-down (UUD) spin structure. This represents the first example of the long-sought SDW-UUD transition in triangular-type quantum magnets.

Anisotropic magnon damping by zero-temperature quantum fluctuations in ferromagnetic CrGeTe3

Spin and lattice are two fundamental degrees of freedom in a solid, and their fluctuations about the equilibrium values in a magnetic ordered crystalline lattice form quasiparticles termed magnons (spin waves) and phonons (lattice waves), respectively. In most materials with strong spin-lattice coupling (SLC), the interaction of spin and lattice induces energy gaps in the spin wave dispersion at the nominal intersections of magnon and phonon modes. Here we use neutron scattering to show that in the two-dimensional (2D) van der Waals honeycomb lattice ferromagnetic CrGeTe₃, spin waves propagating within the 2D plane exhibit an anomalous dispersion, damping, and breakdown of quasiparticle conservation, while magnons along the c axis behave as expected for a local moment ferromagnet. These results indicate the presence of dynamical SLC arising from the zero-temperature quantum fluctuations in CrGeTe₃, suggesting that the observed in-plane spin waves are mixed spin and lattice quasiparticles fundamentally different from pure magnons and phonons.

CrGeTe₃ is a van der Waals honeycomb ferromagnet, known for exhibiting strong coupling between lattice and spin degrees of freedom. Here, Chen et al perform neutron scattering on CrGeTe₃, find a broadened spin-wave excitation resulting from zero-temperature motion of the atoms in the lattice.

Spiral Spin Liquid on a Honeycomb Lattice

Spiral spin liquids are correlated paramagnetic states with degenerate propagation vectors forming a continuous ring or surface in reciprocal space. On the honeycomb lattice, spiral spin liquids present a novel route to realize emergent fracton excitations, quantum spin liquids, and topological spin textures, yet experimental realizations remain elusive. Here, using neutron scattering, we show that a spiral spin liquid is realized in the van der Waals honeycomb magnet FeCl_{3}. A continuous ring of scattering is directly observed, which indicates the emergence of an approximate U(1) symmetry in momentum space. Our work demonstrates that spiral spin liquids can be achieved in two-dimensional systems and provides a promising platform to study the fracton physics in spiral spin liquids.

Dirac Magnons, Nodal Lines, and Nodal Plane in Elemental Gadolinium

We investigate the magnetic excitations of elemental gadolinium (Gd) using inelastic neutron scattering, showing that Gd is a Dirac magnon material with nodal lines at K and nodal planes at half integer ℓ. We find an anisotropic intensity winding around the K-point Dirac magnon cone, which is interpreted to indicate Berry phase physics. Using linear spin wave theory calculations, we show the nodal lines have nontrivial Berry phases, and topological surface modes. We also discuss the origin of the nodal plane in terms of a screw-axis symmetry, and introduce a topological invariant characterizing its presence and effect on the scattering intensity. Together, these results indicate a highly nontrivial topology, which is generic to hexagonal close packed ferromagnets. We discuss potential implications for other such systems.

A super-resolution technique to analyze single-crystal inelastic neutron scattering measurements using direct-geometry chopper spectrometers

Direct-geometry time-of-flight chopper neutron spectroscopy is instrumental in studying dynamics in liquid, powder, and single crystal systems. We report here that real-space techniques in optical imagery can be adapted to obtain reciprocal-space super resolution dispersion for phonon or magnetic excitations from single-crystal neutron spectroscopy measurements. The procedure to reconstruct super-resolution energy dispersion of excitations relies on an accurate determination of the momentum and energy-dependent point spread function and a dispersion correction technique inspired by an image disparity calculation technique commonly used in stereo imaging. Applying these methods to spinwave dispersion data from a virtual neutron experiment demonstrates ∼5-fold improvement over nominal energy resolution.

