George Jackeli

Kitaev-Heisenberg model on a honeycomb lattice: possible exotic phases in iridium oxides A2IrO3.

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.

Zigzag magnetic order in the iridium oxide Na2IrO3.

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.

Magnetically hidden order of Kramers doublets in d;{1} systems: Sr2VO4.

We formulate and study an effective Hamiltonian for low-energy Kramers doublets of d;{1} ions on a square lattice. We find that the system exhibits a magnetically hidden order in which the expectation values of the local spin and orbital moments both vanish. The order parameter responsible for a time-reversal symmetry breaking has a composite nature and is a spin-orbital analog of a magnetic octupole. We argue that such a hidden order is realized in the layered perovskite Sr_{2}VO_{4}.

Valence-bond crystal in a pyrochlore antiferromagnet with orbital degeneracy.

We discuss the ground state of a pyrochlore lattice of threefold orbitally degenerate S=1/2 magnetic ions. We derive an effective spin-orbital Hamiltonian and show that the orbital degrees of freedom can modulate the spin exchange, removing the infinite spin-degeneracy characteristic of pyrochlore structures. The resulting state is a collection of spin-singlet dimers, with a residual degeneracy due to their relative orientation. This latter is lifted by a magnetoelastic interaction, induced in the spin-singlet phase space, that forces a tetragonal distortion. Such a theory provides an explanation for the helical spin-singlet pattern observed in the B spinel MgTi2O4.

Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects

We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from analytic approaches: the linear spin-wave and second-order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model either one of four phases with magnetic long range order: Neel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phase, or one of two distinct spin-liquid phases. Out of these latter disordered phases, the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and phases with long range magnetic order.

Spin, Orbital, and Charge Order at the Interface between Correlated Oxides

The collective behavior of correlated electrons in the VO2 interface layer of the LaVO(3)/SrTiO(3) heterostructure is studied within a quarter-filled t(2g)-orbital Hubbard model on a square lattice. We argue that the ground state is ferromagnetic, driven by the double-exchange mechanism, and is orbitally and charge ordered due to a confined geometry and electron correlations. The orbital and charge density waves open gaps on the entire Fermi surfaces of all orbitals. The theory explains the observed insulating behavior of the p-type interface between LaVO3 and SrTiO3.

Spin-Orbit Dimers and Noncollinear Phases in d 1 Cubic Double Perovskites

We formulate and study a spin-orbital model for a family of cubic double perovskites with d^{1} ions occupying a frustrated fcc sublattice. A variational approach and a complementary analytical analysis reveal a rich variety of phases emerging from the interplay of Hunds rule and spin-orbit coupling. The phase digram includes noncollinear ordered states, with or without a net moment, and, remarkably, a large window of a nonmagnetic disordered spin-orbit dimer phase. The present theory uncovers the physical origin of the unusual amorphous valence bond state experimentally suggested for Ba_{2}BMoO_{6} (B=Y, Lu) and predicts possible ordered patterns in Ba_{2}BOsO_{6} (B=Na, Li) compounds.

Quantum order by disorder in the Kitaev model on a triangular lattice

We identify and discuss the ground state of a quantum magnet on a triangular lattice with bond-dependent Ising-type spin couplings, that is, a triangular analog of the Kitaev honeycomb model. The classical ground-state manifold of the model is spanned by decoupled Ising-type chains, and its accidental degeneracy is due to the frustrated nature of the anisotropic spin couplings. We show how this subextensive degeneracy is lifted by a quantum order-by-disorder mechanism and study the quantum selection of the ground state by treating short-wavelength fluctuations within the linked cluster expansion and by using the complementary spin-wave theory. We find that quantum fluctuations couple next-nearest-neighbor chains through an emergent four-spin interaction, while nearest-neighbor chains remain decoupled. The remaining discrete degeneracy of the ground state is shown to be protected by a hidden symmetry of the model.

Effective spin-orbital Hamiltonian for the double perovskite Sr2FeWO6: Derivation of the phase diagram

We formulate a superexchange theory of insulating double-perovskite compounds such as Sr 2 FeWO 6 . An effective spin-orbital Hamiltonian is derived in the strong-coupling limit of Hubbard model for d electrons on Fe and W ions. The relevant degrees of freedom are the spins S=2 and the threefold orbital degeneracy of Fe 2 + ions. W sites are integrated out by means of a fourth-order perturbative expansion. The magnetically and orbitally ordered ground states of the effective Hamiltonian are discussed as a function of the model parameters. We show that for realistic values of such parameters the ground state is antiferromagnetic, as experimentally observed. The order found is of type II, consisting of {111} ferromagnetic planes stacked antiferro-magnetically. The orbital order energy scale found is one order of magnitude less than the spin one.

Model analysis of magnetic susceptibility of Sr2IrO4 : A two-dimensional Jeff=12 Heisenberg system with competing interlayer couplings

We report the analysis of magnetic susceptibility