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.

Nature of Magnetic Excitations in the High-Field Phase of α-RuCl_{3}.

We present comprehensive electron spin resonance (ESR) studies of in-plane oriented single crystals of α-RuCl_{3}, a quasi-two-dimensional material with honeycomb structure, focusing on its high-field spin dynamics. The measurements were performed in magnetic fields up to 16 T, applied along the [110] and [100] directions. Several ESR modes were detected. Combining our findings with recent inelastic neutron- and Raman-scattering data, we identified most of the observed excitations. Most importantly, we show that the low-temperature ESR response beyond the boundary of the magnetically ordered region is dominated by single- and two-particle processes with magnons as elementary excitations. The peculiarities of the excitation spectrum in the vicinity of the critical field are discussed.

Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet.

Quantum spin liquids (QSLs) are topological states of matter exhibiting remarkable properties such as the capacity to protect quantum information from decoherence. Whereas their featureless ground states have precluded their straightforward experimental identification, excited states are more revealing and particularly interesting owing to the emergence of fundamentally new excitations such as Majorana fermions. Ideal probes of these excitations are inelastic neutron scattering experiments. These we report here for a ruthenium-based material, α-RuCl3, continuing a major search (so far concentrated on iridium materials) for realizations of the celebrated Kitaev honeycomb topological QSL. Our measurements confirm the requisite strong spin-orbit coupling and low-temperature magnetic order matching predictions proximate to the QSL. We find stacking faults, inherent to the highly two-dimensional nature of the material, resolve an outstanding puzzle. Crucially, dynamical response measurements above interlayer energy scales are naturally accounted for in terms of deconfinement physics expected for QSLs. Comparing these with recent dynamical calculations involving gauge flux excitations and Majorana fermions of the pure Kitaev model, we propose the excitation spectrum of α-RuCl3 as a prime candidate for fractionalized Kitaev physics.

Destabilization of Magnetic Order in a Dilute Kitaev Spin Liquid Candidate.

The insulating honeycomb magnet α-RuCl_{3} exhibits fractionalized excitations that signal its proximity to a Kitaev quantum spin liquid state; however, at T=0, fragile long-range magnetic order arises from non-Kitaev terms in the Hamiltonian. Spin vacancies in the form of Ir^{3+} substituted for Ru are found to destabilize this long-range order. Neutron diffraction and bulk characterization of Ru_{1-x}Ir_{x}Cl_{3} show that the magnetic ordering temperature is suppressed with increasing x, and evidence of zizag magnetic order is absent for x>0.3. Inelastic neutron scattering demonstrates that the signature of fractionalized excitations is maintained over the full range of x investigated. The depleted lattice without magnetic order thus hosts a spin-liquid-like ground state that may indicate the relevance of Kitaev physics in the magnetically dilute limit of RuCl_{3}.

Antiferromagnetic Resonance and Terahertz Continuum in α-RuCl_{3}.

We report measurements of optical absorption in the zigzag antiferromagnet α-RuCl_{3} as a function of temperature T, magnetic field B, and photon energy ℏω in the range ∼0.3-8.3 meV, using time-domain terahertz spectroscopy. Polarized measurements show that threefold rotational symmetry is broken in the honeycomb plane from 2 to 300 K. We find a sharp absorption peak at 2.56 meV upon cooling below the Néel temperature of 7 K at B=0 that we identify as the magnetic-dipole excitation of a zero-wave-vector magnon, or antiferromagnetic resonance (AFMR). With the application of B, the AFMR broadens and shifts to a lower frequency as long-range magnetic order is lost in a manner consistent with transitioning to a spin-disordered phase. From a direct, internally calibrated measurement of the AFMR spectral weight, we place an upper bound on the contribution to the dc susceptibility from a magnetic excitation continuum.

Multispinon continua at zero and finite temperature in a near-ideal Heisenberg chain.

The space-and time-dependent response of many-body quantum systems is the most informative aspect of their emergent behavior. The dynamical structure factor, experimentally measurable using neutron scattering, can map this response in wave vector and energy with great detail, allowing theories to be quantitatively tested to high accuracy. Here, we present a comparison between neutron scattering measurements on the one-dimensional spin-1/2 Heisenberg antiferromagnet KCuF3, and recent state-of-the-art theoretical methods based on integrability and density matrix renormalization group simulations. The unprecedented quantitative agreement shows that precise descriptions of strongly correlated states at all distance, time, and temperature scales are now possible, and highlights the need to apply these novel techniques to other problems in low-dimensional magnetism.

Quasi-one-dimensional magnons in an intermetallic marcasite.

