Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates

Abstract

Motivated by recent experiments, we consider a generic spin model in the $j_{\text{eff}}=1/2$ basis for the hyperhoneycomb and harmonic-honeycomb iridates. Based on microscopic considerations, the effect of an additional bond-dependent anisotropic spin exchange interaction ($\Gamma$) beyond the Heisenberg-Kitaev model is investigated. We obtain the magnetic phase diagrams of the hyperhoneycomb and harmonic-honeycomb ($\mathcal{H}\text{–}1$) lattices via a combination of the Luttinger-Tisza approximation, single-$\mathbf{Q}$ variational ansatz, and classical Monte Carlo simulated annealing. The resulting phase diagrams on both systems show the existence of incommensurate, non-coplanar spiral magnetic orders as well as other commensurate magnetic orders. The spiral orders show counter-propagating spiral patterns, which may be favorably compared to recent experimental results on both iridates. The parameter regime of various magnetic orders and ordering wavevectors are quite similar in both systems. We discuss the implications of our work to recent experiments and also compare our results to those of the two dimensional honeycomb iridate systems.

arXiv comment15 pages, 12 figures; added various figures for Γ< 0 results, added section on comparison with experimental results, modified acknowledgements, added appendices, fixed typos

References in corpus (56)

• Topological Insulators
• Topological insulators and superconductors
• Anyons in an exactly solved model and beyond
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Novel Jeff = 1/2 Mott State Induced by Relativistic Spin-Orbit Coupling in Sr2IrO4
• Correlated quantum phenomena in the strong spin-orbit regime
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Mott physics and band topology in materials with strong spin-orbit interaction
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Three-Dimensional Topological Insulators
• Spin waves and revised crystal structure of honeycomb iridate Na2IrO3
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Quantum spin Hall effect in a transition metal oxide Na2IrO3
• Orbital order and fluctuations in Mott insulators
• Direct evidence of a zigzag spin chain structure in the honeycomb lattice: A neutron and x-ray diffraction investigation on single crystal $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$
• An exact chiral spin liquid with non-Abelian anyons
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• A new spin-anisotropic harmonic honeycomb iridate
• Topological insulators and metal-insulator transition in the pyrochlore iridates
• Crystal field splitting and correlation effect on the electronic structure of A2IrO3
• Spin-Orbit Coupling in Iridium-Based 5d Compounds Probed by X-ray Absorption Spectroscopy
• Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations
• Na2IrO3 as a spin-orbit-assisted antiferromagnetic insulator with a 340 meV gap
• First-Principles Study of the Honeycomb-Lattice Iridates Na2IrO3 in the Presence of Strong Spin-Orbit Interaction and Electron Correlations
• Vaporization of Kitaev spin liquids
• Metal-Nonmetal Changeover in Pyrochlore Iridates
• Finite-temperature phase diagram of the Heisenberg-Kitaev model
• Exactly solvable Kitaev model in three dimensions
• Ab initio analysis of the tight-binding parameters and magnetic interactions in Na2IrO3
• Na2IrO3 as a molecular orbital crystal
• Kitaev-Heisenberg-J2-J3 model for the iridates A2IrO3
• Doping a spin-orbit Mott Insulator: Topological Superconductivity from the Kitaev-Heisenberg Model and possible application to (Na2/Li2)IrO3
• Non-coplanar and counter-rotating incommensurate magnetic order stabilized by Kitaev interactions in $\gamma$-Li2IrO3
• Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in $\beta$-Li2IrO3: full solution via magnetic resonant x-ray diffraction
• Kitaev-Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices
• Three dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite-D approximation
• Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice
• Quantum Phase Transition in Heisenberg-Kitaev Model
• Heisenberg-Kitaev model on hyperhoneycomb lattice
• Topological Quantum Phase Transition in 5$d$ Transition Metal Oxide Na${}_2$IrO${}_3$
• Magnetic excitation spectrum of Na2IrO3 probed with resonant inelastic x-ray scattering
• Spiral order in the honeycomb iridate Li2IrO3
• Mosaic spin models with topological order
• Spin-Orbital Locking, Emergent Pseudo-Spin, and Magnetic order in Honeycomb Lattice Iridates
• Global phase diagram of a doped Kitaev-Heisenberg model
• Exact Chiral Spin Liquid with Stable Spin Fermi Surface on the Kagome Lattice
• Evolution of Magnetism in Single-Crystal Honeycomb Iridates
• Effect of nonmagnetic dilution in honeycomb lattice iridates Na${}_2$IrO${}_3$ and Li${}_2$IrO${}_3$
• Strong magnetic instability in correlated metal Bi2Ir2O7
• Effect of isoelectronic doping on honeycomb lattice iridate A_2IrO_3
• Finite-Temperature Phase Transition to a Quantum Spin Liquid in a Three-Dimensional Kitaev Model on a Hyperhoneycomb Lattice
• Anyonic Loops in Three Dimensional Spin liquid and Chiral Spin Liquid
• Order-by-disorder and magnetic field response in Heisenberg-Kitaev model on a hyperhoneycomb lattice
• Topological and magnetic phases with strong spin-orbit coupling on the hyperhoneycomb lattice
• Emergent quantum phases in a frustrated J1-J2 Heisenberg model on hyperhoneycomb lattice