Antiferromagnetic Kitaev interaction inJeff1/2 cobalt honeycomb materials Na3Co2SbO6and Na2Co2TeO6

Finding new materials with antiferromagnetic (AFM) Kitaev interaction is an urgent issue for quantum magnetism research. We conclude that Na₃Co₂SbO₆and Na₂Co₂TeO₆are new honeycomb cobalt-based systems with AFM Kitaev interaction by carrying out inelastic neutron scattering experiments and subsequent analysis. The spin-orbit excitons observed at 20-28 meV in both compounds strongly support the idea that Co²⁺ions of both compounds have a spin-orbital entangledJ_eff= 1/2 state. Furthermore, we found that a generalized Kitaev-Heisenberg Hamiltonian can describe the spin-wave excitations of both compounds with additional 3rd nearest-neighbor interaction. Our best-fit parameters show significant AFM Kitaev terms and off-diagonal symmetric anisotropy terms of a similar magnitude in both compounds. We also found a strong magnon-damping effect at the higher energy part of the spin waves, entirely consistent with observations in other Kitaev magnets. Our work suggests Na₃Co₂SbO₆and Na₂Co₂TeO₆as rare examples of the AFM Kitaev magnets based on the systematic studies of the spin waves and analysis.

Machine learning for magnetic phase diagrams and inverse scattering problems

Machine learning promises to deliver powerful new approaches to neutron scattering from magnetic materials. Large scale simulations provide the means to realise this with approaches including spin-wave, Landau Lifshitz, and Monte Carlo methods. These approaches are shown to be effective at simulating magnetic structures and dynamics in a wide range of materials. Using large numbers of simulations the effectiveness of machine learning approaches are assessed. Principal component analysis and nonlinear autoencoders are considered with the latter found to provide a high degree of compression and to be highly suited to neutron scattering problems. Agglomerative heirarchical clustering in the latent space is shown to be effective at extracting phase diagrams of behavior and features in an automated way that aid understanding and interpretation. The autoencoders are also well suited to optimizing model parameters and were found to be highly advantageous over conventional fitting approaches including being tolerant of artifacts in untreated data. The potential of machine learning to automate complex data analysis tasks including the inversion of neutron scattering data into models and the processing of large volumes of multidimensional data is assessed. Directions for future developments are considered and machine learning argued to have high potential for impact on neutron science generally.

Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model

We study the higher-order topological spin phases based on a spin analogue of Benalcazar-Bernevig-Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.

Neutron Scattering Studies of the Breathing Pyrochlore Antiferromagnet LiGaCr_{4}O_{8}

We report neutron scattering measurements of the spinel oxide LiGaCr_{4}O_{8}, in which magnetic ions Cr^{3+} form a breathing pyrochlore lattice. Our experiments reveal the coexistence of a nearly dispersionless resonance mode and dispersive spin-wave excitations in the magnetically ordered state, which can be quantitatively described by a quantum spin model of hexagonal loops and linear spin-wave theory with the same set of exchange parameters, respectively. Comparison to other Cr spinel oxides reveals a linear relationship between the resonance energy and lattice constant across all these materials, which is in agreement with our hexagonal loop calculations. Our results suggest a unified picture for spin resonances in Cr spinel oxides.

Unusual Exchange Couplings and Intermediate Temperature Weyl State in Co_{3}Sn_{2}S_{2}

Understanding magnetism and its possible correlations to topological properties has emerged to the forefront as a difficult topic in studying magnetic Weyl semimetals. Co_{3}Sn_{2}S_{2} is a newly discovered magnetic Weyl semimetal with a kagome lattice of cobalt ions and has triggered intense interest for rich fantastic phenomena. Here, we report the magnetic exchange couplings of Co_{3}Sn_{2}S_{2} using inelastic neutron scattering and two density functional theory (DFT) based methods: constrained magnetism and multiple-scattering Green's function methods. Co_{3}Sn_{2}S_{2} exhibits highly anisotropic magnon dispersions and linewidths below T_{C}, and paramagnetic excitations above T_{C}. The spin-wave spectra in the ferromagnetic ground state is well described by the dominant third-neighbor "across-hexagon" J_{d} model. Our density functional theory calculations reveal that both the symmetry-allowed 120° antiferromagnetic orders support Weyl points in the intermediate temperature region, with distinct numbers and the locations of Weyl points. Our study highlights the important role Co_{3}Sn_{2}S_{2} can play in advancing our understanding of kagome physics and exploring the interplay between magnetism and band topology.