We present inelastic neutron scattering measurements and first principles calculations examining the intermetallic marcasite CrSb(2). The observed spin-wave dispersion implies that the magnetic interactions are strongly one-dimensional with antiferromagnetic chains parallel to the crystalline c axis. Such low-dimensional excitations are unexpected in a semiconducting intermetallic system. Moreover, we observe a clear anisotropic thermal conductivity indicating that the magnetic anisotropy enhances thermoelectric properties along particular crystallographic directions.

Competing ferri- and antiferromagnetic phases in geometrically frustrated LuFe2O4.

We present a detailed study of magnetism in LuFe(2)O(4), combining magnetization measurements with neutron and soft x-ray diffraction. The magnetic phase diagram in the vicinity of T(N) involves a metamagnetic transition separating an antiferro- and a ferrimagnetic phase. For both phases the spin structure is refined by neutron diffraction. Observed diffuse magnetic scattering far above T(N) is explained in terms of near degeneracy of the magnetic phases.

Quantum wake dynamics in Heisenberg antiferromagnetic chains.

Traditional spectroscopy, by its very nature, characterizes physical system properties in the momentum and frequency domains. However, the most interesting and potentially practically useful quantum many-body effects emerge from local, short-time correlations. Here, using inelastic neutron scattering and methods of integrability, we experimentally observe and theoretically describe a local, coherent, long-lived, quasiperiodically oscillating magnetic state emerging out of the distillation of propagating excitations following a local quantum quench in a Heisenberg antiferromagnetic chain. This "quantum wake" displays similarities to Floquet states, discrete time crystals and nonlinear Luttinger liquids. We also show how this technique reveals the non-commutativity of spin operators, and is thus a model-agnostic measure of a magnetic system's "quantumness."

Unusual relationship between magnetism and superconductivity in FeTe(0.5)Se(0.5).

We use neutron scattering to study magnetic excitations in crystals near the ideal superconducting composition of FeTe(0.5)Se(0.5). Two types of excitations are found, a resonance at (0.5,0.5,0) and incommensurate fluctuations on either side of this position. We show that the two sets of magnetic excitations behave differently with doping, with the resonance being fixed in position while the incommensurate excitations move as the doping is changed. These unusual results show that a common behavior of the low energy magnetic excitations is not necessary for pairing in these materials.

Pulsed spallation neutron spectroscopy of low dimensional magnets: past, present, and future.

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

Evidence for the confinement of magnetic monopoles in quantum spin ice.

Magnetic monopoles are hypothesised elementary particles connected by Dirac strings that behave like infinitely thin solenoids (Dirac 1931 Proc. R. Soc. A 133 60). Despite decades of searching, free magnetic monopoles and their Dirac strings have eluded experimental detection, although there is substantial evidence for deconfined magnetic monopole quasiparticles in spin ice materials (Castelnovo et al 2008 Nature 326 411). Here we report the detection of a hierarchy of unequally-spaced magnetic excitations via high resolution inelastic neutron spectroscopic measurements on the quantum spin ice candidate [Formula: see text] [Formula: see text] [Formula: see text]. These excitations are well-described by a simple model of monopole pairs bound by a linear potential (Coldea et al Science 327 177) with an effective tension of 0.642(8) K [Formula: see text] at 1.65 K. The success of the linear potential model suggests that these low energy magnetic excitations are direct spectroscopic evidence for the confinement of magnetic monopole quasiparticles in the quantum spin ice candidate [Formula: see text] [Formula: see text] [Formula: see text].

Atomic-scale observation of structural and electronic orders in the layered compound α-RuCl3.

A pseudospin-1/2 Mott phase on a honeycomb lattice is proposed to host the celebrated two-dimensional Kitaev model which has an elusive quantum spin liquid ground state, and fascinating physics relevant to the development of future templates towards topological quantum bits. Here we report a comprehensive, atomically resolved real-space study by scanning transmission electron and scanning tunnelling microscopies on a novel layered material displaying Kitaev physics, α-RuCl3. Our local crystallography analysis reveals considerable variations in the geometry of the ligand sublattice in thin films of α-RuCl3 that opens a way to realization of a spatially inhomogeneous magnetic ground state at the nanometre length scale. Using scanning tunnelling techniques, we observe the electronic energy gap of ≈0.25 eV and intra-unit cell symmetry breaking of charge distribution in individual α-RuCl3 surface layer. The corresponding charge-ordered pattern has a fine structure associated with two different types of charge disproportionation at Cl-terminated surface.

The early development of neutron diffraction: science in the wings of the Manhattan Project.

