Fig. 2. Magnetic susceptibility of Na₂Co₂TeO₆ for B ⊥ b-axis.

a, b Temperature dependence of susceptibility χ(T) in NCTO measured at various magnetic fields. The inset of Fig. 2b shows the honeycomb lattices of Co viewed along the c-axis. The cartoon shows the moments to be in the basal plane and parallel to the b-axis^{40, 41}, and the TeO₆ octahedra sit at the center of each honeycomb unit. The first NN ferromagnetic (FM) interaction J originated from a collaboration between Co–O–Co (red bond) superexchange interactions and Co–Co (blue bond) direct exchange interactions. The second NN J₂ has multiple superexchange interaction pathways, which may lead to a wide range of variations, mainly determined by J and J₃. The third NN AFM interaction J₃ arises from the existence of the Te atom in the center of the honeycomb lattice, which leads to the unique superexchange interaction pathway Co–O–Te–O–Co (golden bond). The olive arrow refers to the direction of applied magnetic field B in the magnetization. c The isothermal magnetization M(B) with the applied magnetic field B ⊥ b, B // b, and B // c-axis at 0.5 K, respectively. The dashed line indicates the Van-Vleck paramagnetic background. d The differential isothermal magnetization as functions of fields dM/dB vs. B at different temperatures with B ⊥ b.