Kitaev materials beyond iridates: order by quantum disorder and Weyl magnons in rare-earth double perovskites

Abstract

Motivated by the experiments on the rare-earth double perovskites, we propose a generalized Kitaev-Heisenberg model to describe the generic interaction between the spin-orbit-entangled Kramers' doublets of the rare-earth moments. We carry out a systematic analysis of the mean-field phase diagram of this new model. In the phase diagram, there exist large regions with a continuous U(1) or O(3) degeneracy. Since no symmetry of the model protects such a continuous degeneracy, we predict that the quantum fluctuation lifts the continuous degeneracy and favors various magnetic orders in the phase diagram. From this order by quantum disorder mechanism, we further predict that the magnetic excitations of the resulting ordered phases are characterized by nearly gapless pseudo-Goldstone modes. We find that there exist Weyl magnon excitations for certain magnetic orders. We expect our prediction to inspire further study of Kitaev physics, the order by quantum disorder phenomenon and topological spin wave modes in the rare-earth magnets and the systems alike.

arXiv comment8 pages, 7 figures, 1 table, update author list, to be published in PhysRevB

References in corpus (48)

• Anyons in an exactly solved model and beyond
• Type-II Weyl Semimetals
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Magnetic Pyrochlore Oxides
• 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
• Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl${}_3$
• 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
• Spin waves and revised crystal structure of honeycomb iridate Na2IrO3
• Spin-Liquid State in the S = 1/2 Hyperkagome Antiferromagnet Na4Ir3O8
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Quantum Excitations in Quantum Spin Ice
• Rare-earth triangular lattice spin liquid: a single-crystal study of YbMgGaO${}_4$
• Evidence for a spinon Fermi surface in a triangular lattice quantum spin liquid candidate
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling
• A new spin-anisotropic harmonic honeycomb iridate
• Exotic phases induced by strong spin-orbit coupling in ordered double perovskites
• Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field
• Weyl magnons in breathing pyrochlore antiferromagnets
• Generic quantum spin ice
• Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
• Ferromagnetism in the Mott insulator Ba2NaOsO6
• An anisotropic spin model of strong spin-orbit-coupled triangular antiferromagnets
• Na2IrO3 as a molecular orbital crystal
• Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice
• Quantum fluctuations in the effective pseudospin-1/2 model for magnetic pyrochlore oxides
• Kitaev-Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices
• Spin-orbit coupling in $d^2$ ordered double perovskites
• Spin-orbit effects in Na${}_4$Ir${}_3$O${}_8$, a hyper-kagomé lattice antiferromagnet
• Quantum order by disorder and accidental soft mode Er2Ti2O7
• Magnetic properties of the geometrically frustrated S=1/2 antiferromagnets, La2LiMoO6 and Ba2YMoO6, with the B-site ordered double perovskite structure: Evidence for a Collective Spin Singlet Ground State
• Structural distortion and the spin liquid state in Tb2Ti2O7
• Weyl spin liquids
• Phase Diagram and Quantum Order by Disorder in the Kitaev $K_1$-$K_2$ Honeycomb Magnet
• Symmetry Enriched U(1) Topological Orders for Dipole-Octupole Doublets on a Pyrochlore Lattice
• Strongly frustrated triangular spin lattice emerging from triplet dimer formation in honeycomb Li2IrO3
• 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)
• Order-by-disorder and magnetic field response in Heisenberg-Kitaev model on a hyperhoneycomb lattice
• Anomalous enhancement of Wilson ratio in a quantum spin liquid with strong spin-orbital entanglement: the case of Na4Ir3O8
• A Possible Fermi liquid in the lightly doped Kitaev spin liquid
• Emergent quantum phases in a frustrated J1-J2 Heisenberg model on hyperhoneycomb lattice
• Global Phase Diagram of the Extended Kitaev-Heisenberg Model on Honeycomb Lattice
• Spin-orbit coupled j=1/2 iridium moments on the geometrically frustrated fcc lattice

Cited by in corpus (54)

