Fig. 1 |. Equal-time structure factor in NaCaNi₂F₇.

a, Measured neutron cross-section integrated over the range $0<E<14\mathrm{m}\mathrm{e}\mathrm{V}$ at $T=1.8\left(2\right)\mathrm{K}$. Polarized neutron measurements are labelled by NSF, which measures components of the dynamic spin correlation function that are perpendicular to the $(h,h,\ell )$ scattering plane, and SF, which measures the component of the dynamics spin correlation function polarized within the $(h,h,\ell )$ scattering plane and perpendicular to momentum transfer. Before integration, the data were symmetrized by folding about the lines $h=0$ and $\ell =0$ for data in the $(h,0,\ell )$ scattering plane and the lines $hh=0$ and $\ell =0$ for data in the $(h,h,\ell )$ scattering plane. No smoothing or interpolation was applied to the data. b, Energy-integrated neutron cross-section calculated using the self-consistent Gaussian approximation (SCGA) and exchange parameters $J_1=J_2=3.2\left(1\right)\mathrm{m}\mathrm{e}\mathrm{V},J_3=0.019\left(3\right)\mathrm{m}\mathrm{e}\mathrm{V}{J}_4=-0.070\left(4\right)\mathrm{m}\mathrm{e}\mathrm{V}$ and $J_{\mathrm{N}\mathrm{N}\mathrm{N}}=-0.025\left(5\right)\mathrm{m}\mathrm{e}\mathrm{V}$. Dashed lines delineate the plane of asymmetry in the SF scattering. The dipole approximation for the Ni²⁺ magnetic form factor⁴³ was used when converting the calculated $𝒮\left(\mathrm{q}\right)$ to a neutron cross-section.