Low-energy spin dynamics in rare-earth perovskite oxides

We review recent studies of spin dynamics in rare-earth orthorhombic perovskite oxides of the type RMO₃, where R is a rare-earth ion and M is a transition-metal ion, using single-crystal inelastic neutron scattering (INS). After a short introduction to the magnetic INS technique in general, the results of INS experiments on both transition-metal and rare-earth subsystems for four selected compounds (YbFeO₃, TmFeO₃, YFeO₃, YbAlO₃) are presented. We show that the spectrum of magnetic excitations consists of two types of collective modes that are well separated in energy: gapped magnons with a typical bandwidth of <70 meV, associated with the antiferromagnetically (AFM) ordered transition-metal subsystem, and AFM fluctuations of <5 meV within the rare-earth subsystem, with no hybridization of those modes. We discuss the high-energy conventional magnon excitations of the 3dsubsystem only briefly, and focus in more detail on the spectacular dynamics of the rare-earth sublattice in these materials. We observe that the nature of the ground state and the low-energy excitation strongly depends on the identity of the rare-earth ion. In the case of non-Kramers ions, the low-symmetry crystal field completely eliminates the degeneracy of the multiplet state, creating a rich magnetic field-temperature phase diagram. In the case of Kramers ions, the resulting ground state is at least a doublet, which can be viewed as an effective quantum spin-1/2. Equally important is the fact that in Yb-based materials the nearest-neighbor exchange interaction dominates in one direction, despite the three-dimensional nature of the orthoperovskite crystal structure. The observation of a fractional spinon continuum and quantum criticality in YbAlO₃demonstrates that Kramers rare-earth based magnets can provide realizations of various aspects of quantum low-dimensional physics.

Dimensional reduction by geometrical frustration in a cubic antiferromagnet composed of tetrahedral clusters

Dimensionality is a critical factor in determining the properties of solids and is an apparent built-in character of the crystal structure. However, it can be an emergent and tunable property in geometrically frustrated spin systems. Here, we study the spin dynamics of the tetrahedral cluster antiferromagnet, pharmacosiderite, via muon spin resonance and neutron scattering. We find that the spin correlation exhibits a two-dimensional characteristic despite the isotropic connectivity of tetrahedral clusters made of spin 5/2 Fe3+ ions in the three-dimensional cubic crystal, which we ascribe to two-dimensionalisation by geometrical frustration based on spin wave calculations. Moreover, we suggest that even one-dimensionalisation occurs in the decoupled layers, generating low-energy and one-dimensional excitation modes, causing large spin fluctuation in the classical spin system. Pharmacosiderite facilitates studying the emergence of low-dimensionality and manipulating anisotropic responses arising from the dimensionality using an external magnetic field.

Magnetic structure, excitations and short-range order in honeycomb Na2Ni2TeO6

Na₂Ni₂TeO₆has a layered hexagonal structure with a honeycomb lattice constituted by Ni²⁺and a chiral charge distribution of Na⁺that resides between the Ni layers. In the present work, the antiferromagnetic (AFM) transition temperature of Na₂Ni₂TeO₆is confirmed atT_N≈ 27 K, and further, it is found to be robust up to 8 T magnetic field and 1.2 GPa external pressure; and, without any frequency-dependence. Slight deviations from nominal Na-content (up to 5%) does not seem to influence the magnetic transition temperature,T_N. Isothermal magnetization curves remain almost linear up to 13 T. Our analysis of neutron diffraction data shows that the magnetic structure of Na₂Ni₂TeO₆is faithfully described by a model consisting of two phases described by the commensurate wave vectorsk→c,0.500and0.500.5, with an additional short-range order component incorporated in to the latter phase. Consequently, a zig-zag long-range ordered magnetic phase of Ni²⁺results in the compound, mixed with a short-range ordered phase, which is supported by our specific heat data. Theoretical computations based on density functional theory predict predominantly in-plane magnetic exchange interactions that conform to aJ₁-J₂-J₃model with a strongJ₃term. The computationally predicted parameters lead to a reliable estimate forT_Nand the experimentally observed zig-zag magnetic structure. A spin wave excitation in Na₂Ni₂TeO₆atE≈ 5 meV atT= 5 K is mapped out through inelastic neutron scattering experiments, which is reproduced by linear spin wave theory calculations using theJvalues from our computations. Our specific heat data and inelastic neutron scattering data strongly indicate the presence of short-range spin correlations, atT>T_N, stemming from incipient AFM clusters.

