In this work, we investigate the microscopic nature of the magnetism in honeycomb iridium-based systems by performing a systematic study of how the effective magnetic interactions in these compounds depend on various electronic microscopic parameters. We show that the minimal model describing the magnetism in A2IrO3 includes both isotropic and anisotropic Kitaev-type spin-exchange interactions between nearest and next-nearest neighbor Ir ions, and that the magnitude of the Kitaev interaction between next-nearest neighbor Ir magnetic moments is comparable with nearest neighbor interactions. We also find that, while the Heisenberg and the Kitaev interactions between nearest neighbors are correspondingly antiferro-and ferromagnetic, they both change sign for the next-nearest neighbors. Using classical Monte Carlo simulations we examine the magnetic phase diagram of the derived super-exchange model. Zigzag-type antiferromagnetic order is found to occupy a large part of the phase diagram of the model and, for ferromagnetic next-nearest neighbor Heisenberg interaction relevant for Na2IrO3, it can be stabilized even in the absence of third nearest neighbor coupling. Our results suggest that a natural physical origin of the zigzag phase experimentally observed in Na2IrO3 is due to the interplay of the Kitaev anisotropic interactions between nearest and next-nearest neighbors.

Between May 2009 and May 2010, the IceCube neutrino detector at the South Pole recorded 32 billion muons generated in air showers produced by cosmic rays with a median energy of 20 TeV. With a data set of this size, it is possible to probe the southern sky for per-mille anisotropy on all angular scales in the arrival direction distribution of cosmic rays. Applying a power spectrum analysis to the relative intensity map of the cosmic ray flux in the southern hemisphere, we show that the arrival direction distribution is not isotropic, but shows significant structure on several angular scales. In addition to previously reported large-scale structure in the form of a strong dipole and quadrupole, the data show small-scale structure on scales between 15 • and 30 •. The skymap exhibits several localized regions of significant excess and deficit in cosmic ray intensity. The relative intensity of the smaller-scale structures is about a factor of 5 weaker than that of the dipole and quadrupole structure. The most significant structure, an excess localized at (right ascension α = 122.4 • and declination δ = −47.4 •), extends over at least 20 • in right ascension and has a post-trials significance of 5.3σ. The origin of this anisotropy is still unknown.

In this paper we report the first observation in the Southern hemisphere of an energy dependence in the Galactic cosmic-ray anisotropy up to a few hundred TeV. This measurement was performed using cosmic-ray-induced muons recorded by the partially deployed IceCube observatory between 2009 May and 2010 May. The data include a total of 33 × 10 9 muon events with a median angular resolution of ∼3 •. A sky map of the relative intensity in arrival direction over the Southern celestial sky is presented for cosmic-ray median energies of 20 and 400 TeV. The same large-scale anisotropy observed at median energies around 20 TeV is not present at 400 TeV. Instead, the high-energy sky map shows a different anisotropy structure including a deficit with a post-trial significance of −6.3σ. This anisotropy reveals a new feature of the Galactic cosmic-ray distribution, which must be incorporated into theories of the origin and propagation of cosmic rays.

We study the critical properties of the Kitaev-Heisenberg (KH) model on the honeycomb lattice at finite temperatures that might describe the physics of the quasi two-dimensional (2D) compounds, Na2IrO3 and Li2IrO3. The model undergoes two phase transitions as a function of temperature. At low temperature, thermal fluctuations induce magnetic long-range order by the order-by-disorder mechanism. This magnetically ordered state with a spontaneously broken Z6 symmetry persists up to a certain critical temperature. We find that there is an intermediate phase between the low-temperature, ordered phase and the high-temperature, disordered phase. Finite-sized scaling analysis suggests that the intermediate phase is a critical Kosterlitz-Thouless (KT) phase with continuously variable exponents. We argue that the intermediate phase has been observed above the low-temperature, magnetically ordered phase in Na2IrO3, and also likely exists in Li2IrO3.Introduction. The Ir-based transition metal oxides, in which the orbital degeneracy is accompanied by a strong relativistic spin-orbit coupling (SOC), have recently attracted a lot of theoretical and experimental attention [1][2][3][4][5][6][7][8]. This is because the strong SOC creates a different, and frequently novel, set of magnetic and orbital states due to the unusual anisotropic exchange interactions between localized moments which are in turn determined by the combination of spin and lattice symmetries. The spin-orbital models that describe the low-energy physics of iridium systems often include anisotropic terms that do not reduce to the conventional easy-plane and easy-axis anisotropies because they involve the products of different components of multiple spin operators. These terms are responsible for exotic Mott-insulating states [3], topological insulators [10,11], spin-orbital liquid states [1, 2], and non-trivial long-range magnetic orders [3,4,6].A prominent example of such an anisotropic spinorbital model is the KH model on the honeycomb lattice [12,13] which likely describes the low-energy physics of the quasi 2D compounds, Na 2 IrO 3 and Li 2 IrO 3 . In these compounds, Ir 4+ ions are in a low spin 5d 5 configuration and form weakly coupled hexagonal layers [4,6,8]. Due to strong SOC, the atomic ground state is a doublet where the spin and orbital angular momenta of Ir 4+ ions are coupled into J eff = 1/2. It was suggested [12,13] that the interactions between these effective moments can be described by a spin Hamiltonian containing two competing nearest neighbor (NN) interactions: an isotropic antiferromagnetic (AF) Heisenberg exchange interaction and a highly anisotropic ferromagnetic (FM) Kitaev exchange interaction [14]. This competition can be described with the parameter, 0 ≤ α ≤ 1, which sets the relative strength of these two interactions. At α = 0, the coupling corresponds to the AF Heisenberg interaction, and at α = 1, it corresponds to the Kitaev interaction.This model immediately attracted a lot of attention; several theoretical studies were publis...

We investigate the finite-temperature phase diagram of the classical Kitaev-Heisenberg model on the hexagonal lattice. Due to the anisotropy introduced by the Kitaev interaction, the model is magnetically ordered at low temperatures. The ordered phase is stabilized entropically by an order by disorder mechanism where thermal fluctuations of classical spins select collinear magnetic states in which magnetic moments point along one of the cubic directions. We find that there is an intermediate phase between the low-temperature ordered phase and the high-temperature disordered phase. We show that the intermediate phase is a critical Kosterlitz-Thouless phase exhibiting correlations of the order parameter that decay algebraically in space. Using finite size scaling analysis, we determine the boundaries of the critical phase with reasonable accuracy. We show that the Kitaev interaction plays a crucial role in understanding the finite temperature properties of A2IrO3 systems.