Fig. 2: Neutron scattering data of K₂Cr₈O₁₆.

a Neutron powder diffraction pattern collected at T = 10 K. Experimental data are shown in red, while the calculated refinement profile is shown in black. Tick marks indicate the allowed reflections, and the lower trace shows the difference between the calculated model and the experimental data. The main magnetic peak {1, 2, 1} is indicated (see Supplementary Fig. S3 for high-temperature patterns). The inset compares the measured (I_obs) and calculated (I_calc) intensities from single-crystal magnetic refinement using datasets obtained by subtracting selected peaks at 10 K from those at 200 K. b Temperature dependence of the neutron diffraction peak intensities at the (2, 1, 1) (red circles) and (1, 2, 1) (black squares) reflections. T_MIT denotes the metal-insulator transition temperature. Solid lines represent fits using \(I={I}_{0}{(1-T/{T}_{C})}^{\beta }\). c,d Powder inelastic neutron scattering spectra collected with an incident energy E_i = 9 meV at 5 K and 130 K, respectively. Dashed lines indicate an additional dispersion discussed in the Supplementary Information. e,f Fits to the inelastic neutron scattering spectra obtained using a Heisenberg Hamiltonian at 5 K and 130 K. c–f use the same color scale. The fitting and analysis procedures are provided in the Supplementary materials. Error bars represent the experimental uncertainty.