When viewed as an elementary particle, the electron has spin and charge. When binding to the atomic nucleus, it also acquires an angular momentum quantum number corresponding to the quantized atomic orbital it occupies. Even if electrons in solids form bands and delocalize from the nuclei, in Mott insulators they retain their three fundamental quantum numbers: spin, charge and orbital. The hallmark of one-dimensional physics is a breaking up of the elementary electron into its separate degrees of freedom. The separation of the electron into independent quasi-particles that carry either spin (spinons) or charge (holons) was first observed fifteen years ago. Here we report observation of the separation of the orbital degree of freedom (orbiton) using resonant inelastic X-ray scattering on the one-dimensional Mott insulator Sr2CuO3. We resolve an orbiton separating itself from spinons and propagating through the lattice as a distinct quasi-particle with a substantial dispersion in energy over momentum, of about 0.2 electronvolts, over nearly one Brillouin zone.

Na 2 IrO 3 , a honeycomb 5d 5 oxide, has been recently identified as a potential realization of the Kitaev spin lattice. The basic feature of this spin model is that for each of the three metal-metal links emerging out of a metal site, the Kitaev interaction connects only spin components perpendicular to the plaquette defined by the magnetic ions and two bridging ligands. The fact that reciprocally orthogonal spin components are coupled along the three different links leads to strong frustration effects and nontrivial physics. While the experiments indicate zigzag antiferromagnetic order in Na 2 IrO 3 , the signs and relative strengths of the Kitaev and Heisenberg interactions are still under debate. Herein we report results of ab initio many-body electronic-structure calculations and establish that the nearest-neighbor exchange is strongly anisotropic with a dominant 6 New J. Phys. 16 (2014) 013056 V M Katukuri et al ferromagnetic Kitaev part, whereas the Heisenberg contribution is significantly weaker and antiferromagnetic. The calculations further reveal a strong sensitivity to tiny structural details such as the bond angles. In addition to the large spin-orbit interactions, this strong dependence on distortions of the Ir 2 O 2 plaquettes singles out the honeycomb 5d 5 oxides as a new playground for the realization of unconventional magnetic ground states and excitations in extended systems. IntroductionThe Heisenberg model of magnetic interactions, J S i · S j between spin moments at sites {i, j}, has been successfully used as an effective minimal model to describe the cooperative magnetic properties of both molecular and solid-state many-electron systems. A less conventional spin model-the Kitaev model [1]-has been recently proposed for honeycomb-lattice materials with 90 • metal-oxygen-metal bonds and strong spin-orbit interactions [2]. It has nontrivial topological phases with elementary excitations exhibiting Majorana statistics, which are relevant and much studied in the context of topological quantum computing [1,[3][4][5][6][7]. Candidate materials proposed to host such physics are the honeycomb oxides Na 2 IrO 3 and Li 2 IrO 3 [2]. The magnetically active sites, the Ir 4+ species, display in these compounds a 5d 5 valence electron configuration, octahedral ligand coordination and bonding of nearest-neighbor (NN) Ir ions through two ligands [8,9]. In the simplest approximation, i.e. for sufficiently large t 2g -e g octahedral crystal-field splittings within the Ir 5d shell and degenerate Ir t 2g levels, the ground-state (GS) electron configuration at each Ir site is a t 5 2g effective j = 1/2 spin-orbit doublet [2,[10][11][12]. The anisotropic, Kitaev type coupling then stems from the particular form the superexchange between the Ir j = 1/2 pseudospins takes for 90 • bond angles on the Ir-O 2 -Ir plaquette [2,13,14].Recent measurements on Na 2 IrO 3 [8,9] indicate significant lattice distortions away from the idealized case of cubic IrO 6 octahedra and 90 • Ir-O-Ir bond angles for which the Kitaev-Heis...

Large anisotropic exchange in 5d and 4d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4d5 honeycomb halide α-RuCl3. From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5d5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d5 halides and oxides in general.

The electronic structure of the honeycomb lattice iridates Na(2)IrO(3) and Li(2)IrO(3) has been investigated using resonant inelastic x-ray scattering (RIXS). Crystal-field-split d-d excitations are resolved in the high-resolution RIXS spectra. In particular, the splitting due to noncubic crystal fields, derived from the splitting of j(eff)=3/2 states, is much smaller than the typical spin-orbit energy scale in iridates, validating the applicability of j(eff) physics in A(2)IrO(3). We also find excitonic enhancement of the particle-hole excitation gap around 0.4 eV, indicating that the nearest-neighbor Coulomb interaction could be large. These findings suggest that both Na(2)IrO(3) and Li(2)IrO(3) can be described as spin-orbit Mott insulators, similar to the square lattice iridate Sr(2)IrO(4).

Platelike high-quality NaYbS2 rhombohedral single crystals with lateral dimensions of a few mm have been grown and investigated in great detail by bulk methods like magnetization and specific heat, but also by local probes like nuclear magnetic resonance (NMR), electron-spin resonance (ESR), muon-spin relaxation (µSR), and inelastic neutron scattering (INS) over a wide field and temperature range. Our single-crystal studies clearly evidence a strongly anisotropic quasi-2D magnetism and an emerging spin-orbit entangled S = 1/2 state of Yb towards low temperatures together with an absence of long-range magnetic order down to 260 mK. In particular, the clear and narrow Yb ESR lines together with narrow 23 Na NMR lines evidence an absence of inherent structural distortions in the system, which is in strong contrast to the related spin-liquid candidate YbMgGaO4 falling within the same space group R3m. This identifies NaYbS2 as a rather pure spin-1/2 triangular lattice magnet and a new putative quantum spin liquid.Introduction. -In low-dimensional quantum magnets, competing confined magnetic exchange interactions restrict the magnetic degrees of freedom, which leads to a strong frustration accompanied by enhanced quantum fluctuations. Ultimately this prevents the systems from longrange order, and the ground state is supposed to be a magnetic liquid. There are various types of such quantum spin liquids (QSL) depending on the lattice geometry (in 2D: square-, triangular-, kagome-, or honeycomb-type; in 3D: hyperkagome, hyperhoneycomb, or pyrochlore), the magnetic exchange (e.g. Heisenberg, Kitaev, or Dzyaloshinskii-Moriya type), and the magnetic ion itself [1][2][3][4]. Planar spin-1/2 triangular lattice magnets (TLMs) with antiferromagnetic exchange interactions are ideal QSL candidates as proposed by P. W. Anderson [5]. A few examples are found among the organic materials, such as K-(BEDT-TTF) 2 Cu 2 (CN) 3 [6] and EtnMe 4−n Sb[Pd(DMIT) 2 ] 2 [7], whereas among inorganic compounds such QSL model systems are very rare, e.g. Ba 3 CuSb 2 O 9 [8].