We report discovery of a new iridate family K$_x$Ir$_y$O$_2$ with depleted triangular lattice planes made up of edge sharing IrO$_6$ octahedra separated by K planes. Such a material interpolates between the triangular and honeycomb lattices and is a new playground for Kitaev physics. The materials are Mott insulators with $y = 1 - x/4$. Physical property measurements for the $x \approx 0.85$ material are reported. Using magnetic susceptibility $χ$ versus temperature $T$ measurements we find $S_{eff} = 1/2$ moments interacting strongly with a Weiss temperature $θ\approx - 180$~K and no magnetic order or spin freezing down to $T = 1.8$~K\@. Heat capacity shows a broad maximum around $30$~K which is insensitive to magnetic fields and a $T$-linear low temperature behaviour with $γ\sim 10$~mJ/mol~K$^2$. These results are consistent with a gapless QSL state in K$_{0.85}$Ir$_{0.79}$O$_2$.
Iridates are characterized by a fascinating interplay of spin-orbit and electron-electron interactions. The honeycomb-lattice materials A2IrO3 (A=Na,Li) have been proposed to realize pseudospin-1/2 Mott insulating states with strongly anisotropic exchange interactions, described by the Heisenberg-Kitaev model, but other scenarios involving longer-range exchange interactions or more delocalized electrons have been put forward as well. Here we study the influence of non-magnetic doping, i.e., depleted moments, on the magnetic properties of experimentally relevant variants of the Heisenberg-Kitae…
The Kitaev-Heisenberg (KH) model has been proposed to capture magnetic interactions in iridate Mott insulators on the honeycomb lattice. We show that analogous interactions arise in many other geometries built from edge-sharing IrO_6 octahedra, including the pyrochlore and hyperkagome lattices relevant to Ir2O4 and Na4Ir3O8 respectively. The Kitaev spin liquid exact solution does not generalize to these lattices. However, a different exactly soluble point of the honeycomb lattice KH model, obtained by a four-sublattice transformation to a ferromagnet, generalizes to all these lattices. A Klein…
A linear spin-wave approach, a variational method and exact diagonlization are used to investigate the magnetic long-range order (LRO) of the spin-1/2 Heisenberg antiferromagnet on a two-dimensional 1/7-depleted triangular (maple leaf) lattice consisting of triangles and hexagons only. This lattice has z=5 nearest neighbors and its coordination number z is therefore between those of the triangular (z=6) and the kagome (z=4) lattices. Calculating spin-spin correlations, sublattice magnetization, spin stiffness, spin-wave velocity and spin gap we find that the classical 6-sublattice LRO is stron…
Using thermodynamic measurements, neutron diffraction, nuclear magnetic resonance, and muon spin relaxation, we establish putative quantum spin-liquid behavior in Ba$_3$InIr$_2$O$_9$, where unpaired electrons are localized on mixed-valence Ir$_2$O$_9$ dimers with Ir$^{4.5+}$ ions. Despite the antiferromagnetic Curie-Weiss temperature on the order of 10 K, neither long-range magnetic order nor spin freezing are observed down to at least 20 mK, such that spins are short-range correlated and dynamic over nearly three decades in temperature. Quadratic power-law behavior of both the spin-lattice re…
We study the magnetism of a quantum spin-1/2 antiferromagnet on a maple-leaf lattice which is obtained by regularly depleting 1/7 of the sites of a triangular lattice. Although the interactions are set to be spatially uniform, the ground state shows a stripe Neel order and the temperature dependence of magnetic susceptibility follows that of the one-dimensional XXZ model with a finite spin gap. We examine the nature of frustration by mapping the low energy degenerate manifold of states to the fully packed loop-string model on a dual cluster-depleted honeycomb lattice, finding that the order-by…
We propose an insulating 2D phase of IrO$_{2}$, predicted by $\textit{ab initio}$ evolutionary algorithms. The predicted phase is a van der Waals crystal, in which Ir forms a triangular lattice, and is energetically competitive with the metastable spinel phase, observed experimentally. Electronic structure calculations show that the magnetic properties of this phase are highly nontrivial, with an almost perfect degeneracy of 120$^{\circ}$ $\textit{Neel}$ and $Y$-stripe orders, and unusually soft magnetic moments. The resulting behavior, which we term $\textit{easy plane anisotropy}$, is entire…
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 presen…
We report the synthesis of single crystals of a novel layered iridate Ba$_{21}$Ir$_9$O$_{43}$, and present the crystallographic, transport and magnetic properties of this material. The compound has a hexagonal structure with two iridium oxide layers stacked along the $c$ direction. One layer consists of a triangular arrangement of Ir$_2$O$_9$ dimers while the other layer comprises two regular octahedra and one triangular pyramid, forming inter-penetrated triangular lattices. The resistivity as a function of temperature exhibits an insulating behavior, with a peculiar $T^{-3}$ behavior. Magneti…
