Band topology, or global wave-function structure that enforces novel properties in the bulk and on the surface of crystalline materials, is currently under intense investigations for both fundamental interest and its technological promises [1-4]. While band crossing of non-trivial topological nature was first studied in three dimensions for electrons [4-10], the underlying physical idea is not restricted to fermionic excitations [11-15]. In fact, experiments have confirmed the possibility to have topological band crossing of electromagnetic waves in artificial structures [16]. Fundamental bosonic excitations in real crystals, however, have not been observed to exhibit the counterpart under ambient pressure and magnetic field, where the difficulty is in part because natural materials cannot be precisely engineered like artificial structures. Here, we use inelastic neutron scattering to reveal the presence of topological spin excitations (magnons) in a three-dimensional antiferromagnet, Cu3TeO6, which features a unique lattice of magnetic spin-1/2 Cu 2+ ions [17]. Beyond previous understanding [17,18], we find that the material's spin lattice possesses a variety of exchange interactions, with the interaction between the ninth-nearest neighbours being as strong as that between the nearest neighbours. Although theoretical analysis indicates that the presence of topological magnon band crossing is independent of model details [15], Cu3TeO6 turns out to be highly favourable for the experimental observation, as its optical magnons are spectrally sharp and intense due

Single crystals of ZnFe 2 O 4 are investigated with neutron scattering measurements from the viewpoint of geometrical frustration. Magnetic diffuse scattering was distributed along the first Brillouin zone boundary of the fcc structure. The results show that the frustration occurs between the antiferromagnetically coupled third-neighbor spins, rather than between the similarly coupled first-neighbor spins. In addition, another type of diffuse scattering was found around some nuclear Bragg peak positions. This indicates that the first-neighbor exchange interaction in the 90°configuration is ferromagnetic rather than antiferromagnetic. Energy spectra were investigated at several points. The unusual magnetic behavior originates from the geometrical frustration and a unique property of the first-neighbor interaction.

In this work we present inelastic neutron scattering experiments which probe the single ion ground states of the rare earth pyrochlores R2Ti2O7 (R = Tb, Dy, Ho). Dy2Ti2O7 and Ho2Ti2O7 are dipolar spin ices, now often described as hosts of emergent magnetic monopole excitations; the low temperature state of Tb2Ti2O7 has features of both spin liquids and spin glasses, and strong magnetoelastic coupling. We measured the crystal field excitations of all three compounds and obtained a unified set of crystal field parameters. Additional measurements of a single crystal of Tb2Ti2O7 clarified the assignment of the crystal field levels in this material and also revealed a new example of a bound state between a crystal field level and an optical phonon mode.

In order to elucidate the magnetism and Li diffusion in LiFePO 4 , we have measured muon-spin rotation and relaxation (μ + SR) spectra for the polycrystalline LiFePO 4 sample in the temperature range between 1.8 and 500 K. Below T N ∼ 52 K, two oscillatory signals together with one fast relaxation signal were clearly found in the zero-field (ZF) μ + SR spectrum. The three signals are reasonably explained using an antiferromagnetic (AF) spin structure proposed by neutron measurements, because electrostatic potential calculations suggests multiple different muon sites in the LiFePO 4 lattice. However, the AF ordered moment estimated from μ + SR was about 3/4 of that reported by neutron, probably due to a different time window between the two techniques. In the paramagnetic state, ZF and longitudinal-field (LF) μ + SR spectra exhibited a dynamic nuclear field relaxation. From the temperature dependence of the field fluctuation rate, a diffusion coefficient of Li + ions (D Li) at 300 K was estimated about 3.6 × 10 −10 cm 2 /s, assuming that diffusing Li + ions jump between the regular site and interstitial sites.

The perovskite LaCoO 3 evolves from a nonmagnetic Mott insulator to a spin cluster ferromagnet (FM) with the substitution of Sr 2 for La 3 in La 1ÿx Sr x CoO 3 . The clusters increase in size and number with x and the charge percolation through the clusters leads to a metallic state. Using elastic neutron scattering on La 1ÿx Sr x CoO 3 single crystals, we show that an incommensurate spin superstructure coexists with the FM spin clusters. The incommensurability increases continuously with x, with the intensity rising in the insulating phase and dropping in the metallic phase as it directly competes with the commensurate FM, itinerant clusters. The spin incommensurability arises from local order of Co 3 -Co 4 clusters but no longrange static or dynamic spin stripes develop. The coexistence and competition of the two magnetic phases explain the residual resistivity at low temperatures in samples with metalliclike transport.