Fig. 4: Signature of long-range RKKY interactions in CeIn₃.

a1–c1 Magnon dispersion near the magnetic zone center R along the respective lines RΓ, RX, and RM. The color-coding reflects the imaginary part of the dynamic susceptibility, \({\tilde{\chi }}^{{\prime\prime} }({{{{{{{\bf{Q}}}}}}}},E)\), recorded with incident neutron energy E_i = 3.315 meV (see Methods for details). Squares and circles correspond to the locations of Gaussian profiles inferred from constant-energy cuts with one and two Gaussian profiles, respectively. All cuts investigated and the corresponding fits are shown in the Supplementary Information. The solid blue and light green lines denote the magnon dispersions calculated from our microscopic model and a fit of a short-range Heisenberg model with a single nearest-neighbor exchange constant J₁ to our data, respectively. The dashed black line is a linear fit of the magnon dispersion close to the zone center used to extract the magnon velocity. a2–c2 At higher energies, where the splitting is larger than the FWHM of the experimental resolution, the profiles of constant-energy cuts were fitted by two Gaussian profiles. a3–c3 At energies below 0.6 meV for the RΓ and RX direction and below 0.4 meV for the RM direction, the splitting is restricted by the experimental resolution as indicated by the shaded profile. Error bars in panels a2–c2 and a3–c3 represent the statistical error.