Dynamical Response of the Kitaev Spin Liquid under Third-Nearest-Neighbor Heisenberg Interaction

Abstract

Motivated by growing evidence for the significance of the third-nearest-neighbor Heisenberg ($J_3$) interaction in candidate Kitaev materials, we investigate the dynamical properties of the Kitaev spin liquid (KSL) under a $J_3$ perturbation, focusing on its spin dynamical structure factor (DSF) and Raman scattering. Within a self-consistent parton mean-field plus random-phase approximation framework, we find that $J_3$ induces coherent, paramagnon-like collective modes that coexist with a high-energy Majorana continuum in the spin DSF. The softening of these modes with increasing $|J_3|$ signals a quantum phase transition to magnetic order. Remarkably, magnetic ordering sets in at a common critical $J_3$ for both ferromagnetic ($K<0$) and antiferromagnetic ($K>0$) Kitaev models, with the resulting ordered states forming exact dual pairs under a four-sublattice duality transformation that maps $(K,J_3)\to (-K,J_3)$. An external magnetic field further softens the preexisting paramagnon modes, thereby enhancing magnetic order. Perturbative Raman calculations show that while the Kitaev-like Raman vertex probes only itinerant matter Majorana fermions, the response from the $J_3$-like vertex features both matter Majoranas and visons. Four-vison excitations produce a sharp peak accompanied by a two-fermion continuum, whereas two-vison excitations yield a continuum closely resembling the single-matter-fermion density of states. These results provide a unified perspective on the dynamical signatures of $J_3$-perturbed KSL and are helpful for interpreting experimental spectra in candidate Kitaev materials with sizable $J_3$ interactions.

17 pages, 11 figures. Comments are welcome!

References in corpus (51)

• 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
• Quantum Spin Liquids
• Quantum Spin Liquid States
• Quantum Spin Liquids
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Quantum Orders and Symmetric Spin Liquids
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Kitaev quantum spin liquid - concept and materialization
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Neutron tomography of magnetic Majorana fermions in a proximate quantum spin liquid
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Inelastic Light Scattering From Correlated Electrons
• Spin waves and revised crystal structure of honeycomb iridate Na2IrO3
• A Field Guide to Spin Liquids
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Dynamics of a two-dimensional quantum spin liquid: signatures of emergent Majorana fermions and fluxes
• Excitations in the field-induced quantum spin liquid state of alpha-RuCl3
• Half-integer quantized anomalous thermal Hall effect in the Kitaev material $\alpha$-RuCl${}_3$
• Fermionic response from fractionalization in an insulating two-dimensional magnet
• 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
• Raman Scattering Signatures of Kitaev Spin Liquids in A${}_2$ IrO${}_3$ Iridates
• Field-induced quantum spin disordered state in spin-1/2 honeycomb magnet Na2Co2TeO6
• Dynamics of Fractionalization in Quantum Spin Liquids
• The planar thermal Hall conductivity in the Kitaev magnet α-RuCl3
• Kitaev interactions in the Co honeycomb antiferromagnets Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• The sign of the overlap of HFB wave functions
• Theory of the field-revealed Kitaev spin liquid
• Rethinking $\alpha$-RuCl${}_3$
• Antiferromagnetic Kitaev interaction in $J_\rm{eff}=1/2$ cobalt honeycomb materials Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• Evidence of a Phonon Hall Effect in the Kitaev Spin Liquid Candidate $\alpha$-RuCl${}_3$
• Magnetic field induced quantum phases in a tensor network study of Kitaev magnets
• One Proximate Kitaev Spin Liquid in the $K$-$J$-$\Gamma$ Model on the Honeycomb Lattice
• Sign structure of thermal Hall conductivity for in-plane-field polarized Kitaev magnets
• Static and dynamic magnetic properties of honeycomb lattice antiferromagnets Na${}_2{M}_2$TeO${}_6$, $M$ = Co and Ni
• Excitations in the ordered and paramagnetic states of honeycomb magnet Na2Co2TeO6
• Dominant Kitaev interactions in the honeycomb materials Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Dynamics of a quantum spin liquid beyond integrability $-$ the Kitaev-Heisenberg-$\Gamma$ model in an augmented parton mean-field theory
• Variational study of the Kitaev-Heisenberg-Gamma model
• The Heart of Entanglement: Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field
• Field-induced QCD${}_3$-Chern-Simons quantum criticalities in Kitaev materials
• How to detect weak emergent broken-symmetries of the Kagome antiferromagnet from Raman spectroscopy
• Oscillations in the magnetothermal conductivity of $\mathbf{\alpha }$-RuCl${}_3$: Evidence of transition anomalies
• Kitaev Quantum Spin Liquids
• The Saga of $\alpha$-RuCl${}_3$: Parameters, Models, and Phase Diagrams
• Proximate Kitaev system for an intermediate magnetic phase in in-plane magnetic fields
• Dynamical response theory of interacting Majorana fermions and its application to generic Kitaev quantum spin liquids in a field
• Multinode quantum spin liquids in extended Kitaev honeycomb models: the view from variational Monte Carlo