Order-by-disorder from bond-dependent exchange and intensity signature of nodal quasiparticles in a honeycomb cobaltate.

Recent theoretical proposals have argued that cobaltates with edge-sharing octahedral coordination can have significant bond-dependent exchange couplings thus offering a platform in 3d ions for such physics beyond the much-explored realisations in 4d and 5d materials. Here we present high-resolution inelastic neutron scattering data within the magnetically ordered phase of the stacked honeycomb magnet CoTiO3 revealing the presence of a finite energy gap and demonstrate that this implies the presence of bond-dependent anisotropic couplings. We also show through an extensive theoretical analysis that the gap further implies the existence of a quantum order-by-disorder mechanism that, in this material, crucially involves virtual crystal field fluctuations. Our data also provide an experimental observation of a universal winding of the scattering intensity in angular scans around linear band-touching points for both magnons and dispersive spin-orbit excitons, which is directly related to the non-trivial topology of the quasiparticle wavefunction in momentum space near nodal points.

Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb_{2}Ti_{2}O_{7} in a Magnetic Field.

The frustrated pyrochlore magnet Yb_{2}Ti_{2}O_{7} has the remarkable property that it orders magnetically but has no propagating magnons over wide regions of the Brillouin zone. Here we use inelastic neutron scattering to follow how the spectrum evolves in cubic-axis magnetic fields. At high fields we observe, in addition to dispersive magnons, a two-magnon continuum, which grows in intensity upon reducing the field and overlaps with the one-magnon states at intermediate fields leading to strong renormalization of the dispersion relations, and magnon decays. Using heat capacity measurements we find that the low- and high-field regions are smoothly connected with no sharp phase transition, with the spin gap increasing monotonically in field. Through fits to an extensive data set of dispersion relations combined with magnetization measurements, we reevaluate the spin Hamiltonian, finding dominant quantum exchange terms, which we propose are responsible for the anomalously strong fluctuations and quasiparticle breakdown effects observed at low fields.

Magnetic Field Dependence of Excitations Near Spin-Orbital Quantum Criticality.

The spinel FeSc_{2}S_{4} has been proposed to realize a near-critical spin-orbital singlet (SOS) state, where entangled spin and orbital moments fluctuate in a global singlet state on the verge of spin and orbital order. Here we report powder inelastic neutron scattering measurements that observe the full bandwidth of magnetic excitations and we find that spin-orbital triplon excitations of an SOS state can capture well key aspects of the spectrum in both zero and applied magnetic fields up to 8.5 T. The observed shift of low-energy spectral weight to higher energies upon increasing applied field is naturally explained by the entangled spin-orbital character of the magnetic states, a behavior that is in strong contrast to spin-only singlet ground state systems, where the spin gap decreases upon increasing applied field.

Single crystal growth from separated educts and its application to lithium transition-metal oxides.

Thorough mixing of the starting materials is the first step of a crystal growth procedure. This holds true for almost any standard technique, whereas the intentional separation of educts is considered to be restricted to a very limited number of cases. Here we show that single crystals of α-Li2IrO3 can be grown from separated educts in an open crucible in air. Elemental lithium and iridium are oxidized and transported over a distance of typically one centimeter. In contrast to classical vapor transport, the process is essentially isothermal and a temperature gradient of minor importance. Single crystals grow from an exposed condensation point placed in between the educts. The method has also been applied to the growth of Li2RuO3, Li2PtO3 and ß-Li2IrO3. A successful use of this simple and low cost technique for various other materials is anticipated.

Noncoplanar and counterrotating incommensurate magnetic order stabilized by Kitaev interactions in γ-Li(2)IrO(3).

Materials that realize Kitaev spin models with bond-dependent anisotropic interactions have long been searched for, as the resulting frustration effects are predicted to stabilize novel forms of magnetic order or quantum spin liquids. Here, we explore the magnetism of γ-Li(2)IrO(3), which has the topology of a three-dimensional Kitaev lattice of interconnected Ir honeycombs. Using magnetic resonant x-ray diffraction, we find a complex, yet highly symmetric incommensurate magnetic structure with noncoplanar and counterrotating Ir moments. We propose a minimal Kitaev-Heisenberg Hamiltonian that naturally accounts for all key features of the observed magnetic structure. Our results provide strong evidence that γ-Li(2)IrO(3) realizes a spin Hamiltonian with dominant Kitaev interactions.

Spin waves and revised crystal structure of honeycomb iridate Na2IrO3.

