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.

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 report a high-resolution neutron diffraction study of the crystal and magnetic structure of the orbitally degenerate frustrated metallic magnet AgNiO 2 . At high temperatures the structure is hexagonal with a single crystallographic Ni site, low-spin Ni 3+ with spin 1/2 and twofold orbital degeneracy, arranged in an antiferromagnetic triangular lattice with frustrated spin and orbital order. A structural transition occurs upon cooling below 365 K to a tripled hexagonal unit cell containing three crystallographically distinct Ni sites with expanded and contracted NiO 6 octahedra, naturally explained by spontaneous charge order on the Ni triangular layers. No Jahn-Teller distortions occur, suggesting that charge order occurs in order to lift the orbital degeneracy. Symmetry analysis of the inferred Ni charge order pattern and the observed oxygen displacement pattern suggests that the transition could be mediated by charge fluctuations at the Ni sites coupled to a soft oxygen optical phonon breathing mode. At low temperatures the electron-rich Ni sublattice ͑assigned to a valence close to Ni 2+ with S =1͒ orders magnetically into a collinear stripe structure of ferromagnetic rows ordered antiferromagnetically in the triangular planes. We discuss the stability of this uncommon spin order pattern in the context of an easy-axis triangular antiferromagnet with additional weak second-neighbor interactions and interlayer couplings.

Neutron diffraction studies of polycrystalline R3Cu4Sn4 (R = Tb, Dy, Ho, Er) intermetallic compounds with the orthorhombic Gd3Cu4Ge4-type crystal structure indicate the existence of different magnetic structures. Rare earth atoms occupy two non-equivalent 2d and 4e sublattices. The rare earth magnetic moments order at low temperatures. For R = Tb and Dy the magnetic structures below the Néel temperature are described by the propagation vectors k = (0, 0, 1/2 + δ). In these compounds both rare earth sublattices order. For R = Ho the magnetic structure is more complicated. There are two vectors; one of them is k = (0, 1/2, 0) whereas the second one changes with temperature. For the Er compound there is the propagation vector k = (1/2, 1/2, 0) which describes the magnetic ordering in the 2d sublattice and at low temperatures is accompanied by the propagation vector k = (0, 0,δ) describing the ordering in the 4e sublattice.