Fig. 3: Optical exciton and spin-exciton coupling in Cu₃Co₂SbO₆.

a σ₁(ω) at 6 K with polarization along the bond-perpendicular direction (open circles) and Lorentz-Gaussian oscillator fitting (solid lines) for Cu₃Co₂SbO₆. The peak is assigned based on orbital-projected density of states in Fig. 3b. b the orbital-projected density of state of bond-perpendicular oriented zigzag ordering Cu₃Co₂SbO₆ obtained from DFT + U. The horizontal dashed line is Fermi level. The solid arrows indicate the optical transition from Cu 3 d to Co 3 d (shown in Fig. 3a). The T-dependent c, the ellipsometry data Ψ d, exciton peak position, e peak intensity, and f scattering rate. The error bars in c correspond to standard deviations derived from random noise, while error bars in d, e and f represent the figure of merit, calculated as the standard 90% confidence limit multiplied by square root of the mean-squared error. The red line in Fig. 3d is Bose-Einstein statistics fitting functions implemented at high T data, generically found in spectra due to phonon contribution of thermal broadening. The black arrows indicate the T_N and T_H. The distinct kink below T_N in all fitting parameters implies the existence of coupling between the exciton and antiferromagnetic ordering. The clear additional anomaly in Ψ and peak position at T_H indicates the presence of non-zero short-range spin-spin correlation functions above T_N.