• Pseudospin exchange interactions in d^7 cobalt compounds: Possible realization of the Kitaev model
• Hunting Majorana Fermions in Kitaev Magnets
• Orbital effects in solids: basics, recent progress and opportunities
• Kitaev-Heisenberg Hamiltonian for High-Spin $d^7$ Mott Insulators
• Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism
• Two-dimensional spin liquid behaviour in the triangular-honeycomb antiferromagnet TbInO${}_3$
• The Spinon Fermi Surface U(1) Spin Liquid in a Spin-Orbit-Coupled Triangular Lattice Mott Insulator YbMgGaO4
• Antiferromagnetic Kitaev Interaction in $f$-Electron Based Honeycomb Magnets
• Pseudo-Goldstone gaps and order-by-quantum-disorder in frustrated magnets
• Toward Kitaev's sixteenfold way in a honeycomb lattice model
• A Néel-type antiferromagnetic order in the spin 1/2 rare-earth honeycomb YbCl${}_3$
• Thermal Hall effects in quantum magnets
• Spin-orbit entangled j=1/2 moments in Ba${}_2$CeIrO${}_6$ -- a frustrated fcc quantum magnet
• Topological Phases in Magnonics
• Weyl magnons in pyrochlore antiferromagnets with all-in-all-out orders
• Selective measurements of intertwined multipolar orders: non-Kramers doublets on a triangular lattice
• Novel Strongly Spin-Orbit Coupled Quantum Dimer Magnet: Yb${}_2$Si${}_2$O${}_7$
• Intrinsic quantum Ising model on a triangular lattice magnet TmMgGaO${}_4$ and beyond
• Synthesis, magnetization and heat capacity of triangular lattice materials NaErSe${}_2$ and KErSe${}_2$
• Rare-earth chalcohalides: A family of van der Waals layered Kitaev spin liquid candidates
• Collective excitations in the tetravalent lanthanide honeycomb antiferromagnet, Na2PrO3
• Tunneling spectroscopy as a probe of fractionalization in 2D magnetic heterostructures
• Competing phases and topological excitations of spin-one pyrochlore antiferromagnets
• Kitaev Quantum Spin Liquids
• Magnonic Weyl states in Cu2OSeO3
• Calculated magnetic exchange interactions in Dirac magnon material Cu3TeO6
• Quantum Spin Dynamics Due to Strong Kitaev Interactions in the Triangular-Lattice Antiferromagnet CsCeSe${}_2$
• Intrinsic transverse field in frustrated quantum Ising magnets: its physical origin and quantum effects
• Quantum versus thermal fluctuations in the fcc antiferromagnet: alternative routes to order by disorder
• Antiferromagnetic Kitaev Interactions in Polar Spin-Orbit Mott Insulators
• Honeycomb rare-earth magnets with anisotropic exchange interactions
• Spiral-spin-liquid behaviors and persistent reciprocal kagomé structure in frustrated van der Waals magnets and beyond
• Magnon quantum anomalies in Weyl ferromagnets
• Ground state selection by magnon interactions in the fcc antiferromagnet
• Non-Kitaev spin liquids in Kitaev materials
• Quadrupolar spin liquid, octupolar Kondo coupling and odd-frequency superconductivity in an exactly solvable model
• Antiferromagnetic resonance in the cubic iridium hexahalides (NH${}_4$)${}_2$IrCl${}_6$ and K${}_2$IrCl${}_6$
• Upper branch magnetism in quantum magnets: Collapses of excited levels and emergent selection rules
• Dirac Hamiltonians for bosonic spectra
• Dirac cones and mass terms in bosonic spectra
• Spin gaps in the ordered states of La${}_2$LiXO${}_6$ (X = Ru, Os) and their relation to distortion of the cubic double perovskite structure in 4$d^3$ and 5$d^3$ magnets
• Symmetry-protected topological magnons in three dimensional Kitaev materials
• Anisotropic exchange and non-collinear antiferromagnets on a noncentrosymmetric fcc structure as in the half-Heuslers
• $J=1/2$ Pseudospins and $d$-$p$ Hybridization in the Kitaev Spin Liquid Candidates Ru$X_3$ ($X$ = Cl, Br, I)
• Magnetic properties of a spin-orbit entangled Jeff = 1/2 honeycomb lattice
• Quantum-classical crossover in the spin-1/2 Heisenberg-Kitaev kagome magnet
• Canted antiferromagnetism in a spin-orbit coupled $S_{\text{eff}}=3/2$ triangular-lattice magnet DyAuGe
• Unraveling the magnetic ground-state in alkali-metal lanthanide oxide Na${}_2$PrO${}_3$
• Exchange Interactions in Rare-earth Magnets $A_2$PrO${}_3$ ($A$= alkali metals): Revisited
• Interplay of itinerant electrons and Ising moments in a hybrid honeycomb quantum magnet TmNi${}_3$Al${}_9$
• Bosonic Weyl excitations induced by $p$-orbital interactions in a cubic optical lattice
• Field-induced multipolar character in the dipolar ground state of the honeycomb rare-earth chalcohalide NdOF
• Magnetic-field induced melting of long-range magnetic order akin to Kitaev insulators in the metallic compound Tb5Si3
• Ligand-SOC enhanced $4f^5$ Kitaev antiferromagnet: Application to ${\mathrm{SmI}}_3$