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Register a new userThe ground state in a proximity to a possible Kitaev spin liquid: An undistorted honeycomb iridate NaxIrO3 (0.60 < x < 0.80)
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We report results of our study of a newly synthesized honeycomb iridate NaxIrO3 (0.60 < x < 0.80). Single-crystal NaxIrO3 adopts a honeycomb lattice noticeably without distortions and stacking disorder inherently existent in its sister compound Na2IrO3. The oxidation state of the Ir ion is a mixed valence state resulting from a majority Ir5+(5d4) ion and a minority Ir6+(5d3) ion. NaxIrO3 is a Mott insulator likely with a predominant pseudospin = 1 state. It exhibits an effective moment of 1.1 Bohr Magneton/Ir and a Curie-Weiss temperature of -19 K but with no discernable long-range order above 1 K. The physical behavior below 1 K features two prominent anomalies at Th = 0.9 K and Tl = 0.12 K in both the heat capacity and AC magnetic susceptibility. Intermediate between Th and Tl lies a pronounced temperature linearity of the heat capacity with a large slope of 77 mJ/mole K2, a feature expected for highly correlated metals but not at all for insulators. These results along with comparison drawn with the honeycomb lattices Na2IrO3 and (Na0.2Li0.8)2IrO3 point to an exotic ground state in a proximity to a possible Kitaev spin liquid.
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The electronic ground state in many iridate materials is described by a complex wave-function in which spin and orbital angular momenta are entangled due to relativistic spin-orbit coupling (SOC). Such a localized electronic state carries an effective total angular momentum of $J_{eff}=1/2$. In materials with an edge-sharing octahedral crystal structure, such as the honeycomb iridates Li2IrO3 and Na2IrO3, these $J_{eff}=1/2$ moments are expected to be coupled through a special bond-dependent magnetic interaction, which is a necessary condition for the realization of a Kitaev quantum spin liquid. However, this relativistic electron picture is challenged by an alternate description, in which itinerant electrons are confined to a benzene-like hexagon, keeping the system insulating despite the delocalized nature of the electrons. In this quasi-molecular orbital (QMO) picture, the honeycomb iridates are an unlikely choice for a Kitaev spin liquid. Here we show that the honeycomb iridate Li2IrO3 is best described by a $J_{eff}=1/2$ state at ambient pressure, but crosses over into a QMO state under the application of small (~ 0.1 GPa) hydrostatic pressure. This result illustrates that the physics of iridates is extremely rich due to a delicate balance between electronic bandwidth, spin-orbit coupling, crystal field, and electron correlation.
We propose a theoretical model for a gapless spin liquid phase that may have been observed in a recent experiment on $mathrm{H_3Li Ir_2 O_6}$. Despite the insulating and non-magnetic nature of the material, the specific heat coefficient $C/T sim 1/sqrt{T}$ in zero magnetic field and $C/T sim T/ B^{3/2}$ with finite magnetic field $B$ have been observed. In addition, the NMR relaxation rate shows $1/(T_1T) sim (C/T)^2$. Motivated by the fact that the interlayer/in-plane lattice parameters are reduced/elongated by the hydrogen-intercalation of the parent compound $mathrm{Li_2 Ir O_3}$, we consider four layers of the Kitaev honeycomb lattice model with additional interlayer exchange interactions. It is shown that the resulting spin liquid excitations reside mostly in the top and bottom layers of such a layered structure and possess a quartic dispersion. In an applied magnetic field, each quartic mode is split into four Majorana cones with the velocity $v sim B^{3/4}$. We suggest that the spin liquid phase in these defect layers, placed between different stacking patterns of the honeycomb layers, can explain the major phenomenology of the experiment, which can be taken as evidence that the Kitaev interaction plays the primary role in the formation of a quantum spin liquid in this material.
Motivated by the recent experimental observation of a Mott insulating state for the layered Iridate Na2IrO3, we discuss possible ordering states of the effective Iridium moments in the presence of strong spin-orbit coupling and a magnetic field. For a field pointing in the [111] direction - perpendicular to the hexagonal lattice formed by the Iridium moments - we find that a combination of Heisenberg and Kitaev exchange interactions gives rise to a rich phase diagram with both symmetry breaking magnetically ordered phases as well as a topologically ordered phase that is stable over a small range of coupling parameters. Our numerical simulations further indicate two exotic multicritical points at the boundaries between these ordered phases.
The realization of Kitaev spin liquid, where spins on a honeycomb lattice are coupled ferromagnetically by bond-dependent anisotropic interactions, has been a sought-after dream. 5d iridium oxides $alpha$-Li2IrO3 and $alpha$-Na2IrO3 with a honeycomb lattice of Jeff = 1/2 moments recently emerged as a possible materialization. Strong signature of Kitaev physics, however, was not captured. Here we report the discovery of a complex iridium oxide $beta$-Li2IrO3 with Jeff = 1/2 moments on hyper-honeycomb lattice, a three-dimensional analogue of honeycomb lattice. A positive Curie-Weiss temperature $theta_{CW}$ ~ 40 K indicated dominant ferromagnetic interactions among Jeff = 1/2 moments in $beta$-Li2IrO3. A magnetic ordering with a small entropy change was observed at Tc = 38 K, which, with the application of magnetic field of only 3 T, changed to a fully polarized state of Jeff = 1/2 moments. Those results imply that hyper-honeycomb beta-Li2IrO3 is located in the vicinity to a Kitaev spin liquid.
We present an exact solution of an experimentally realizable and strongly interacting one-dimensional spin system which is a limiting case of a quantum Ising model with long range interaction in a transverse and longitudinal field. Pronounced quantum fluctuations lead to a strongly correlated liquid ground state. For open boundary conditions the ground state manifold consists of four degenerate sectors whose quantum numbers are determined by the orientation of the edge spins. Explicit expressions for the entanglement properties, the excitation gap as well as the exact wave functions for a couple of excited states are analytically derived and discussed.
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