Intercalation of Li in TiO2 anatase results in a phase separation in a Li-poor and a Li-rich phase. The local lithium configuration in the coexisting crystallographic phases is resolved by detailed analysis of neutron diffraction data. In each of the phases, two distinct positions within the octahedral interstices are found, with a temperature-dependent occupancy. A combination of quasi-elastic neutron scattering and force field molecular dynamics simulations shows that Li is hopping on a picosecond time scale between the two sites in the octahedral interstices. The results also suggest a specific Li arrangement along the crystallographic a direction, albeit without long range order. It is likely that multiple discrete Li sites within a distorted oxygen octahedron occur not only in intercalated TiO2 anatase but also in other (transition metal) oxides.

Bose-Einstein condensation denotes the formation of a collective quantum ground state of identical particles with integer spin or intrinsic angular momentum. In magnetic insulators, the magnetic properties are due to the unpaired shell electrons that have half-integer spin. However, in some such compounds (KCuCl3 and TlCuCl3), two Cu2+ ions are antiferromagnetically coupled to form a dimer in a crystalline network: the dimer ground state is a spin singlet (total spin zero), separated by an energy gap from the excited triplet state (total spin one). In these dimer compounds, Bose-Einstein condensation becomes theoretically possible. At a critical external magnetic field, the energy of one of the Zeeman split triplet components (a type of boson) intersects the ground-state singlet, resulting in long-range magnetic order; this transition represents a quantum critical point at which Bose-Einstein condensation occurs. Here we report an experimental investigation of the excitation spectrum in such a field-induced magnetically ordered state, using inelastic neutron scattering measurements of TlCuCl3 single crystals. We verify unambiguously the theoretically predicted gapless Goldstone mode characteristic of the Bose-Einstein condensation of the triplet states.

Determination of the electronic energy spectrum of a trigonal-symmetry mononuclear Yb(3+) single-molecule magnet (SMM) by high-resolution absorption and luminescence spectroscopies reveals that the first excited electronic doublet is placed nearly 500 cm(-1) above the ground one. Fitting of the paramagnetic relaxation times of this SMM to a thermally activated (Orbach) model {τ = τ0 × exp[ΔOrbach/(kBT)]} affords an activation barrier, ΔOrbach, of only 38 cm(-1). This result is incompatible with the spectroscopic observations. Thus, we unambiguously demonstrate, solely on the basis of experimental data, that Orbach relaxation cannot a priori be considered as the main mechanism determining the spin dynamics of SMMs. This study highlights the fact that the general synthetic approach of optimizing SMM behavior by maximization of the anisotropy barrier, intimately linked to the ligand field, as the sole parameter to be tuned, is insufficient because of the complete neglect of the interaction of the magnetic moment of the molecule with its environment. The Orbach mechanism is expected dominant only in the cases in which the energy of the excited ligand field state is below the Debye temperature, which is typically low for molecular crystals and, thus, prevents the use of the anisotropy barrier as a design criterion for the realization of high-temperature SMMs. Therefore, consideration of additional design criteria that address the presence of alternative relaxation processes beyond the traditional double-well picture is required.

The material class of skutterudites is believed to have strong potential for thermoelectric application due to the very low thermal conductivity of the filled structures. It is generally assumed that the atoms filling the skutterudite cages act as 'rattlers' and essentially induce a disordered lattice dynamics referred to as 'phonon glass'. Here, we present neutron spectroscopy experiments and ab initio computational work on phonons in LaFe(4)Sb(12) and CeFe(4)Sb(12). Our results give unequivocal evidence of essentially temperature-independent lattice dynamics with well-defined phase relations between guest and host dynamics, indicative of a quasi-harmonic coupling between the guests and the host lattice. These conclusions are in disagreement with the 'phonon glass' paradigm based on individual 'rattling' of the guest atoms. These findings should have an essential impact on the design and improvement of thermoelectric materials and on the development of microscopic models needed for these efforts.

The physics of spin ice materials is intimately connected with the pyrochlore lattice, composed of corner-sharing tetrahedra. On the corners of these tetrahedra reside rare-earth magnetic moments J i , which, as a consequence of the strong crystal electric field, are constrained to point along their local trigonal axes z i , and behave like Ising spins. The magnetic interactions are composed of nearestneighbour exchange J and dipolar interactions between spins i and j separated by a distance r ij (ref. 7):wherenn ), µ 0 is the permeability of free space, g J is the Landé factor of the magnetic moment, µ B is the Bohr magneton and r nn is the nearest-neighbour distance between rareearth ions. The nearest-neighbour spin ice Hamiltonian is obtained by truncating the Hamiltonian (1), yielding:When the effective interaction J eff = (−J + 5D)/3 is positivethat is, when the dipolar term overcomes the antiferromagnetic exchange-a very unusual magnetic state develops, known as the spin ice state. The system remains in a highly correlated but disordered ground state where the local magnetization fulfils the so-called 'ice rule': each tetrahedron has two spins pointing in and two spins pointing out (see Fig. 1a), in close analogy with the rule which controls the hydrogen position in water ice 8 . The extensive degeneracy of this ground state results in a residual entropy at low temperature which is well approximated by the Pauling entropy for water ice 9 . Such highly degenerate states, where the organizing principle is dictated by a local constraint, belong to the class of Coulomb phases 5,10,11 : the constraint (the ice rule for spin ice) can be interpreted as a divergence-free condition of an emergent gauge field. This field has correlations that fall off with distance like the dipolar interaction 12,13 . In reciprocal space, this power-law character leads to bow-tie singularities, called pinch points, in the magnetic structure factor. They form a key experimental signature of the Coulomb phase physics. They have been observed by neutron diffraction in the spin ice materials Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7 , in excellent agreement with theoretical predictions 14,15 . Classical excitations above the spin ice manifold are defects that locally violate the ice rule and so the divergence-free condition: by reversing the orientation of a moment, 'three in-one out' and 'one in-three out' configurations are created (see Fig. 1b). Considering the Ising spins as dumbbells with two opposite magnetic charges at their extremities, such defects result in a magnetic charge in the centre of the tetrahedron, called a magnetic monopole, that give rise to a non-zero divergence of the local magnetization 4 . Recently, theoreticians have introduced the concept of magnetic moment fragmentation 6 , whereby the local magnetic moment field fragments into the sum of two parts, a divergence-full and a divergence-free part (see Fig. 1c): for example, a monopole in the spin configuration m = {1, 1, 1, −1} on a tetrahedron can be written m = 1/2{1, ...