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• Kitaev quantum spin liquid - concept and materialization
• Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials
• Models and Materials for Generalized Kitaev Magnetism
• The monoclinic crystal structure of $\alpha$-RuCl${}_3$ and the zigzag antiferromagnetic ground state
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Incommensurate Counterrotating Magnetic Order Stabilized by Kitaev Interactions in the Layered Honeycomb $\alpha$-Li${}_2$IrO${}_3$
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• Unified theory of spiral magnetism in the harmonic-honeycomb iridates α, β, γ Li2IrO3
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• Theory of Raman response in three-dimensional Kitaev spin liquids: application to $\beta -$ and $\gamma -$Li${}_2$IrO${}_3$ compounds
• Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models
• Field-induced intertwined orders in 3D Mott-Kitaev honeycomb $\beta$-Li2IrO3
• Pressure-tuning of bond-directional exchange interactions and magnetic frustration in hyperhoneycomb iridate $\beta$-$\mathrm{L}{\mathrm{i}}_2\mathrm{Ir}{\mathrm{O}}_3$
• Heisenberg-Kitaev model in a magnetic field: $1/S$ expansion
• Semiclassical ground-state phase diagram and multi-Q phase of a spin-orbit coupled model on triangular lattice
• Magnetic structure and excitation spectrum of the hyperhoneycomb Kitaev magnet $\beta$-Li${}_2$IrO${}_3$
• The vicinity of hyper-honeycomb $\beta$-Li2IrO3 to a three-dimensional Kitaev spin liquid state
• Magnetoelastic coupling and effects of uniaxial strain in $\alpha$-RuCl${}_3$ from first principles
• Two iridates, two models, two approaches: a comparative study on magnetism in 3D honeycomb materials
• Highly-anisotropic exchange interactions of $j_{\mathrm{eff}}=1/2$ iridium moments on the fcc lattice in La${}_{2}B$IrO${}_6$ ($B$ $=$ Mg, Zn)
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• Predominance of the Kitaev interaction in a three-dimensional honeycomb iridate: from ab-initio to spin model
• Magnetic field-induced evolution of intertwined orders in the Kitaev magnet $\beta$-Li${}_2$IrO${}_3$
• Spin dynamics and field-induced magnetic phase transition in the honeycomb Kitaev magnet $\alpha$-Li${}_2$IrO${}_3$
• Revealing frustrated local moment model for pressurized hyperhoneycomb iridate: paving a way toward quantum spin liquid
• Resonant x-ray scattering reveals possible disappearance of magnetic order under hydrostatic pressure in the Kitaev candidate $\gamma$-Li${}_2$IrO${}_3$
• Functional renormalization group study of the Kitaev-$\Gamma$ model on the honeycomb lattice and emergent incommensurate magnetic correlations
• Robust spin correlations at high magnetic fields in the honeycomb iridates
• Computational design of $f$-electron Kitaev magnets: honeycomb and hyperhoneycomb compounds $A_2$PrO${}_3$ ($A=$ alkali metals)
• Neutron scattering signatures of the 3D hyper-honeycomb Kitaev quantum spin-liquid
• Kitaev magnetism through the prism of lithium iridate
• Counter-rotating spiral order in three dimensional iridates: signature of hidden symmetry in Kitaev-$\Gamma$ model
• Generic model for hyperkagome iridate in the local moment regime
• Magnon-spinon dichotomy in the Kitaev hyperhoneycomb $\beta$-Li${}_2$IrO${}_3$
• Signatures of fractionalization in spin liquids from interlayer thermal transport
• Photoexcited states of the harmonic honeycomb iridate γ-Li${}_2$IrO${}_3$
• Raman scattering in correlated thin films as a probe of chargeless surface states
• Extent of frustration in the classical Kitaev-$\Gamma$ model via bond anisotropy
• Classification and properties of quantum spin liquids on the hyperhoneycomb lattice
• Spin dynamics of counterrotating Kitaev spirals via duality
• Resonant inelastic x-ray scattering spectra in the hyperhoneycomb iridate $\beta$-Li${}_2$IrO${}_3$: First principles calculations
• Heisenberg-Kitaev Models on Hyperhoneycomb and Stripyhoneycomb Lattices: 3D-2D Equivalence of Ordered States and Phase Diagrams
• Magnetic Excitations and Interactions in the Kitaev Hyperhoneycomb Iridate $\beta$-Li${}_2$IrO${}_3$
• Reentrant incommensurate order and anomalous magnetic torque in the Kitaev magnet $\beta$-${\text{Li}}_2{\text{IrO}}_3$
• Unconventional magnetic field response of the hyperhoneycomb Kitaev magnet $\beta -{\text{Li}}_2{\text{IrO}}_3$
• Symmetry-protected topological magnons in three dimensional Kitaev materials
• Ground-State Phase Diagram of the Kitaev-Heisenberg Model on a Three-dimensional Hyperhoneycomb Lattice
• Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice
• From chiral d-wave to nodal line superconductivity in the harmonic honeycomb lattices
• Minimal models of $\alpha$-Li${}_2$IrO${}_3$: On the range of the interactions, ground state properties, and magnetization processes
• Quantum incommensurate Skyrmion crystals and Commensurate to In-commensurate transitions in cold atoms and materials with spin orbit couplings in a Zeeman field
• Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part I -- static properties
• Signature of Topological Semimetal in Harmonic-honeycomb ReO3
• Non-Loudon-Fleury Raman scattering in spin-orbit coupled Mott insulators
• Collapse of susceptibility and non-trivial spin dynamics in the hyper-honeycomb magnet $\beta$-Li${}_2$IrO${}_3$ under high pressure