We report inelastic neutron scattering measurements on Na2IrO3, a candidate for the Kitaev spin model on the honeycomb lattice. We observe spin-wave excitations below 5 meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zigzag magnetic order. The onset of long-range magnetic order below T(N)=15.3 K is confirmed via the observation of oscillations in zero-field muon-spin rotation experiments. Combining single-crystal diffraction and density functional calculations we propose a revised crystal structure model with significant departures from the ideal 90° Ir-O-Ir bonds required for dominant Kitaev exchange.

Direct observation of charge order in triangular metallic AgNiO2 by single-crystal resonant X-ray scattering.

We report resonant x-ray scattering measurements on a single crystal of the orbitally degenerate triangular metallic antiferromagnet 2H-AgNiO2 to probe the spontaneous transition to a triple-cell superstructure at temperatures below T(S)=365 K. We observe a strong resonant enhancement of the supercell reflections through the Ni K edge. The empirically extracted K-edge shift between the crystallographically distinct Ni sites of 2.5(3) eV is much larger than the value expected from the shift in final states, and implies a core-level shift of ∼1 eV, thus providing direct evidence for the onset of spontaneous honeycomb charge order in the triangular Ni layers. We also provide band-structure calculations that explain quantitatively the observed edge shifts in terms of changes in the Ni electronic energy levels due to charge order and hybridization with the surrounding oxygens.

Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry.

Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8 Lie group with a spectrum of eight particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by using strong transverse magnetic fields to tune the quasi-one-dimensional Ising ferromagnet CoNb2O6 (cobalt niobate) through its critical point. Spin excitations are observed to change character from pairs of kinks in the ordered phase to spin-flips in the paramagnetic phase. Just below the critical field, the spin dynamics shows a fine structure with two sharp modes at low energies, in a ratio that approaches the golden mean predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviors.

Anomalous high-energy spin excitations in the high-Tc superconductor-parent antiferromagnet La2CuO4.

Inelastic neutron scattering is used to investigate the collective magnetic excitations of the high-temperature superconductor-parent antiferromagnet La2CuO4. We find that while the lower energy excitations are well described by spin-wave theory, including one- and two-magnon scattering processes, the high-energy spin waves are strongly damped near the (1/2, 0) position in reciprocal space and merge into a momentum dependent continuum. This anomalous damping indicates the decay of spin waves into other excitations, possibly unbound spinon pairs.

Anomalous temperature evolution of the internal magnetic field distribution in the charge-ordered triangular antiferromagnet AgNiO2.

Zero-field muon-spin relaxation measurements of the frustrated triangular quantum magnet AgNiO2 are consistent with a model of charge disproportionation that has been advanced to explain the structural and magnetic properties of this compound. Below an ordering temperature of TN=19.9(2) K we observe six distinct muon precession frequencies, due to the magnetic order, which can be accounted for with a model describing the probable muon sites. The precession frequencies show an unusual temperature evolution which is suggestive of the separate evolution of two opposing magnetic sublattices.

Orbital degeneracy removed by charge order in triangular antiferromagnet AgNiO2.

We report a high-resolution neutron diffraction study on the orbitally degenerate spin-1/2 hexagonal metallic antiferromagnet AgNiO2. A structural transition to a tripled unit cell with expanded and contracted NiO6 octahedra indicates sqrt[3]xsqrt[3] charge order on the Ni triangular lattice. This suggests charge order as a possible mechanism of lifting the orbital degeneracy in the presence of charge fluctuations, as an alternative to the more usual Jahn-Teller distortions. A novel magnetic ground state is observed at low temperatures with the electron-rich S=1 Ni sites arranged in alternating ferromagnetic rows on a triangular lattice, surrounded by a honeycomb network of nonmagnetic and metallic Ni ions. We also report first-principles band-structure calculations that explain microscopically the origin of these phenomena.

Quantum dynamics and entanglement of spins on a square lattice.

Bulk magnetism in solids is fundamentally quantum mechanical in nature. Yet in many situations, including our everyday encounters with magnetic materials, quantum effects are masked, and it often suffices to think of magnetism in terms of the interaction between classical dipole moments. Whereas this intuition generally holds for ferromagnets, even as the size of the magnetic moment is reduced to that of a single electron spin (the quantum limit), it breaks down spectacularly for antiferromagnets, particularly in low dimensions. Considerable theoretical and experimental progress has been made in understanding quantum effects in one-dimensional quantum antiferromagnets, but a complete experimental description of even simple two-dimensional antiferromagnets is lacking. Here we describe a comprehensive set of neutron scattering measurements that reveal a non-spin-wave continuum and strong quantum effects, suggesting entanglement of spins at short distances in the simplest of all two-dimensional quantum antiferromagnets, the square lattice Heisenberg system.

