Fig. 4: Inelastic neutron scattering results of Co₃Sn_2-xIn_xS₂ (x = 0.12).

a Select energy dependence of the spin excitations at T = 35, 110, 155, and 165 K (see supplementary information for fit details). b Temperature dependence of the spin wave gap and fitting results with different parameters with T_C = 165 K. c Dispersion curve of the spin wave excitations along [H,0,3] at 5 and 200 K fit to a q²-dependence and compared to x = 0 data from⁹ as shown in square points. After data analysis⁹, claims a gapless spectrum at 200 K. d Temperature dependence of the in-plane spin-wave stiffness D_H and fitting results with different parameters and T_C = 165 K. D_H was determined using fixed E_g determined from energy scans (Fig. 4a) and then fitting the dispersions along H (Fig. 4c). The vertical error bars in (a) are statistical errors of 1 standard deviation. The horizontal and vertical error bars in (b–d) represent the estimated uncertainty obtained in fitting procedures.