Are Kitaev couplings significant in cobalt honeycomb magnets?
In plain words
Theory in 2018 proposed that cobalt honeycomb compounds could realize the Kitaev model with weaker competing couplings than the ruthenium and iridium ones. Neutron studies of BaCo2(AsO4)2 instead fit simpler models without large Kitaev terms, and the magnetic pattern of $\mathrm{Na_2Co_2TeO_6}$ is itself debated.
Precise statement
For $\mathrm{Na_2Co_2TeO_6}$, $\mathrm{Na_3Co_2SbO_6}$ and BaCo2(AsO4)2 (Co2+ d7 pseudospin-1/2 on honeycomb lattices), determine $|K|/\max(|J1|, |J3|, |\Gamma|)$ from fits of the full magnon spectra, and for $\mathrm{Na_2Co_2TeO_6}$ whether the zero-field order is single-q zigzag in three domains or a triple-q state. An answer gives the exchange set with error bars per compound and the ordering-wavevector content.
What would settle it
Inelastic neutron scattering on single-domain or detwinned crystals with field-angle-dependent spectroscopy that distinguishes bond-dependent from XXZ exchange.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Halloran et al. (PNAS 2023) fit BaCo2(AsO4)2 with an XXZ $J1-J3$ model with small Kitaev terms, while Kruger et al. (PRL 2023) argued for triple-q order in $\mathrm{Na_2Co_2TeO_6}$ near a hidden-$\mathrm{SU}(2)$-symmetric point.
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