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 8 particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by tuning the quasi-one-dimensional Ising ferromagnet CoNb 2 O 6 through its critical point using strong transverse magnetic fields. The 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 as predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviours.

Unlike conventional magnets where the magnetic moments are partially or completely static in the ground state, in a quantum spin liquid they remain in collective motion down to the lowest temperatures. The importance of this state is that it is coherent and highly entangled without breaking local symmetries. Such phenomena is usually sought in simple lattices where antiferromagnetic interactions and/or anisotropies that favor specific alignments of the magnetic moments are frustrated by lattice geometries incompatible with such order e.g. triangular structures. Despite an extensive search among such compounds, experimental realizations remain very few. Here we describe the investigation of a novel, unexplored magnetic system consisting of strong ferromagnetic and weaker antiferromagnetic isotropic interactions as realized by the compound Ca10Cr7O28. Despite its exotic structure we show both experimentally and theoretically that it displays all the features expected of a quantum spin liquid including coherent spin dynamics in the ground state and the complete absence of static magnetism.A quantum spin liquid is a macroscopic lattice of interacting magnetic ions with quantum spin number S=½, whose ground state has no static long-range magnetic order, instead the magnetic moments fluctuate coherently down to the lowest temperatures [1, 2]. It contrasts with the static long-range magnetically ordered ground states usually observed, and also with spin glass states where the spins are frozen into static short-range ordered configurations [3]. The excitations are believed to be spinons which have fractional quantum spin number S=½, and are very different from spin-waves or magnons that possess quantum spin number S=1 and are the characteristic excitations of conventional magnets. Spin liquids exist in one-dimensional magnets and the chain of spin-½ magnetic ions coupled by nearestneighbor, Heisenberg (isotropic), antiferromagnetic interactions is a well-established example [4]. This system has no static long-range magnetic order and the excitations are spinons. There is no energetic reason for the spinons to bind together, indeed if a spin-1 excitation is created e.g. by reversing a spin in the chain, it fractionalizes into two spin-½ spinons [5][6][7][8][9][10][11][12].The existence of spin liquids in dimensions greater than one is much less established. While static order does not occur in one-dimensional magnets, conventional two-and three-dimensional magnets order at temperatures at or above zero Kelvin [13]. This order can be suppressed by introducing competition (known as frustration) between the interactions that couple the magnetic ions. Geometrical frustration is achieved when the magnetic ions are located on lattices constructed from triangular motifs and are coupled by antiferromagnetic interactions. The antiferromagnetic coupling favors antiparallel spin alignment between nearest neighbor spins which can never be fully satisfied since the number of spins around the triangle is odd. This typically leads to h...

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.

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...

A spin liquid is a new state of matter with topological order where the spin moments continue to fluctuate coherently down to the lowest temperatures rather than develop static long-range magnetic order as found in conventional magnets. For spin liquid behavior to arise in a material the magnetic Hamiltonian must be "frustrated" where the combination of lattice geometry, interactions and anisotropies gives rise to competing spin arrangements in the ground state. Theoretical Hamiltonians which produce spin liquids are spin ice, the Kitaev honeycomb model and the kagome antiferromagnet. Spin liquid behavior however in real materials is rare because they can only approximate these Hamiltonians and often have weak higher order terms that destroy the spin liquid state. Ca10Cr7O28 is a new quantum spin liquid candidate with magnetic Cr 5+ ions that possess quantum spin number S= 1 /2. The spins are entirely dynamic in the ground state and the excitation spectrum is broad and diffuse as is typical of spinons which are the excitations of a spin liquid. In this paper we determine the Hamiltonian of Ca10Cr7O28 using inelastic neutron scattering under high magnetic field to induce a field polarized paramagnetic ground state and spin-wave excitations that can be fitted to extract the interactions. We further explore the phase diagram by using inelastic neutron scattering and heat capacity measurements and establish the boundaries of the spin liquid phase as a function of magnetic field and temperature. Our results show that Ca10Cr7O28 consists of distorted kagome bilayers with several isotropic ferromagnetic and antiferromagnetic interactions where unexpectedly the ferromagnetic interactions are stronger than the antiferromagnetic ones. This complex Hamiltonian does not correspond to any known spin liquid model and points to new directions in the search for quantum spin liquid behavior. INTRODUCTIONConventional magnets in condensed matter typically develop long-range magnetic order when cooled to low temperatures [1]. Below their ordering temperature the magnetic moments develop a static component which acts as the order parameter for the phase transition and the spin ordering is observable as magnetic Bragg peaks which characterize the type of order. The excitations are usually spin-waves which are collective oscillations of the spins about their ordering directions. The transition can be described by Landau theory where symmetry is broken and the new phase is characterized by a local order parameter [2].It was recently realized that some states of matter are characterized by topological order, rather than by symmetry breaking and a local order parameter [3]. This important discovery promises new, exotic and potentially useful properties that could be of relevance e.g. to information technologies. For example topological order gives rise to coherent states which can be highly robust to the usual perturbations that destroy coherence in ordinary states due to the non-local nature of their correlations.One potential applicati...