The triangular-lattice Heisenberg antiferromagnet (HAF) is known to carry topological Z_2 vortex excitations which form a gas at finite temperatures. Here we show that the spin-orbit interaction, introduced via a Kitaev term in the exchange Hamiltonian, condenses these vortices into a triangular $Z_2$ vortex crystal at zero temperature. The cores of the Z_2 vortices show abrupt, soliton-like magnetization modulations and arise by a special intertwining of three honeycomb superstructures of ferromagnetic domains, one for each of the three sublattices of the 120-degree state of the pure HAF. Thi…
With large spin-orbit coupling, the $t_{2g}^5$ electron configuration in $d$-metal oxides is prone to highly anisotropic exchange interactions and exotic magnetic properties. In $5d^5$ iridates, given the existing variety of crystal structures, the magnetic anisotropy can be tuned from antisymmetric to symmetric Kitaev-type, with interaction strengths that outsize the isotropic terms. By many-body electronic-structure calculations we here address the nature of the magnetic exchange and the intriguing spin-glass behavior of Li$_2$RhO$_3$, a $4d^5$ honeycomb oxide. For pristine crystals without …
We study the antiferromagnetic classical Ising (AFI) model on the sorrel net, a 1/9th site depleted and 1/7th bond depleted triangular lattice. Our classical Monte Carlo simulations, verified by exact results for small system sizes, show that the AFI model on this corner-shared triangle net (with coupling constant $J_1$) is highly frustrated, with a residual entropy of $\frac{S}{N}$= 0.48185$\pm$0.00008. Anticipating that it may be difficult to achieve perfect bond depletion, we investigate the physics originating from turning back on the deleted bonds ($J_2$) to create a lattice of edge-shari…
We introduce the idea of emergent lattices, where a simple lattice decouples into two weakly-coupled lattices as a way to stabilize spin liquids. In LiZn2Mo3O8, the disappearance of 2/3rds of the spins at low temperatures suggests that its triangular lattice decouples into an emergent honeycomb lattice weakly coupled to the remaining spins, and we suggest several ways to test this proposal. We show that these orphan spins act to stabilize the spin-liquid in the $J_1-J_2$ honeycomb model and also discuss a possible 3D analogue, Ba2MoYO6 that may form a "depleted fcc lattice."
Spangolite, Cu6Al(SO4)(OH)12Cl.3H2O, is a hydrated layered copper sulphate mineral. The Cu2+ ions of each layer form a systematically depleted triangular lattice which approximates a maple leaf lattice. We present details of the crystal structure, which suggest that in spangolite this lattice actually comprises two species of edge linked trimers with different exchange parameters. However, magnetic susceptibility measurements show that despite the structural trimers, the magnetic properties are dominated by dimerization. The high temperature magnetic moment is strongly reduced below that expec…
We study the magnetization process in two-dimensional S=1/2 spin systems, to discuss the appearance of a plateau structure. The following three cases are considered: (1) the Heisenberg antiferromagnet and multiple-spin exchange model on the triangular lattice, (2) Shastry-Sutherland type lattice, [which is a possible model for SrCu2(BO3)2,] (3) 1/5-depleted lattice (for CaV4O9). We find in these systems that magnetization plateaus can appear owing to a transition from superfluid to a Mott insulator of magnetic excitations. The plateau states have CDW order of the excitations. The magnetization…
We have carried out detailed bulk and local probe studies on the hexagonal oxides Ba3MIr2O9 (M=Sc,Y) where Ir is expected to have a fractional oxidation state of +4.5. In the structure, Ir-Ir dimers are arranged in an edge shared triangular network parallel to the ab plane. Whereas only weak anomalies are evident in the susceptibility data, clearer anomalies are present in the heat capacity data. Our 45Sc nuclear magnetic resonance (NMR) lineshape (first order quadrupole split) is symmetric at room temperature but becomes progressively asymmetric with decreasing temperatures. This is suggestiv…
The antiferromagnetic Heisenberg model on the icosahedron, which consists of 20 edge-sharing triangles and belongs to the icosahedral $I_h$ symmetry group, presents unconventional properties at the classical and quantum level. These originate in the frustrated nature of the interactions between the spins. For classical spins the magnetization is discontinuous in a magnetic field. Here we examine the importance of the connectivity of the icosahedron for the appearance of the magnetization discontinuity, and also investigate the transition from the classical to the quantum limit. The influence o…
