The recently-synthesized iridate $beta$-Li$_2$IrO$_3$ has been proposed as a candidate to display novel magnetic behavior stabilized by frustration effects from bond-dependent, anisotropic interactions (Kitaev model) on a three-dimensional hyperhoney
comb lattice. Here we report a combined study using neutron powder diffraction and magnetic resonant x-ray diffraction to solve the complete magnetic structure. We find a complex, incommensurate magnetic order with non-coplanar and counter-rotating Ir moments, which surprisingly shares many of its features with the related structural polytype stripyhoneycomb $gamma$-Li$_2$IrO$_3$, where dominant Kitaev interactions have been invoked to explain the stability of the observed magnetic structure. The similarities of behavior between those two structural polytypes, which have different global lattice topologies but the same local connectivity, is strongly suggestive that the same magnetic interactions and the same underlying mechanism governs the stability of the magnetic order in both materials, indicating that both $beta$- and $gamma$-Li$_2$IrO$_3$ are strong candidates to realize dominant Kitaev interactions in a solid state material.
Materials that realize Kitaev spin models with bond-dependent anisotropic interactions have long been searched for, as the resulting frustration effects are predicted to stabilize novel forms of magnetic order or quantum spin liquids. Here we explore
the magnetism of $gamma$-Li$_2$IrO$_3$, which has the topology of a 3D Kitaev lattice of inter-connected Ir honeycombs. Using resonant magnetic x-ray diffraction we find a complex, yet highly-symmetric incommensurate magnetic structure with non-coplanar and counter-rotating Ir moments. We propose a minimal Kitaev-Heisenberg Hamiltonian that naturally accounts for all key features of the observed magnetic structure. Our results provide strong evidence that $gamma$-Li$_2$IrO$_3$ realizes a spin Hamiltonian with dominant Kitaev interactions.
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 wi
th 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 CoNb2O6 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 resonant X-ray scattering measurements on the orbitally-degenerate triangular metallic antiferromagnet 2H-AgNiO2 to probe the spontaneous transition to a triple-cell superstructure at temperatures below 365 K. We observe a strong resonant e
nhancement of the supercell reflections through the Ni K-edge. The empirically extracted K-edge shift between the crystallographically-distinct Ni sites of 2.5(3) eV is much larger than the value expected from the shift in final states, and implies a core-level shift of ~1 eV, thus providing direct evidence for the onset of spontaneous honeycomb charge order in the triangular Ni layers. We also provide band-structure calculations that explain quantitatively the observed edge shifts in terms of changes in the Ni electronic energy levels due to charge order and hybridization with the surrounding oxygens.