Machine learning for neutron scattering at ORNL*

Machine learning (ML) offers exciting new opportunities to extract more information from scattering data. At neutron scattering user facilities, ML has the potential to help accelerate scientific productivity by empowering facility users with insight into their data which has traditionally been supplied by scattering experts. Such support can help in both speeding up common modeling problems for users, as well as help solve harder problems that are normally time consuming and difficult to address with standard methods. This article explores the recent ML work undertaken at Oak Ridge National Laboratory involving neutron scattering data. We cover materials structure modeling for diffuse scattering, powder diffraction, and small-angle scattering. We also discuss how ML can help to model the response of the instrument more precisely, as well as enable quick extraction of information from neutron data. The application of super-resolution techniques to small-angle scattering and peak extraction for diffraction will be discussed.

Interpretable, calibrated neural networks for analysis and understanding of inelastic neutron scattering data

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.

Spin texture induced by non-magnetic doping and spin dynamics in 2D triangular lattice antiferromagnet h-Y(Mn,Al)O3

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.

Quantum fluctuation effects on the ordered moments in a two dimensional frustrated ferrimagnet

We propose a novel two-dimensional (2D) frustrated quantum spin-1/2 anisotropic Heisenberg model with alternating ferromagnetic and antiferromagnetic magnetic chains along one direction and antiferromagnetic interactions along the other. The (mean-field) ground state is ferrimagnetic in certain range of the interaction space. Spin-wave theory analysis of the reduction of ordered moments at inequivalent spin sites and the instability of the spin waves suggest a quantum phase transition which has the characteristics of both the frustrated 2D antiferromagneticS= 1/2 (J₁,J₂) model and 1DS₁= 1,S₂= 1/2 quantum ferrimagnetic model.

Magnetoelastic coupling and spin contributions to entropy and thermal transport in biferroic yttrium orthochromite. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021;33:125702. [PMID: 33378273 DOI: 10.1088/1361-648x/abd781] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Direct engineering of material properties through exploitation of spin, phonon, and charge-coupled degrees of freedom is an active area of development in materials science. However, the relative contribution of the competing orders to controlling the desired behavior is challenging to decipher. In particular, the independent role of phonons, magnons, and electrons, quasiparticle coupling, and relative contributions to the phase transition free energy largely remain unexplored, especially for magnetic phase transitions. Here, we study the lattice and magnetic dynamics of biferroic yttrium orthochromite using Raman, infrared, and inelastic neutron spectroscopy techniques, supporting our experimental results with first-principles lattice dynamics and spin-wave simulations across the antiferromagnetic transition atT_N∼ 138 K. Spectroscopy data and simulations together with the heat capacity (C_p) measurements, allow us to quantify individual entropic contributions from phonons (0.01 ± 0.01k_Batom^-1), dilational (0.03 ± 0.01k_Batom^-1), and magnons (0.11 ± 0.01k_Batom^-1) acrossT_N. High-resolution phonon measurements conducted in a magnetic field show that anomalousT-dependence of phonon energies acrossT_Noriginates from magnetoelastic coupling. Phonon scattering is primarily governed by the phonon-phonon coupling, with little contribution from magnon-phonon coupling, short-range spin correlations, or magnetostriction effects; a conclusion further supported by our thermal conductivity measurements conducted up to 14 T, and phenomenological modeling.