Bose-Einstein condensation of magnons in Cs2CuCl4.

We report on results of specific heat measurements on single crystals of the frustrated quasi-2D spin-1/2 antiferromagnet Cs2CuCl4 (T(N)=0.595 K) in external magnetic fields B<12 T and for temperatures T>30 mK. Decreasing B from high fields leads to the closure of the field-induced gap in the magnon spectrum at a critical field Bc approximately = 8.51 T and a magnetic phase transition is clearly seen below Bc. In the vicinity of Bc, the phase transition boundary is well described by the power law Tc(B) proportional, variant (Bc-B)(1/phi), with the measured critical exponent phi approximately =1.5. These findings are interpreted as a Bose-Einstein condensation of magnons.

Three-dimensional spin fluctuations in Na0.75CoO2.

We report polarized- and unpolarized-neutron scattering measurements of magnetic excitations in single-crystal Na0.75CoO2. The data confirm ferromagnetic correlations within the cobalt layers and reveal antiferromagnetic correlations perpendicular to the layers, consistent with an A-type antiferromagnetic ordering. The magnetic modes propagating perpendicular to the layers are sharp, and reach a maximum energy of approximately 12 meV. From a minimal spin-wave model, containing only nearest-neighbor Heisenberg exchange interactions, we estimate the interlayer and intralayer exchange constants to be 12.2+/-0.5 meV and -6+/-2 meV, respectively. We conclude that the magnetic fluctuations in Na0.75CoO2 are highly three dimensional.

Ferromagnetic in-plane spin fluctuations in NaxCoO2 observed by neutron inelastic scattering.

We present neutron scattering spectra taken from a single crystal of Na0.75CoO2, the precursor to a novel cobalt-oxide superconductor. The data contain a prominent inelastic signal at low energies ( approximately 10 meV), which is localized in wave vector about the origin of two-dimensional reciprocal space. The signal is highly dispersive, and decreases in intensity with increasing temperature. We interpret these observations as direct evidence for the existence of ferromagnetic spin fluctuations within the cobalt-oxygen layers.

Direct measurement of the spin Hamiltonian and observation of condensation of magnons in the 2D frustrated quantum magnet Cs2CuCl4.

We propose a method for measuring spin Hamiltonians and apply it to the spin- 1/2 Heisenberg antiferromagnet Cs2CuCl4, which shows a 2D fractionalized resonating valence bond state at low fields. By applying strong fields we fully align the spin moment of Cs2CuCl4, transforming it into an effective ferromagnet. In this phase the excitations are conventional magnons and their dispersion relation measured using neutron scattering give the exchange couplings directly, which are found to form an anisotropic triangular lattice with small Dzyaloshinskii-Moriya terms. Using the field to control the excitations we observe Bose condensation of magnons into an ordered ground state.

Multiparticle states in the S = 1 chain system CsNiCl3.

A continuum of magnetic states has been observed by neutron scattering from the spin-1 chain compound CsNiCl3 in its disordered gapped one-dimensional phase. Results using both triple-axis and time-of-flight spectrometers show that around the antiferromagnetic point Qc = pi, the continuum lies higher in energy than the Haldane gapped excitations. At 6 K the integrated intensity of the continuum is about 12(2)% of the total spectral weight. This result is considerably larger than the 1%-3% weight predicted by the nonlinear sigma model for the three-particle continuum.

Spin dynamics of the 2D spin 1/2 quantum antiferromagnet copper deuteroformate tetradeuterate (CFTD).

The magnetic excitation spectrum in the two-dimensional (2D) S = 1/2 Heisenberg antiferromagnet copper deuteroformate tetradeuterate has been measured for temperatures up to T approximately J/2, where J = 6.31+/-0.02 meV is the 2D exchange coupling. For T<

Spin waves and electronic interactions in La2CuO4.

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.

Experimental realization of a 2D fractional quantum spin liquid.

The ground-state ordering and dynamics of the two-dimensional S = 1/2 frustrated Heisenberg antiferromagnet Cs(2)CuCl(4) are explored using neutron scattering in high magnetic fields. We find that the dynamic correlations show a highly dispersive continuum of excited states, characteristic of the resonating valence bond state, arising from pairs of S = 1/2 spinons. Quantum renormalization factors for the excitation energies (1.65) and incommensuration (0.56) are large.