A magnetic continuum in the cobalt-based honeycomb magnet BaCo2(AsO4)2.

Quantum spin liquids (QSLs) are topologically ordered states of matter that host fractionalized excitations. A particular route towards a QSL is via strongly bond-dependent interactions on the hexagonal lattice. A number of Ru- and Ir-based candidate Kitaev QSL materials have been pursued, but all have appreciable non-Kitaev interactions. Using time-domain terahertz spectroscopy, we observed a broad magnetic continuum over a wide range of temperatures and fields in the honeycomb cobalt-based magnet BaCo2(AsO4)2, which has been proposed to be a more ideal version of a Kitaev QSL. Applying an in-plane magnetic field of ~0.5 T suppresses the magnetic order, and at higher fields, applying the field gives rise to a spin-polarized state. Under a 4 T magnetic field that was oriented principally out of plane, a broad magnetic continuum was observed that may be consistent with a field-induced QSL. Our results indicate BaCo2(AsO4)2 is a promising QSL candidate.

A flexible neutron spectrometer concept with a new ultra-high field steady-state vertical-bore magnet.

The proposed facility explores materials under ultra-high magnetic fields. By combining the power of high fields to tune materials and of neutron scattering to probe the resulting changes down to the atomic scale, this facility will enable transformative progress in the study of quantum materials and is named for the "TITAN" subset of Greek gods to reflect this transformation. TITAN will offer DC magnetic fields up to at least 20 T. Exploiting the record brightness and bandwidth of the Second Target Station at the Spallation Neutron Source, TITAN will probe atomic-scale responses through high efficiency neutron spectroscopy up to 80 meV energy transfer, high resolution diffraction, and small angle neutron scattering. Focusing neutron optics will maximize flux on accurately positioned samples, while radial collimation and optimized shielding and detection strategies will minimize backgrounds.

Monopolar and dipolar relaxation in spin ice Ho2Ti2O7.

Ferromagnetically interacting Ising spins on the pyrochlore lattice of corner-sharing tetrahedra form a highly degenerate manifold of low-energy states. A spin flip relative to this "spin-ice" manifold can fractionalize into two oppositely charged magnetic monopoles with effective Coulomb interactions. To understand this process, we have probed the low-temperature magnetic response of spin ice to time-varying magnetic fields through stroboscopic neutron scattering and SQUID magnetometry on a new class of ultrapure Ho2Ti2O7 crystals. Covering almost 10 decades of time scales with atomic-scale spatial resolution, the experiments resolve apparent discrepancies between prior measurements on more disordered crystals and reveal a thermal crossover between distinct relaxation processes. Magnetic relaxation at low temperatures is associated with monopole motion through the spin-ice vacuum, while at elevated temperatures, relaxation occurs through reorientation of increasingly spin-like monopolar bound states. Spin fractionalization is thus directly manifest in the relaxation dynamics of spin ice.

Quantum spin liquids.

Spin liquids are quantum phases of matter with a variety of unusual features arising from their topological character, including "fractionalization"-elementary excitations that behave as fractions of an electron. Although there is not yet universally accepted experimental evidence that establishes that any single material has a spin liquid ground state, in the past few years a number of materials have been shown to exhibit distinctive properties that are expected of a quantum spin liquid. Here, we review theoretical and experimental progress in this area.

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.

Intrinsic Low-Temperature Magnetism in SmB_{6}.

By means of new muon spin relaxation experiments, we disentangle extrinsic and intrinsic sources of low-temperature bulk magnetism in the candidate topological Kondo insulator (TKI) SmB_{6}. Results on Al-flux-grown SmB_{6} single crystals are compared to those on a large floating-zone-grown ^{154}Sm ^{11}B_{6} single crystal in which a 14 meV bulk spin exciton has been detected by inelastic neutron scattering. Below ∼10 K, we detect the gradual development of quasistatic magnetism due to rare-earth impurities and Sm vacancies. Our measurements also reveal two additional forms of intrinsic magnetism: (1) underlying low-energy (∼100 meV) weak magnetic moment (∼10^{-2} µ_{B}) fluctuations similar to those detected in the related candidate TKI YbB_{12} that persist down to millikelvin temperatures, and (2) magnetic fluctuations consistent with a 2.6 meV bulk magnetic excitation at zero magnetic field that appears to hinder surface conductivity above ∼4.5 K. We discuss potential origins of the magnetism.

Incommensurate Magnetism Near Quantum Criticality in CeNiAsO.

We report the discovery of incommensurate magnetism near quantum criticality in CeNiAsO through neutron scattering and zero field muon spin rotation. For T

Magnetic Excitations of the Classical Spin Liquid MgCr_{2}O_{4}.

