Proximate Dirac spin liquid in the honeycomb lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mtext>−</mml:mtext><mml:msub><mml:mi>J</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> XXZ model: Numerical study and application to cobaltates

Abstract

Recent theoretical and experimental work suggests 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 zigzag (ZZ) order at large ${J}_{3}/{J}_{1}$, separated by an intermediate phase, which we label as $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathrm{SL}}$. This $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathrm{SL}}$ phase is shown to exhibit spin-liquid-like correlations in DMRG, although we cannot preclude weak broken symmetries, e.g., weak Ising type N\'eel order, given the limits on our explored system sizes. Using a modified parton mean field theory and variational Monte Carlo on Gutzwiller projected wave functions, we show that the optimal FM and ZZ orders as well as the intermediate $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathrm{SL}}$ 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 ${\mathrm{BaCo}}_{2}{({\mathrm{AsO}}_{4})}_{2}$, and the reported low-temperature metallic thermal conductivity in ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$ and ${\mathrm{BaCo}}_{2}{({\mathrm{AsO}}_{4})}_{2}$ upon incorporating disorder-induced broadening.

Topics & Concepts