Van Hove singularity in the magnon spectrum of the antiferromagnetic quantum honeycomb lattice

In quantum magnets, magnetic moments fluctuate heavily and are strongly entangled with each other, a fundamental distinction from classical magnetism. Here, with inelastic neutron scattering measurements, we probe the spin correlations of the honeycomb lattice quantum magnet YbCl₃. A linear spin wave theory with a single Heisenberg interaction on the honeycomb lattice, including both transverse and longitudinal channels of the neutron response, reproduces all of the key features in the spectrum. In particular, we identify a Van Hove singularity, a clearly observable sharp feature within a continuum response. The demonstration of such a Van Hove singularity in a two-magnon continuum is important as a confirmation of broadly held notions of continua in quantum magnetism and additionally because analogous features in two-spinon continua could be used to distinguish quantum spin liquids from merely disordered systems. These results establish YbCl₃ as a benchmark material for quantum magnetism on the honeycomb lattice.

Multiphase magnetism in Yb2Ti2O7

We use neutron scattering to show that ferromagnetism and antiferromagnetism coexist in the low T state of the pyrochlore quantum magnet [Formula: see text] While magnetic Bragg peaks evidence long-range static ferromagnetic order, inelastic scattering shows that short-range correlated antiferromagnetism is also present. Small-angle neutron scattering provides direct evidence for mesoscale magnetic structure that we associate with metastable antiferromagnetism. Classical Monte Carlo simulations based on exchange interactions inferred from [Formula: see text]-oriented high-field spin wave measurements confirm that antiferromagnetism is metastable within the otherwise ferromagnetic ground state. The apparent lack of coherent spin wave excitations and strong sensitivity to quenched disorder characterizing [Formula: see text] is a consequence of this multiphase magnetism.

Cluster Frustration in the Breathing Pyrochlore Magnet LiGaCr_{4}S_{8}

We present a comprehensive neutron scattering study of the breathing pyrochlore magnet LiGaCr_{4}S_{8}. We observe an unconventional magnetic excitation spectrum with a separation of high- and low-energy spin dynamics in the correlated paramagnetic regime above a spin-freezing transition at 12(2) K. By fitting to magnetic diffuse-scattering data, we parametrize the spin Hamiltonian. We find that interactions are ferromagnetic within the large and small tetrahedra of the breathing pyrochlore lattice, but antiferromagnetic further-neighbor interactions are also essential to explain our data, in qualitative agreement with density-functional-theory predictions [Ghosh et al., npj Quantum Mater. 4, 63 (2019)2397-464810.1038/s41535-019-0202-z]. We explain the origin of geometrical frustration in LiGaCr_{4}S_{8} in terms of net antiferromagnetic coupling between emergent tetrahedral spin clusters that occupy a face-centered-cubic lattice. Our results provide insight into the emergence of frustration in the presence of strong further-neighbor couplings, and a blueprint for the determination of magnetic interactions in classical spin liquids.

Spin-phonon coupling and thermodynamic behaviour in YCrO3and LaCrO3: inelastic neutron scattering and lattice dynamics

We report detailed temperature-dependent inelastic neutron scattering andab initiolattice dynamics investigation of magnetic perovskites YCrO₃and LaCrO₃. The magnetic neutron scattering from the Cr ions exhibits significant changes with temperature and dominates at low momentum transfer regime.Ab initiocalculations performed including magnetic interactions show that the effect of magnetic interactions is very significant on the low- as well as high-energy phonon modes. We have also shown that the inelastic neutron spectrum of YCrO₃mimics the magnon spectrum from a G-type antiferromagnetic system, which is consistent with previously reported magnetic structure in the compound. The pressure-dependentab initiolattice dynamics calculations are used to calculate the anisotropic thermal expansion behaviour in orthorhombic YCrO₃, which is in excellent agreement with the available experimental data in the paramagnetic phase. We identify that the low energy anharmonic phonon modes involving Y vibrations contribute maximum to the thermal expansion behaviour.