We report a comprehensive inelastic neutron-scattering study of the frustrated pyrochlore antiferromagnet MgCr_{2}O_{4} in its cooperative paramagnetic regime. Theoretical modeling yields a microscopic Heisenberg model with exchange interactions up to third-nearest neighbors, which quantitatively explains all of the details of the dynamic magnetic response. Our work demonstrates that the magnetic excitations in paramagnetic MgCr_{2}O_{4} are faithfully represented in the entire Brillouin zone by a theory of magnons propagating in a highly correlated paramagnetic background. Our results also suggest that MgCr_{2}O_{4} is proximate to a spiral spin-liquid phase distinct from the Coulomb phase, which has implications for the magnetostructural phase transition in MgCr_{2}O_{4}.

Homogeneous reduced moment in a gapful scalar chiral kagome antiferromagnet.

We present a quantitative experimental investigation of the scalar chiral magnetic order with in Nd3Sb3Mg2O14. Static magnetization reveals a net ferromagnetic ground state, and inelastic neutron scattering from the hyperfine coupled nuclear spin reveals a local ordered moment of 1.76(6) µB, just 61(2)% of the saturated moment size. The experiments exclude static disorder as the source of the reduced moment. A 38(1) µeV gap in the magnetic excitation spectrum inferred from heat capacity rules out thermal fluctuations and suggests a multipolar explanation for the moment reduction. We compare Nd3Sb3Mg2O14 to Nd pyrochlores and show that Nd2Zr2O7 is in a spin fragmented state using nuclear Schottky heat capacity.

Universal geometric frustration in pyrochlores.

Materials with the pyrochlore/fluorite structure have diverse technological applications, from magnetism to nuclear waste disposal. Here we report the observation of structural instability present in the pyrochlores A2Zr2O6O' (A = Pr, La) and Yb2Ti2O6O', that exists despite ideal stoichiometry, ideal cation-ordering, the absence of lone pair effects, and a lack of magnetic order. Though these materials appear to have good long-range order, local structure probes find displacements, of the order of 0.01 nm, within the pyrochlore framework. The pattern of displacements of the A2O' sublattice mimics the entropically-driven fluxional motions characteristic of and well-known in the silica mineral ß-cristobalite. The universality of such displacements within the pyrochlore structure adds to the known structural diversity and explains the extreme sensitivity to composition found in quantum spin ices and the lack of ferroelectric behavior in pyrochlores.

Screened moments and extrinsic in-gap states in samarium hexaboride.

Samarium hexaboride (SmB6) is a Kondo insulator, with a narrow gap due to hybridization between localized and conduction electrons. Despite being an insulator, many samples show metal-like properties. Rare-earth purification is exceedingly difficult, and nominally pure samples may contain 2% or more of impurities. Here to determine the effects of rare-earth doping on SmB6, we synthesized and probed a series of gadolinium-doped samples. We found a relationship between specific heat and impurity moment screening which scales systematically. Consistent with this finding, our neutron scattering experiments of a high purity sample of doubly isotopic 154Sm11B6 show no intrinsic excitations below the well-established 13 meV spin-exciton. The result of introducing impurities into a Kondo insulator is incompletely understood, but it is clear from our measurements that there is a systematic relationship between rare-earth impurities and metal-like properties in SmB6.

Continuum of quantum fluctuations in a three-dimensional S = 1 Heisenberg magnet.

Conventional crystalline magnets are characterized by symmetry breaking and normal modes of excitation called magnons, with quantized angular momentum ℏ. Neutron scattering correspondingly features extra magnetic Bragg diffraction at low temperatures and dispersive inelastic scattering associated with single magnon creation and annihilation. Exceptions are anticipated in so-called quantum spin liquids, as exemplified by the one-dimensional spin-1/2 chain, which has no magnetic order and where magnons accordingly fractionalize into spinons with angular momentum ℏ/2. This is spectacularly revealed by a continuum of inelastic neutron scattering associated with two-spinon processes. Here, we report evidence for these key features of a quantum spin liquid in the three-dimensional antiferromagnet NaCaNi2F7. We show that despite the complication of random Na1+-Ca2+ charge disorder, NaCaNi2F7 is an almost ideal realization of the spin-1 antiferromagnetic Heisenberg model on a pyrochlore lattice. Magnetic Bragg diffraction is absent and 90% of the neutron spectral weight forms a continuum of magnetic scattering with low-energy pinch points, indicating NaCaNi2F7 is in a Coulomb-like phase. Our results demonstrate that disorder can act to freeze only the lowest-energy magnetic degrees of freedom; at higher energies, a magnetic excitation continuum characteristic of fractionalized excitations persists.

Disordered Route to the Coulomb Quantum Spin Liquid: Random Transverse Fields on Spin Ice in Pr_{2}Zr_{2}O_{7}.

Inelastic neutron scattering reveals a broad continuum of excitations in Pr_{2}Zr_{2}O_{7}, the temperature and magnetic field dependence of which indicate a continuous distribution of quenched transverse fields (Δ) acting on the non-Kramers Pr^{3+} crystal field ground state doublets. Spin-ice correlations are apparent within 0.2 meV of the Zeeman energy. A random phase approximation provides an excellent account of the data with a transverse field distribution ρ(Δ)∝(Δ^{2}+Γ^{2})^{-1}, where Γ=0.27(1) meV. Established during high temperature synthesis due to an underlying structural instability, it appears disorder in Pr_{2}Zr_{2}O_{7} actually induces a quantum spin liquid.

