We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between Ir4+ ions in a family of layered iridates A2IrO3 (A=Li,Na). Depending on the microscopic parameters, the Hamiltonian interpolates between the Heisenberg and exactly solvable Kitaev models. Exact diagonalization and a complementary spin-wave analysis reveal the presence of an extended spin-liquid phase near the Kitaev limit and a conventional Néel state close to the Heisenberg limit. The two phases are separated by an unusual stripy antiferromagnetic state, which is the exact ground state of the model at the midpoint between two limits.

We explore the phase diagram of spin-orbit Mott insulators on a honeycomb lattice, within the Kitaev-Heisenberg model extended to its full parameter space. Zigzag-type magnetic order is found to occupy a large part of the phase diagram of the model, and its physical origin is explained as due to interorbital t2g − eg hopping. Magnetic susceptibility and spin wave spectra are calculated and compared to the experimental data, obtaining thereby the spin coupling constants in Na2IrO3 and Li2IrO3.

Intense paramagnon excitations in a large family of high-temperature superconductor

Condensed-matter analogues of the Higgs boson in particle physics allow insights into its behaviour in di erent symmetries and dimensionalities 1 . Evidence for the Higgs mode has been reported in a number of di erent settings, including ultracold atomic gases 2 , disordered superconductors 3 , and dimerized quantum magnets 4 . However, decay processes of the Higgs mode (which are eminently important in particle physics)have not yet been studied in condensed matter due to the lack of a suitable material system coupled to a direct experimental probe. A quantitative understanding of these processes is particularly important for low-dimensional systems, where the Higgs mode decays rapidly and has remained elusive to most experimental probes. Here, we discover and study the Higgs mode in a two-dimensional antiferromagnet using spin-polarized inelastic neutron scattering. Our spin-wave spectra of Ca 2 RuO 4 directly reveal a well-defined, dispersive Higgs mode, which quickly decays into transverse Goldstone modes at the antiferromagnetic ordering wavevector. Through a complete mapping of the transverse modes in the reciprocal space, we uniquely specify the minimal model Hamiltonian and describe the decay process. We thus establish a novel condensed-matter platform for research on the dynamics of the Higgs mode.For a system of interacting spins, amplitude fluctuations of the local magnetization-the Higgs mode-can exist as well-defined collective excitations near a quantum critical point (QCP). We consider here a magnetic instability driven by the intra-ionic spinorbit coupling, which tends towards a non-magnetic state through complete cancellation of orbital (L) and spin (S) moments when they are antiparallel and of equal magnitude 5,6 . This mechanism should be broadly relevant for d 4 compounds of such ions as Ir(V), Ru(IV), Os(IV) and Re(III) with sizable spin-orbit coupling but remains little explored. We investigate the magnetic insulator Ca 2 RuO 4 , a quasi-two-dimensional antiferromagnet 7 with nominally L = 1 and S = 1 (Fig. 1). Because the local symmetry around the Ru(IV) ion is very low 8,9 (having only inversion symmetry), it is widely believed that the orbital moment is completely quenched by the crystalline electric field 10-13 , which is dominated by the compressive distortion of the RuO 6 octahedra along the c-axis (Fig. 1). In the absence of an orbital moment, the nearest-neighbour magnetic exchange interaction is necessarily isotropic. Deviations from this behaviour are a sensitive indicator of an unquenched orbital moment. If this moment is sufficiently strong, it can drive Ca 2 RuO 4 close to a QCP with novel Higgs physics.Our comprehensive set of time-of-flight (TOF) inelastic neutron scattering (INS) data over the full Brillouin zone (Fig. 2a) indeed reveal qualitative deviations of the transverse spin-wave dispersion from those of a Heisenberg antiferromagnet. In particular, the global maximum of the dispersion is found at q = (0,0), in sharp contrast to a Heisenberg antiferromagnet, which has a...

We have explored the hidden symmetries of a generic four-parameter nearest-neighbor spin model, allowed in honeycomb lattice compounds under trigonal compression. Our method utilizes a systematic algorithm to identify all dual transformations of the model that map the Hamiltonian on itself, changing the parameters and providing exact links between different points in its parameter space. We have found the complete set of points of hidden SU (2) symmetry at which seemingly highly anisotropic model can be mapped back on the Heisenberg model and inherits therefore its properties such as the presence of gapless Goldstone modes. The procedure used to search for the hidden symmetries is quite general and may be extended to other bond-anisotropic spin models and other lattices, such as the triangular, kagome, hyper-honeycomb, or harmonic-honeycomb lattices. We apply our findings to the honeycomb lattice iridates Na2IrO3 and Li2IrO3, and illustrate how they help to identify plausible values of the model parameters that are compatible with the available experimental data.

