We present a unique study of the frustrated spinel MgV2O4 which possesses highly coupled spin, lattice and orbital degrees of freedom. Using large single-crystal and powder samples, we find a distortion from spinel at room temperature (space group F 43m) which allows for a greater trigonal distortion of the VO6 octahedra and a low temperature space group (I4m2) that maintains the mirror plane symmetry. The magnetic structure that develops below 42 K consists of antiferromagnetic chains with a strongly reduced moment while inelastic neutron scattering reveals one-dimensional behavior and a single band of excitations. The implications of these results are discussed in terms of various orbital ordering scenarios. We conclude that although spin-orbit coupling must be significant to maintain the mirror plane symmetry, the trigonal distortion is large enough to mix the 3d levels leading to a wave function of mixed real and complex orbitals. PACS numbers: 75.25.+z,75.10.Jm, 61.12.Ex Geometrically frustrated magnets are characterized by competing interactions resulting in a highly degenerate lowest energy manifold. In many cases the degeneracy is eventually lifted at low temperatures by a lattice distortion. In compounds where the magnetic ions also possess orbital degeneracy, orbital-ordering can influence the exchange interactions and lift the frustration. The vanadium spinels AV 2 O 4 , where A is diamagnetic Cd 2+ , Zn 2+ , or Mg 2+ provide ideal systems to study the interactions between spin, lattice and orbital degrees of freedom [1]. In these compounds the magnetic V 3+ -ions possess orbital degeneracy and form a frustrated pyrochlore lattice with direct exchange interactions between nearest neighbors providing a direct coupling to the orbital configuration. The interplay of orbital and spin physics has been studied in other systems like the perovskite vanadates (RVO 3 , R is a rare earth) which show a strong correlation between orbital ordering and magnetic structure [2]. However in these compounds the couplings are unfrustrated and indirect, occurring via super exchange through oxygen. In contrast the magnetic structure and excitations in the spinel vanadates are more sensitive to orbital ordering and thus characteristic of it. Furthermore the additional component of frustration allows for the possibility of exotic ground states. Indeed the nature of the ground state in the spinel compounds has generated intense theoretical interest over the past eight years [4-7] but has remained an unresolved experimental issue which we will address in this paper.The electronic configuration of V 3+ is 3d 2 leading to a single-ion spin S=1. Each V 3+ -ion is located at the center of edge sharing VO 6 octahedra which create a crystal-field that splits the d-orbitals and lowers the energy of the three t 2g orbitals by approximately 2.5 eV [3].These levels are usually assumed to be degenerate (ignoring the small trigonal distortion which will be discussed later) so that the two d-electrons of V 3+ randomly occupy the three t 2...

Confinement is a process by which particles with fractional quantum numbers bind together to form quasiparticles with integer quantum numbers. The constituent particles are confined by an attractive interaction whose strength increases with increasing particle separation and as a consequence, individual particles are not found in isolation. This phenomenon is well known in particle physics where quarks are confined in baryons and mesons. An analogous phenomenon occurs in certain spatially anisotropic magnetic insulators. These can be thought of in terms of weakly coupled chains of spins S=1/2, and a spin flip thus carries integer spin S=1. Interestingly the collective excitations in these systems, called spinons, turn out to carry fractional spin quantum number S=1/2. Interestingly, at sufficiently low temperatures the weak coupling between chains can induce an attractive interaction between pairs of spinons that increases with their separation and thus leads to confinement. In this paper, we employ inelastic neutron scattering to investigate the spinonconfinement process in the quasi-one dimensional, spin-1/2, antiferromagnet with Heisenberg-Ising (XXZ) anisotropy SrCo2V2O8. A wide temperature range both above and below the long-range ordering temperature TN =5.2 K is explored. Spinon excitations are observed above TN in quantitative agreement with established theory. Below TN the pairs of spinons are confined and two sequences of meson-like bound states with longitudinal and transverse polarizations are observed. Several theoretical approaches are used to explain the data. These are based on a description in terms of a one-dimensional, S=1/2 XXZ antiferromagnetic spin chain, where the interchain couplings are modelled by an effective staggered magnetic mean-field. A wide range of exchange anisotropies are investigated and the parameters specific to SrCo2V2O8 are identified. A new theoretical technique based on Tangent-space Matrix Product States gives a very complete description of the data and provides good agreement not only with the energies of the bound modes but also with their intensities. We also successfully explained the effect of temperature on the excitations including the experimentally observed thermally induced resonance between longitudinal modes below TN , and the transitions between thermally excited spinon states above TN . In summary, our work establishes SrCo2V2O8 as a beautiful paradigm for spinon confinement in a quasi-one dimensional quantum magnet and provides a comprehensive picture of this process.

Sr3Cr2O8 consist of a lattice of spin-1/2 Cr 5+ ions, which form hexagonal bilayers and which are paired into dimers by the dominant antiferromagnetic intrabilayer coupling. The dimers are coupled three-dimensionally by frustrated interdimer interactions. A structural distortion from hexagonal to monoclinic leads to orbital order and lifts the frustration giving rise to spatially anisotropic exchange interactions. We have grown large single crystals of Sr3Cr2O8 and have performed DC susceptibility, high field magnetisation and inelastic neutron scattering measurements. The neutron scattering experiments reveal three gapped and dispersive singlet to triplet modes arising from the three twinned domains that form below the transition thus confirming the picture of orbital ordering. The exchange interactions are extracted by comparing the data to a Random Phase Approximation model and the dimer coupling is found to be J0 = 5.55 meV, while the ratio of interdimer to intradimer exchange constants is J ′ /J0 = 0.64. The results are compared to those for other gapped magnets.

The quantum spin liquid is a highly entangled magnetic state characterized by the absence of static magnetism in its ground state. Instead, the spins fluctuate in a highly correlated way down to the lowest temperatures. Quantum spin liquids are very rare and are confined to a few specific cases where the interactions between the magnetic ions cannot be simultaneously satisfied (known as frustration). Lattices with magnetic ions in triangular or tetrahedral arrangements, which interact via isotropic antiferromagnetic interactions, can generate such a frustration. Three-dimensional isotropic spin liquids have mostly been sought in materials where the magnetic ions form pyrochlore or hyperkagome lattices. Here we present a three-dimensional lattice called the hyper-hyperkagome that enables spin liquid behaviour and manifests in the compound PbCuTe 2 O 6. Using a combination of experiment and theory, we show that this system exhibits signs of being a quantum spin liquid with no detectable static magnetism together with the presence of diffuse continua in the magnetic spectrum suggestive of fractional spinon excitations.

Almost a century ago, string states-complex bound states of magnetic excitations-were predicted to exist in one-dimensional quantum magnets. However, despite many theoretical studies, the experimental realization and identification of string states in a condensed-matter system have yet to be achieved. Here we use high-resolution terahertz spectroscopy to resolve string states in the antiferromagnetic Heisenberg-Ising chain SrCoVO in strong longitudinal magnetic fields. In the field-induced quantum-critical regime, we identify strings and fractional magnetic excitations that are accurately described by the Bethe ansatz. Close to quantum criticality, the string excitations govern the quantum spin dynamics, whereas the fractional excitations, which are dominant at low energies, reflect the antiferromagnetic quantum fluctuations. Today, Bethe's result is important not only in the field of quantum magnetism but also more broadly, including in the study of cold atoms and in string theory; hence, we anticipate that our work will shed light on the study of complex many-body systems in general.