Eric Kin-Ho Lee

Generic spin model for the honeycomb iridates beyond the Kitaev limit.

Recently, realizations of Kitaev physics have been sought in the A2IrO3 family of honeycomb iridates, originating from oxygen-mediated exchange through edge-shared octahedra. However, for the jeff=1/2 Mott insulator in these materials, exchange from direct d-orbital overlap is relevant, and it was proposed that a Heisenberg term should be added to the Kitaev model. Here, we provide the generic nearest-neighbor spin Hamiltonian when both oxygen-mediated and direct overlap are present, containing a bond-dependent off-diagonal exchange in addition to Heisenberg and Kitaev terms. We analyze this complete model using a combination of classical techniques and exact diagonalization. Near the Kitaev limit, we find new magnetic phases, 120° and incommensurate spiral order, as well as extended regions of zigzag and stripy order. Possible applications to Na2IrO3 and Li2IrO3 are discussed.

Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials

Recently, the effects of spin-orbit coupling (SOC) in correlated materials have become one of the most actively studied subjects in condensed matter physics, as correlations and SOC together can lead to the discovery of new phases. Examples include unconventional magnetism, spin liquids, and strongly correlated topological phases such as topological superconductivity. Among candidate materials, iridium oxides (iridates) have been an excellent playground to uncover such novel phenomena. In this review, we discuss recent progress in iridates and related materials, focusing on the basic concepts, relevant microscopic Hamiltonians, and unusual properties of iridates in perovskite- and honeycomb-based structures. Perspectives on SOC and correlation physics beyond iridates are also discussed.

Theory of Magnetic Phases in Hyperhoneycomb and Harmonic-honeycomb Iridates

Motivated by recent experiments, we consider a generic spin model in the

Recent progress on correlated electron systems with strong spin-orbit coupling

j_{\text{eff}}=1/2

Topological Spinon Semimetals and Gapless Boundary States in Three Dimensions

basis for the hyperhoneycomb and harmonic-honeycomb iridates. Based on microscopic considerations, the effect of an additional bond-dependent anisotropic spin exchange interaction (

Two iridates, two models, and two approaches: A comparative study on magnetism in three-dimensional honeycomb materials

\Gamma

Predominance of the Kitaev interaction in a three-dimensional honeycomb iridate: From ab initio to spin model

) beyond the Heisenberg-Kitaev model is investigated. We obtain the magnetic phase diagrams of the hyperhoneycomb and harmonic-honeycomb (

Magnetic excitation spectra in pyrochlore iridates

\mathcal{H}\text{--}1

Order-by-disorder and magnetic field response in the Heisenberg-Kitaev model on a hyperhoneycomb lattice

) lattices via a combination of the Luttinger-Tisza approximation, single-

Generic model for the hyperkagome iridate Na 4 Ir 3 O 8 in the local-moment regime

\mathbf{Q}