Proximate Dirac spin liquid in honeycomb lattice $J_1$-$J_3$ XXZ model: Numerical study and application to cobaltates

Abstract

Recent theoretical and experimental work suggest that the honeycomb cobaltates, initially proposed as candidate Kitaev quantum magnets, are in fact described by a pseudospin-$1/2$ easy-plane spin Hamiltonian with nearest neighbor ferromagnetic (FM) exchange $J_1$ being frustrated by antiferromagnetic third-neighbor exchange $J_3$ and weaker compass anisotropies. Using exact diagonalization and density-matrix renormalization group (DMRG) calculations, we show that this model exhibits FM order at small $J_3/J_1$ and zig-zag (ZZ) order at large $J_3/J_1$, separated by an intermediate phase, which we label as $\widetilde{\mathrm{SL}}$. This $\widetilde{\mathrm{SL}}$ phase is shown to exhibit spin-liquid-like correlations in DMRG, although we cannot preclude weak broken symmetries, e.g. weak Ising type Néel order, given the limits on our explored system sizes. Using a modified parton mean field theory and variational Monte Carlo on Gutzwiller projected wavefunctions, we show that the optimal FM and ZZ orders as well as the intermediate $\widetilde{\mathrm{SL}}$ state are proximate to a `parent' Dirac spin liquid (SL). This Dirac SL is shown to capture the broad continuum in the temperature and magnetic field dependent terahertz spectroscopy of BaCo${}_2$(AsO${}_4$)${}_2$, and the reported low temperature metallic thermal conductivity in Na${}_2$Co${}_2$TeO${}_6$ and BaCo${}_2$(AsO${}_4$)${}_2$ upon incorporating disorder induced broadening.

Final PRB version - 13 pages, 11 figures. Special thanks to Federico Becca, Sasha Chernyshev, Martin Klanjsek

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Cited by in corpus (12)

• Quantum Spin Supersolid as a precursory Dirac Spin Liquid in a Triangular Lattice Antiferromagnet
• The Saga of $\alpha$-RuCl${}_3$: Parameters, Models, and Phase Diagrams
• Suppression of Antiferromagnetic Order by Strain in Honeycomb Cobaltate: Implication for Quantum Spin Liquid
• BaCo${}_2$(AsO${}_4$)${}_2$: Strong Kitaev, After All
• On the multi-$\mathbf{q}$ characteristics of magnetic ground states of honeycomb cobalt oxides
• Intermediate field-induced phase of the honeycomb magnet BaCo${}_2$(AsO${}_4$)${}_2$
• Fractionalized fermionic multicriticality in anisotropic Kitaev spin-orbital liquids
• Spin-orbit entangled moments and magnetic exchange interactions in cobalt-based honeycomb magnets BaCo${}_2$($X$O${}_4$)${}_2$ ($X$ = P, As, Sb)
• Quantum Spin Liquids in Weak Mott Insulators with a Spin-Orbit Coupling
• Scaling behavior and giant field-enhancement of the thermal conductivity in the honeycomb antiferromagnet BaCo2(AsO4)2
• Demystifying quantum escapism on the honeycomb lattice
• Stabilization of zigzag order in NiPS${}_3$ via positive biquadratic interaction