Heisenberg interactions are ubiquitous in magnetic materials and have been prevailing in modeling and designing quantum magnets. Bonddirectional interactions 1-3 offer a novel alternative to Heisenberg exchange and provide the building blocks of the Kitaev model 4 , which has a quantum spin liquid (QSL) as its exact ground state. Honeycomb iridates, A 2 IrO 3 (A=Na,Li), offer potential realizations of the Kitaev model, and their reported magnetic behaviors may be interpreted within the Kitaev framework. However, the extent of their relevance to the Kitaev model remains unclear, as evidence for bonddirectional interactions remains indirect or conjectural. Here, we present direct evidence for dominant bond-directional interactions in antiferromagnetic Na 2 IrO 3 and show that they lead to strong magnetic frustration. Diffuse magnetic xray scattering reveals broken spin-rotational symmetry even above T N , with the three spin components exhibiting nano-scale correlations along distinct crystallographic directions. This spinspace and real-space entanglement directly manifests the bond-directional interactions, provides the missing link to Kitaev physics in honeycomb iridates, and establishes a new design strategy toward frustrated magnetism.Iridium (IV) ions with pseudospin-1/2 moments form in Na 2 IrO 3 a quasi-two-dimensional (2D) honeycomb network, which is sandwiched between two layers of oxygen ions that frame edge-shared octahedra around the magnetic ions and mediate superexchange interactions between neighboring pseudospins (Fig. 1a). Owing to the particular spin-orbital structure of the pseudospin 5,6 , the isotropic part of the magnetic interaction is strongly suppressed in the 90• bonding geometry of the edgeshared octahedra 2,3 , thereby allowing otherwise subdominant bond-dependent anisotropic interactions to play the main role and manifest themselves at the forefront of magnetism. This bonding geometry, common to many transition-metal oxides, in combination with the pseudospin that arises from strong spin-orbit coupling gives rise to an entirely new class of magnetism beyond the traditional paradigm of Heisenberg magnets. On a honeycomb lattice, for instance, the leading anisotropic interactions take the form of the Kitaev model 3 , which is a rare example of exactly solvable models with nontrivial properties such as Majorana fermions and non-abelian statistics, and with potential links to quantum computing 4 . Realization of the Kitaev model is now being intensively sought out in a growing number of materials 7-13 , including 3D extensions of the honeycomb Li 2 IrO 3 , dubbed "hyper-honeycomb" 7 and "harmonichoneycomb" 8 , and 4d transition-metal analogs such as RuCl 3 12 and Li 2 RhO 3 13 . Although most of these are known to magnetically order at low temperature, they exhibit a rich array of magnetic structures including zigzag 14-16 , spiral 17 , and other more complex non-coplanar structures 18,19 that are predicted to occur in the vicinity of the Kitaev QSL phase [20][21][22][23] , which hosts man...

We study the ordered moment direction in the extended Kitaev-Heisenberg model relevant to honeycomb lattice magnets with strong spin-orbit coupling. We utilize numerical diagonalization and analyze the exact cluster groundstates using a particular set of spin coherent states, obtaining thereby quantum corrections to the magnetic anisotropy beyond conventional perturbative methods. It is found that the quantum fluctuations strongly modify the moment direction obtained at a classical level, and are thus crucial for a precise quantification of the interactions. The results show that the moment direction is a sensitive probe of the model parameters in real materials. Focusing on the experimentally relevant zigzag phases of the model, we analyze the currently available neutron and resonant x-ray diffraction data on Na2IrO3 and RuCl3, and discuss the parameter regimes plausible in these Kitaev-Heisenberg model systems.

We study the exchange interactions and resulting magnetic phases in the honeycomb cobaltates. For a broad range of trigonal crystal fields acting on Co 2þ ions, the low-energy pseudospin-1=2 Hamiltonian is dominated by bond-dependent Ising couplings that constitute the Kitaev model. The non-Kitaev terms nearly vanish at small values of trigonal field Δ, resulting in spin liquid ground state. Considering Na 3 Co 2 SbO 6 as an example, we find that this compound is proximate to a Kitaev spin liquid phase, and can be driven into it by slightly reducing Δ by ∼20 meV, e.g., via strain or pressure control. We argue that, due to the more localized nature of the magnetic electrons in 3d compounds, cobaltates offer the most promising search area for Kitaev model physics.