Orbital Magnetic Moment of Magnons

In experiments and their interpretation usually the spin magnetic moment of magnons is considered. In this Letter, we identify a complementing orbital magnetic moment of magnons brought about by spin-orbit coupling. Our microscopic theory uncovers that spin magnetization M^{S} and orbital magnetization M^{O} are independent quantities; they are not necessarily collinear. Even when the total spin moment is compensated due to antiferromagnetism, M^{O} may be nonzero. This scenario of orbital weak ferromagnetism is realized in paradigmatic kagome antiferromagnets with Dzyaloshinskii-Moriya interaction. We demonstrate that magnets exhibiting a magnonic orbital moment are omnipresent and propose transport experiments for probing it.

Probing the Ferromagnetism and Spin Wave Gap in VI3 by Helicity-Resolved Raman Spectroscopy

Circularly polarized light carries light spin angular momentum, which may lead helicity-resolved Raman scattering to be sensitive to the electronic spin configuration in magnetic materials. Here, we demonstrate that all Raman modes in the 2D ferromagnet VI₃ show different scattering intensities to left and right circularly polarized light at low temperatures, which gives direct evidence of the time-reversal symmetry breaking. By measuring the circular polarization of the dominant Raman mode with respect to the temperature and magnetic field, the ferromagnetic (FM) phase transition and hysteresis behavior can be clearly resolved. Besides the lattice excitations, quasielastic scattering is detected in the paramagnetic phase, and it gradually evolves into the acoustic magnon mode at 18.5 cm^-1 in the FM state, which gives the spin wave gap that results from large magnetic anisotropy. Our findings demonstrate that helicity-resolved Raman spectroscopy is an effective tool to directly probe the ferromagnetism in 2D magnets.

Coexistence and Interaction of Spinons and Magnons in an Antiferromagnet with Alternating Antiferromagnetic and Ferromagnetic Quantum Spin Chains

In conventional quasi-one-dimensional antiferromagnets with quantum spins, magnetic excitations are carried by either magnons or spinons in different energy regimes: they do not coexist independently, nor could they interact with each other. In this Letter, by combining inelastic neutron scattering, quantum Monte Carlo simulations, and random phase approximation calculations, we report the discovery and discuss the physics of the coexistence of magnons and spinons and their interactions in Botallackite-Cu_{2}(OH)_{3}Br. This is a unique quantum antiferromagnet consisting of alternating ferromagnetic and antiferromagnetic spin-1/2 chains with weak interchain couplings. Our study presents a new paradigm where one can study the interaction between two different types of magnetic quasiparticles: magnons and spinons.

Momentum-Dependent Magnon Lifetime in the Metallic Noncollinear Triangular Antiferromagnet CrB_{2}

Noncollinear 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 noncollinear antiferromagnet CrB_{2}, in which Cr atoms form a triangular lattice and display incommensurate magnetic order. Our data show intrinsic magnon damping and continuumlike excitations that cannot be explained by linear spin wave theory. The intrinsic magnon linewidth Γ(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 noncollinear antiferromagnets. It reveals, for the first time, definite experimental evidence of the higher-order effects in metallic antiferromagnets.

Three-dimensional magnetism and the Dzyaloshinskii-Moriya interaction in S = 3/2 kagome staircase Co3V2O8

Time-of-flight neutron data reveal spin waves in the ferromagnetic ground state of the kagome staircase material Co₃V₂O₈. While previous work has treated this material as quasi-two-dimensional, we find that an inherently three-dimensional description is needed to describe the spin wave spectrum throughout reciprocal space. Moreover, spin wave branches show gaps that point to an unexpectedly large Dzyaloshinskii-Moriya interaction on the nearest-neighbor bond, with D ₁ ≥ J ₁/2. A better understanding of the Dzyaloshinskii-Moriya interaction in this material should shed light on the multiferroicity of the related Ni₃V₂O₈. At a higher temperature where Co₃V₂O₈ displays an antiferromagnetic spin density wave structure, there are no well-defined spin wave excitations, with most of the spectral weight observed in broad diffuse scattering centered at the (0, 0.5, 0) antiferromagnetic Bragg peak.

