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Register a new userKitaev-Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices
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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 four-group =Z2xZ2 structure is associated with this mapping (hence Klein duality). A finite lattice admits the duality if a simple geometrical condition is met. This duality predicts fluctuation free ordered states on these different 2D and 3D lattices, which are analogs of the honeycomb lattice KH stripy order. This result is used in conjunction with a semiclassical Luttinger-Tisza approximation to obtain phase diagrams for KH models on the different lattices. We also discuss a Majorana fermion based mean field theory at the Kitaev point, which is exact on the honeycomb lattice, for the KH models on the different lattices. We attribute the rich behavior of these models to the interplay of geometric frustration and frustration induced by spin-orbit coupling.
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A Kitaev-Heisenberg-J2-J3 model is proposed to describe the Mott-insulating layered iridates A2IrO3 (A=Na,Li). The model is a combination of the Kitaev honeycomb model and the Heisenberg model with all three nearest neighbor couplings J1, J2 and J3. A rich phase diagram is obtained at the classical level, including the experimentally suggested zigzag ordered phase; as well as the stripy phase, which extends from the Kitaev-Heisenberg limit to the J1-J2-J3 one. Combining the experimentally observed spin order with the optimal fitting to the uniform magnetic susceptibility data gives an estimate of possible parameter values, which in turn reaffirms the necessity of including both the Kitaev and farther neighbor couplings.
Motivated by various spin-1/2 compounds like Cs$_2$CuCl$_4$ or $kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$, we derive a Raman-scattering operator {it `a la} Shastry and Shraiman for various geometries. For T=0, the exact spectra is computed by Lanczos algorithm for finite-size clusters. We perform a systematic investigation as a function of $J_2/J_1$, the exchange constant ratio: ranging from $J_2=0$, the well known square-lattice case, to $J_2/J_1=1$ the isotropic triangular lattice. We discuss the polarization dependence of the spectra and show how it can be used to detect precursors of the instabilities of the ground state against quantum fluctuations.
Fully relativistic first-principles electronic structure calculations based on a noncollinear local spin density approximation (LSDA) are performed for pyrochlore iridates Y$_2$Ir$_2$O$_7$ and Pr$_2$Ir$_2$O$_7$. The all-in, all-out antiferromagnetic (AF) order is stablized by the on-site Coulomb repulsion $U>U_c$ in the LSDA+$U$ scheme, with $U_csim1.1$~eV and 1.3~eV for Y$_2$Ir$_2$O$_7$ and Pr$_2$Ir$_2$O$_7$, respectively. AF semimetals with and without Weyl points and then a topologically trivial AF insulator successively appear with further increasing $U$. For $U=1.3$~eV, Y$_2$Ir$_2$O$_7$ is a topologically trivial narrow-gap AF insulator having an ordered local magnetic moment $sim0.5mu_B$/Ir, while Pr$_2$Ir$_2$O$_7$ is barely a paramagnetic semimetal with electron and hole concentrations of $0.016$/Ir, in overall agreements with experiments. With decreasing oxygen position parameter $x$ describing the trigonal compression of IrO$_6$ octahedra, Pr$_2$Ir$_2$O$_7$ is driven through a non-Fermi-liquid semimetal having only an isolated Fermi point of $Gamma_8^+$, showing a quadratic band touching, to a $Z_2$ topological insulator.
On Archimedean lattices, the Ising model exhibits spontaneous ordering. Three examples of these lattices of the majority-vote model with noise are considered and studied through extensive Monte Carlo simulations. The order/disorder phase transition is observed in this system. The calculated values of the critical noise parameter are q_c=0.089(5), q_c=0.078(3), and q_c=0.114(2) for honeycomb, Kagome and triangular lattices, respectively. The critical exponents beta/nu, gamma/nu and 1/nu for this model are 0.15(5), 1.64(5), and 0.87(5); 0.14(3), 1.64(3), and 0.86(6); 0.12(4), 1.59(5), and 1.08(6) for honeycomb, Kagome and triangular lattices, respectively. These results differs from the usual Ising model results and the majority-vote model on so-far studied regular lattices or complex networks. The effective dimensionalities of the system D_{eff}= 1.96(5) (honeycomb), D_{eff} =1.92(4) (Kagome), and D_{eff}= 1.83(5) (triangular) for these networks are just compatible to the embedding dimension two.
We show that the mesoscopic incommensurate $mathbb{Z}_2$ vortex crystals proposed for layered triangular anisotropic magnets can be most saliently identified by two distinctive signatures in dynamical spin response experiments: The presence of pseudo-Goldstone `phonon modes at low frequencies $omega$, associated with the collective vibrations of the vortex cores, and a characteristic multi-scattered intensity profile at higher $omega$, arising from a large number of Bragg reflections and magnon bandgaps. These are direct fingerprints of the large vortex sizes and magnetic unit cells and the solitonic spin profile around the vortex cores.
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