Although neutron diffraction was first observed using radioactive decay sources shortly after the discovery of the neutron, it was only with the availability of higher intensity neutron beams from the first nuclear reactors, constructed as part of the Manhattan Project, that systematic investigation of Bragg scattering became possible. Remarkably, at a time when the war effort was singularly focused on the development of the atomic bomb, groups working at Oak Ridge and Chicago carried out key measurements and recognized the future utility of neutron diffraction quite independent of its contributions to the measurement of nuclear cross sections. Ernest O. Wollan, Lyle B. Borst and Walter H. Zinn were all able to observe neutron diffraction in 1944 using the X-10 graphite reactor and the CP-3 heavy water reactor. Subsequent work by Wollan and Clifford G. Shull, who joined Wollan's group at Oak Ridge in 1946, laid the foundations for widespread application of neutron diffraction as an important research tool.

Quantum oscillations of nitrogen atoms in uranium nitride.

The vibrational excitations of crystalline solids corresponding to acoustic or optic one-phonon modes appear as sharp features in measurements such as neutron spectroscopy. In contrast, many-phonon excitations generally produce a complicated, weak and featureless response. Here we present time-of-flight neutron scattering measurements for the binary solid uranium nitride, showing well-defined, equally spaced, high-energy vibrational modes in addition to the usual phonons. The spectrum is that of a single atom, isotropic quantum harmonic oscillator and characterizes independent motions of light nitrogen atoms, each found in an octahedral cage of heavy uranium atoms. This is an unexpected and beautiful experimental realization of one of the fundamental, exactly solvable problems in quantum mechanics. There are also practical implications, as the oscillator modes must be accounted for in the design of generation IV nuclear reactors that plan to use uranium nitride as a fuel.

Static and dynamic magnetism in underdoped superconductor BaFe1.92Co0.08As2.

We report neutron scattering measurements on single crystals of BaFe1.92Co0.08As2. The magnetic Bragg peak intensity is reduced by 6% upon cooling through TC. The spin dynamics exhibit a gap of 8 meV with anisotropic three-dimensional interactions. Below TC additional intensity appears at an energy of approximately 4.5(0.5) meV, similar to previous observations of a spin resonance in other Fe-based superconductors. No further gapping of the spin excitations is observed below TC for energies down to 2 meV. These observations suggest the redistribution of spectral weight from the magnetic Bragg position to a spin resonance, demonstrating the direct competition between static magnetic order and superconductivity.

Two-dimensional resonant magnetic excitation in BaFe1.84Co0.16As2.

Inelastic neutron scattering measurements on single crystals of superconducting BaFe1.84Co0.16As2 reveal a magnetic excitation located at wave vectors (1/2 1/2 L) in tetragonal notation. On cooling below T_{C}, a clear resonance peak is observed at this wave vector with an energy of 8.6(0.5) meV, corresponding to 4.5(0.3) k_{B}T_{C}. This is in good agreement with the canonical value of 5 k_{B}T_{C} observed in the cuprates. The spectrum shows strong dispersion in the tetragonal plane but very weak dispersion along the c axis, indicating that the magnetic fluctuations are two dimensional in nature. This is in sharp contrast to the anisotropic three dimensional spin excitations seen in the undoped parent compounds.

Magnetic and orbital ordering in the spinel MnV2O4.

Neutron inelastic scattering and diffraction techniques have been used to study the MnV2O4 spinel system. Our measurements show the existence of two transitions to long-range ordered ferrimagnetic states, the first collinear and the second noncollinear. The lower temperature transition, characterized by development of antiferromagnetic components in the basal plane, is accompanied by a tetragonal distortion and the appearance of a gap in the magnetic excitation spectrum. The low-temperature noncollinear magnetic structure has been definitively resolved. Taken together, the crystal and magnetic structures indicate a staggered ordering of the V d orbitals. The anisotropy gap is a consequence of unquenched V orbital angular momentum.

Three-dimensional magnetic correlations in multiferroic LuFe2O4.

We present single crystal neutron diffraction measurements on multiferroic LuFe(2)O(4). Magnetic reflections are observed below transitions at 240 and 175 K indicating that the magnetic interactions in LuFe(2)O(4) are three-dimensional in character. The magnetic structure is refined as a ferrimagnetic spin configuration below the 240 K transition. Below 175 K a significant broadening of the magnetic peaks is observed along with the buildup of a diffuse component to the magnetic scattering.

Charge order in LuFe2O4: antiferroelectric ground state and coupling to magnetism.

X-ray scattering by multiferroic LuFe2O4 is reported. Below 320 K, superstructure reflections indicate an incommensurate charge order with propagation close to (1/3 1/3 3/2). The corresponding charge configuration, also found by electronic structure calculations as most stable, contains polar Fe/O double layers with antiferroelectric stacking. Diffuse scattering at 360 K, with (1/3 1/3 0) propagation, indicates ferroelectric short-range correlations between neighboring double layers. The temperature dependence of the incommensuration indicates that charge order and magnetism are coupled.