Fig. 4: SW transfer from different temperature range to explore the origin of T_H and bond-dependent spin exchange interaction.

a The σ₁(ω) of Cu₃Co₂SbO₆ at 6 K and room temperature. The red circle indicates the isosbestic point. Solid and dotted lines are σ₁(ω) along the bond-perpendicular (E_bond⊥) and the bond-parallel directions (E_bond//), respectively. The inset visualizes the relationship between the polarization and bond directions of Cu₃Co₂SbO₆. b T-dependence of effective number of electrons accord with excitonic transition, N_eff (ω=ω_iso, T) = 2m₀V/πe²\({\int }_{0}^{{\omega }_{{iso}}} {\sigma }_{1}(\omega ^{\prime} ){{\rm{d}}}\omega ^{\prime}\). The vertical lines display both characteristic temperature T_N and T_H. Black closed squares and red open squares indicate the bond-parallel and bond-perpendicular polarizations, respectively. The difference effective number of electrons along each direction between three different temperature range c, f above T_H (40 K–75 K), d, g between T_N and T_H (16 K–40 K), and e, h below T_N (6 K–16 K). Red and blue contours, divided by the isosbestic point, represent SW transfer before and after the isosbestic point, suggesting that the origin of T_H is linked to the magnetic structure. The quantitative differences between the bond-parallel and bond-perpendicular directions indicate a considerable anisotropic Kitaev spin exchange interaction.