We report inelastic neutron scattering measurements on Na2IrO3, a candidate for the Kitaev spin model on the honeycomb lattice. We observe spin-wave excitations below 5 meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zig-zag magnetic order. The onset of long-range magnetic order below TN = 15.3 K is confirmed via the observation of oscillations in zero-field muon-spin rotation experiments. Combining single-crystal diffraction and density functional calculations we propose a revised crystal structure model with significant departures from the ideal 90• Ir-O-Ir bonds required for dominant Kitaev exchange. [6,7], in which edge-sharing IrO 6 octahedra form a honeycomb lattice [see Fig. 1b)], have been predicted to display novel magnetic states for composite spin-orbital moments coupled via frustrated exchanges. The exchange between neighboring Ir moments (called S i,j , S=1/2) is proposed to be [2]where J K > 0 is an Ising ferromagnetic (FM) term arising from superexchange via the Ir-O-Ir bond, and J 1 > 0 is the antiferromagnetic (AFM) Heisenberg exchange via direct Ir-Ir 5d overlap. Due to the strong spin-orbital admixture the Kitaev term J K couples only the components in the direction γ, normal to the plane of the Ir-O-Ir bond [8,9]. Because of the orthogonal geometry, different spin components along the cubic axes (γ = x, y, z) of the IrO 6 octahedron are coupled for the three bonds emerging out of each site in the honeycomb lattice. This leads to the strongly-frustrated Kitaev-Heisenberg (KH) model [2], which has conventional Néel order [see Fig. 3a)] for large J 1 , a stripy collinear AFM phase [see Fig. 3c)] for 0.4 α 0.8, where α = J K / (J K + 2J 1 ) (exact ground state at α = 1/2), and a quantum spin liquid with Majorana fermion excitations [10] at large J K (α 0.8). Measurements of the spin excitations are very important to determine the overall energy scale and the relevant magnetic interactions, however because Ir is a strong neutron absorber inelastic neutron scattering (INS) experiments are very challenging. Using an optimized setup we here report the first observation of dispersive spin wave excitations of Ir moments via INS. We show that the dispersion can be quantitatively accounted for by including substantial further-neighbor in-plane exchanges, which in turn stabilize zig-zag order. To inform future ab initio studies of microscopic models of the interactions we combine single-crystal xray diffraction with density functional calculations to determine precisely the oxygen positions, which are key in mediating the exchange and controlling the spin-orbital admixture via crystal field effects. We propose a revised crystal structure with much more symmetric IrO 6 octahedra, but with substantial departures from the ideal 90• Ir-O-Ir bonds required for dominant Kitaev exchange [9], and with frequent structural stacking faults. This differs from the currentlyadopted model, used by several band-structure calculations [14,15], with asymme...

Spin and orbital quantum numbers play a key role in the physics of Mott insulators, but in most systems they are connected only indirectly -via the Pauli exclusion principle and the Coulomb interaction. Iridium-based oxides (iridates) introduce strong spin-orbit coupling directly, such that the Mott physics has a strong orbital character.In the layered honeycomb iridates this is thought to generate highly spin-anisotropic magnetic interactions, coupling the spin orientation to a given spatial direction of exchange and leading to strongly frustrated magnetism. Here we report a new iridate structure that has the same local connectivity as the layered honeycomb and exhibits striking evidence for highly spin-anisotropic exchange. The basic structural units of this material suggest that a new family of three-dimensional structures could exist, the 'harmonic honeycomb' iridates, of which the present compound is the first example.

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...

The recently-synthesized iridate β-Li2IrO3 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 "hyperhoneycomb" 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" γ-Li2IrO3, 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 β-and γ-Li2IrO3 are strong candidates to realize dominant Kitaev interactions in a solid state material.

The layered honeycomb magnet α-Li 2 IrO 3 has been theoretically proposed as a candidate to display unconventional magnetic behaviour associated with Kitaev interactions between spin-orbit entangled j eff = 1/2 magnetic moments on a honeycomb lattice. Here we report single crystal magnetic resonant x-ray diffraction combined with powder magnetic neutron diffraction to reveal an incommensurate magnetic order in the honeycomb layers with Ir magnetic moments counterrotating on nearest-neighbor sites. This unexpected type of magnetic structure for a honeycomb magnet cannot be explained by a spin Hamiltonian with dominant isotropic (Heisenberg) couplings. The magnetic structure shares many key features with the magnetic order in the structural polytypes β-and γ -Li 2 IrO 3 , understood theoretically to be stabilized by dominant Kitaev interactions between Ir moments located on the vertices of three-dimensional hyperhoneycomb and stripyhoneycomb lattices, respectively. Based on this analogy and a theoretical soft-spin analysis of magnetic ground states for candidate spin Hamiltonians, we propose that Kitaev interactions also dominate in α-Li 2 IrO 3 , indicative of universal Kitaev physics across all three members of the harmonic honeycomb family of Li 2 IrO 3 polytypes.