Reentrant Phase Diagram of Yb_{2}Ti_{2}O_{7} in a ⟨111⟩ Magnetic Field.

We present a magnetic phase diagram of rare-earth pyrochlore Yb_{2}Ti_{2}O_{7} in a ⟨111⟩ magnetic field. Using heat capacity, magnetization, and neutron scattering data, we show an unusual field dependence of a first-order phase boundary, wherein a small applied field increases the ordering temperature. The zero-field ground state has ferromagnetic domains, while the spins polarize along ⟨111⟩ above 0.65 T. A classical Monte Carlo analysis of published Hamiltonians does account for the critical field in the low T limit. However, this analysis fails to account for the large bulge in the reentrant phase diagram, suggesting that either long-range interactions or quantum fluctuations govern low field properties.

Block Magnetic Excitations in the Orbitally Selective Mott Insulator BaFe_{2}Se_{3}.

Iron pnictides and selenides display a variety of unusual magnetic phases originating from the interplay between electronic, orbital, and lattice degrees of freedom. Using powder inelastic neutron scattering on the two-leg ladder BaFe_{2}Se_{3}, we fully characterize the static and dynamic spin correlations associated with the Fe_{4} block state, an exotic magnetic ground state observed in this low-dimensional magnet and in Rb_{0.89}Fe_{1.58}Se_{2}. All the magnetic excitations of the Fe_{4} block state predicted by an effective Heisenberg model with localized spins are observed below 300 meV and quantitatively reproduced. However, the data only account for 16(3)µ_{B}^{2} per Fe^{2+}, approximatively 2/3 of the total spectral weight expected for localized S=2 moments. Our results highlight how orbital degrees of freedom in iron-based magnets can conspire to stabilize an exotic magnetic state.

Interaction driven subgap spin exciton in the Kondo insulator SmB6.

Using inelastic neutron scattering, we map a 14 meV coherent resonant mode in the topological Kondo insulator SmB6 and describe its relation to the low energy insulating band structure. The resonant intensity is confined to the X and R high symmetry points, repeating outside the first Brillouin zone and dispersing less than 2 meV, with a 5d-like magnetic form factor. We present a slave-boson treatment of the Anderson Hamiltonian with a third neighbor dominated hybridized band structure. This approach produces a spin exciton below the charge gap with features that are consistent with the observed neutron scattering. We find that maxima in the wave vector dependence of the inelastic neutron scattering indicate band inversion.

Molecular quantum magnetism in LiZn2Mo3O8.

Inelastic neutron scattering at low temperatures T≤30 K from a powder of LiZn2Mo3O8 demonstrates this triangular-lattice antiferromagnet hosts collective magnetic excitations from spin-1/2 Mo3O13 molecules. Apparently gapless (Δ<0.2 meV) and extending at least up to 2.5 meV, the low-energy magnetic scattering cross section is surprisingly broad in momentum space and involves one-third of the spins present above 100 K. The data are compatible with the presence of valence bonds involving nearest-neighbor and next-nearest-neighbor spins forming a disordered or dynamic state.

Quantum fluctuations in spin-ice-like Pr2Zr2O7.

Spin ice is a magnetic analog of H2O ice that harbors dense static disorder. Dipolar interactions between classical spins yield a frozen frustrated state with residual configurational Pauling entropy and emergent magnetic monopolar quasiparticles. Introducing quantum fluctuations is of great interest as this could melt spin ice and allow coherent propagation of monopoles. Here, we report experimental evidence for quantum dynamics of magnetic monopolar quasiparticles in a new class of spin ice based on exchange interactions, Pr2Zr2O7. Narrow pinch point features in otherwise diffuse elastic neutron scattering reflects adherence to a divergence-free constraint for disordered spins on long time scales. Magnetic susceptibility and specific heat data correspondingly show exponentially activated behaviors. In sharp contrast to conventional ice, however, >90% of the neutron scattering is inelastic and devoid of pinch points furnishing evidence for magnetic monopolar quantum fluctuations.

Magnetic field splitting of the spin resonance in CeCoIn5.

Neutron scattering in strong magnetic fields is used to show the spin resonance in superconducting CeCoIn(5) (T(c)=2.3 K) is a doublet. The underdamped resonance (hΓ=0.069±0.019 meV) Zeeman splits into two modes at E(±)=hΩ(0)±αµ(B)µ(0)H with α=0.96±0.05. A linear extrapolation of the lower peak reaches zero energy at 11.2±0.5 T, near the critical field for the incommensurate "Q phase." Kenzelmann et al. [Science 321, 1652 (2008)] This, taken with the integrated weight and polarization of the low-energy mode (E(-)), indicates that the Q phase can be interpreted as a Bose condensate of spin excitons.