Nature of the density-wave order in ambient-pressure $\mathrm{La_3Ni_2O_7}$
In plain words
At normal pressure $\mathrm{La_3Ni_2O_7}$ does not superconduct but forms a density wave, a periodic pattern of spins and possibly charges, near $150\ \mathrm{K}$; its form and its link to superconductivity are uncertain.
Precise statement
Identify the spin and charge density-wave order of $\mathrm{La_3Ni_2O_7}$ at ambient pressure (onset near $150\ \mathrm{K}$): wavevector, moment size and arrangement on the bilayer, and any charge component. Determine whether suppression of this order under pressure or strain is necessary for superconductivity. An answer is a refined magnetic structure from neutron or resonant x-ray scattering plus a phase diagram showing where the order vanishes relative to the superconducting onset.
What would settle it
Single-crystal neutron diffraction and resonant x-ray scattering on stoichiometric crystals, followed under pressure to the superconducting regime.
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