Analysis of the spin lattice model for the spin-gapped layered compounds Na₃Cu₂SbO₆ and Na₂Cu ₂TeO₆ on the basis of electronic structure calculations

The spin lattice model for the spin-gapped layered magnetic solids Na ₃Cu₂SbO₆ and Na₂Cu ₂TeO₆ was examined by evaluating the three spin exchange interactions of their Cu₂MO₆ (M = Sb, Te) layers in terms of spin dimer analysis based on extended Hückel tight binding calculations and mapping analysis based on first principles density functional theory electronic band structure calculations. For both compounds, our calculations show that the two strongest spin exchange interactions, that is, the Cu-O⋯O-Cu super-superexchange (J₂) and the Cu-O-Cu superexchange (J₁) interactions, form alternating chains that interact weakly through the Cu-O-Cu superexchange (J₃) interactions. The dominant one of the three spin exchange interactions is J₂, and it is antiferromagnetic in agreement with the fact that both of the compounds are spin gapped. For Na₃Cu₂SbO₆ and Na ₂Cu₂TeO₆, the superexchange J₁ is calculated to be ferromagnetic, hence, leading to the alternating chain model in which antiferromagnetic and ferromagnetic spin exchange interactions alternate. This picture does not agree with the recent experimental analysis, which showed that the temperature-dependent magnetic susceptibilities of both compounds should be described by the alternating chain model in which two antiferromagnetic spin exchange interactions of different strengths alternate.