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).

The electronic structure of Sr3CuIrO6, a model system for the 5d Ir ion in an octahedral environment, is studied through a combination of resonant inelastic x-ray scattering (RIXS) and theoretical calculations. RIXS spectra at the Ir L3-edge reveal an Ir t2g manifold that is split into three levels, in contrast to the expectations of the strong spin-orbit-coupling limit. Effective Hamiltonian and ab inito quantum chemistry calculations find a strikingly large non-cubic crystal field splitting comparable to the spin-orbit coupling, which results in a strong mixing of the j eff = 1 2 and j eff = 3 2 states and modifies the isotropic wavefunctions on which many theoretical models are based.

Iridium oxides with a honeycomb lattice have been identified as platforms for the much anticipated Kitaev topological spin liquid: the spin-orbit entangled states of Ir4+ in principle generate precisely the required type of anisotropic exchange. However, other magnetic couplings can drive the system away from the spin-liquid phase. With this in mind, here we disentangle the different magnetic interactions in Li2IrO3, a honeycomb iridate with two crystallographically inequivalent sets of adjacent Ir sites. Our ab initio many-body calculations show that, while both Heisenberg and Kitaev nearest-neighbour couplings are present, on one set of Ir–Ir bonds the former dominates, resulting in the formation of spin-triplet dimers. The triplet dimers frame a strongly frustrated triangular lattice and by exact cluster diagonalization we show that they remain protected in a wide region of the phase diagram.