Inelastic neutron scattering, susceptibility, and high-field magnetization identify LiCuVO4 as a nearest-neighbour ferromagnetic, next-nearest-neighbour frustrated, quasi-onedimensional helimagnet, which is largely influenced by quantum fluctuations. Complementary band structure calculations provide a microscopic model with the correct sign and magnitude of the major exchange integrals.

One of the simplest quantum many-body systems is the spin-1/2 Heisenberg antiferromagnetic chain, a linear array of interacting magnetic moments. Its exact ground state is a macroscopic singlet entangling all spins in the chain. Its elementary excitations, called spinons, are fractional spin-1/2 quasiparticles created and detected in pairs by neutron scattering. Theoretical predictions show that two-spinon states exhaust only 71% of the spectral weight and higher-order spinon states, yet to be experimentally located, are predicted to participate in the remaining. Here, by accurate absolute normalization of our inelastic neutron scattering data on a spin-1/2 Heisenberg antiferromagnetic chain compound, we account for the full spectral weight to within 99(8)%. Our data thus establish and quantify the existence of higher-order spinon states. The observation that, within error bars, the experimental line shape resembles a rescaled two-spinon one with similar boundaries allows us to develop a simple picture for understanding multi-spinon excitations.O ne hundred years ago, Max von Laue and co-workers discovered X-ray diffraction 1 , thereby giving birth to the field of crystallography to which we owe much of our understanding of materials on the atomic scale. The very first diffraction image was recorded from a single crystal of copper sulphate pentahydrate 1,2 . In addition to vast practical use including herbicide, wood impregnation and algae control in swimming pools, copper sulphate also carries great educational importance. Generations of school children have been inspired in chemistry classes across the globe by growing from evaporating solution beautiful blue crystals of copper sulphate (in 2008, artist Roger Hiorns created an installation called Seizure 3 covering an entire apartment in copper sulphate crystals). When cooled close to absolute zero temperature, copper sulphate has even more fascinating lessons to teach-it becomes a quantum spin liquid. Moreover, it materializes one of the simplest models hosting complex quantum many-body physics, the one-dimensional spin-1/2 Heisenberg antiferromagnet, for which there exists an exact analytic solution-namely the Bethe ansatz 4 . Quantum spin liquid ground states entangle a macroscopic number of spins and give rise to astonishing and counterintuitive phenomena. Quantum spin liquids occur in a variety of contexts ranging from the quantum spin Hall effect 5,6 and high-T c superconductivity 7-9 to confined ultracold gases and carbon nanotubes 10 . A particularly clear form of a gapless algebraic quantum spin liquid is realized in a one-dimensional array of spins-1/2 that are coupled by nearest-neighbour isotropic exchange, the spin-1/2 Heisenberg antiferromagnetic chain. At zero temperature, this spin liquid is critical with respect to long-range antiferromagnetic order as well as with respect to dimerization 11,12 . Its emerging gapless fractionalized excitations are called spinons 13 . The concept of fractional excitations has been applied to magnetic monopoles ...

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. antiferromagnetism ͉ entanglement ͉ multimagnons ͉ spin waves O ne of the most fundamental exercises in quantum mechanics is to consider a pair of S ϭ 1/2 spins with an interaction J between them that favors either parallel (ferromagnetic) or antiparallel (antiferromagnetic) alignment. The former results in a spin S tot ϭ 1 ground state, which is a degenerate triplet. Two of the states in this triplet are the possible classical ground states ͉11͘ and ͉22͘, whereas the third is the coherent symmetric superposition ͉12͘ϩ͉21͘, which has no classical analogue. Even more interesting is antiferromagnetic J, for which the ground state is the entirely nonclassical S tot ϭ 0 singlet ͉0͘ ϭ ͉12͘ Ϫ ͉21͘ consisting of the antisymmetric coherent superposition of the two classical ground states of the pair. The state ͉0͘ is an example of maximal entanglement, i.e., a wavefunction for two coupled systems that cannot be written as the product of eigenfunctions for the two separate systems, which in this case are of course the two spins considered individually.

Polarized and unpolarized neutron scattering experiments on the frustrated ferromagnetic spin-1/2 chain LiCuVO4 show that the phase transition at H(Q) of 8 T is driven by quadrupolar fluctuations and that dipolar correlations are short range with moments parallel to the applied magnetic field in the high-field phase. Heat-capacity measurements evidence a phase transition into this high-field phase, with an anomaly clearly different from that at low magnetic fields. Our experimental data are consistent with a picture where the ground state above H(Q) has a next-nearest neighbor bond-nematic order along the chains with a fluidlike coherence between weakly coupled chains.

NaxCoO2, the parent compound of the recently synthesized superconductor Na(x)CoO(2):yH(2)O, exhibits bulk antiferromagnetic order below approximately 20 K for 0.75