Direct observation of a spin-nematic phase in a magnet
In plain words
In a spin-nematic phase the spins pair up so that no single spin points anywhere on average, yet the pairs share a common axis. Theory predicts it near magnetic saturation in several frustrated magnets, but no experiment has measured this hidden pair order directly.
Precise statement
In a frustrated J1-J2 magnet with J1 < 0 (candidate $\mathrm{LiCuVO_4}$ near saturation) or a spin-1 magnet with bound two-magnon states (candidate Na2BaNi(PO4)2), demonstrate quadrupolar order $\langle S^{+}_{i}S^{+}_{j}\rangle \ne 0$ with $\langle S_{i}\rangle=0$ using a direct probe (resonant x-ray scattering, NMR lineshape and relaxation, or two-magnon bound-state spectroscopy). An answer is a material and field range with a measured quadrupolar order parameter.
What would settle it
A measurement of long-range quadrupolar order or a two-magnon condensate together with absence of dipolar order in the same field window.
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.
Evidence in $\mathrm{LiCuVO_4}$ near saturation remains indirect (NMR, magnetization, magnetostriction); condensation of a two-magnon bound state was reported in spin-1 Na2BaNi(PO4)2 (Sheng et al., Research Square preprint 2024) without a direct measurement of the quadrupolar order parameter.
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