Stripe Discommensuration and Spin Dynamics of Half-Doped Pr_{3/2}Sr_{1/2}NiO_{4}

We present inelastic neutron scattering measurements of magnetic excitations in stripe ordered Pr_{3/2}Sr_{1/2}NiO_{4} at T∼10  K. For the observed magnetic incommensurability ε=0.4, we have incorporated a stripe discommensuration model in our linear spin wave calculation and obtained best agreement with the measured spin wave dispersion, especially to explain the symmetrical outward shift of the magnetic peaks from Néel ordered zone center in energy range 35 to 45 meV. Our study indicates the prerequisite to consider a discommensurated spin stripe unit with proper out-of-plane and in-plane exchange interactions in between Ni^{2+} spins to describe the observed spin wave characteristics in Pr_{3/2}Sr_{1/2}NiO_{4}.

Machine learning and big scientific data

This paper reviews some of the challenges posed by the huge growth of experimental data generated by the new generation of large-scale experiments at UK national facilities at the Rutherford Appleton Laboratory (RAL) site at Harwell near Oxford. Such 'Big Scientific Data' comes from the Diamond Light Source and Electron Microscopy Facilities, the ISIS Neutron and Muon Facility and the UK's Central Laser Facility. Increasingly, scientists are now required to use advanced machine learning and other AI technologies both to automate parts of the data pipeline and to help find new scientific discoveries in the analysis of their data. For commercially important applications, such as object recognition, natural language processing and automatic translation, deep learning has made dramatic breakthroughs. Google's DeepMind has now used the deep learning technology to develop their AlphaFold tool to make predictions for protein folding. Remarkably, it has been able to achieve some spectacular results for this specific scientific problem. Can deep learning be similarly transformative for other scientific problems? After a brief review of some initial applications of machine learning at the RAL, we focus on challenges and opportunities for AI in advancing materials science. Finally, we discuss the importance of developing some realistic machine learning benchmarks using Big Scientific Data coming from several different scientific domains. We conclude with some initial examples of our 'scientific machine learning' benchmark suite and of the research challenges these benchmarks will enable. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'.

Order out of a Coulomb Phase and Higgs Transition: Frustrated Transverse Interactions of Nd_{2}Zr_{2}O_{7}

The pyrochlore material Nd_{2}Zr_{2}O_{7} with an "all-in-all-out" (AIAO) magnetic order shows novel quantum moment fragmentation with gapped flat dynamical spin ice modes. The parametrized spin Hamiltonian with a dominant frustrated ferromagnetic transverse term reveals a proximity to a U(1) spin liquid. Here we study the magnetic excitations of Nd_{2}Zr_{2}O_{7} above the ordering temperature (T_{N}) using high-energy-resolution inelastic neutron scattering. We find strong spin ice correlations at zero energy with the disappearance of gapped magnon excitations of the AIAO order. It seems that the gap to the dynamical spin ice closes above T_{N} and the system enters a quantum spin ice state competing with and suppressing the AIAO order. Classical Monte Carlo simulations, molecular dynamics, and quantum boson calculations support the existence of a Coulombic phase above T_{N}. Our findings relate the magnetic ordering of Nd_{2}Zr_{2}O_{7} with the Higgs mechanism and provide explanations for several previously reported experimental features.

Low-energy magnons in the chiral ferrimagnet Cu2OSeO3: A coarse-grained approach

We report a comprehensive neutron scattering study of low energy magnetic excitations in the breathing pyrochlore helimagnetic Cu₂OSeO₃. Fully documenting the four lowest energy magnetic modes that leave the ferrimagnetic configuration of the "strong tetrahedra" intact ( | ℏ ω | < 13 meV), we find gapless quadratic dispersion at the point for energies above 0.2 meV, two doublets separated by 1.6(2) meV at the R point, and a bounded continuum at the X point. Our constrained rigid spin cluster model relates these features to Dzyaloshinskii-Moriya (DM) interactions and the incommensurate helical ground state. Combining conventional spin wave theory with a spin cluster form factor accurately reproduces the measured equal time structure factor through multiple Brillouin zones. An effective spin Hamiltonian describing complex anisotropic intercluster interactions is obtained.