Interpretation of the magnetic structures of Cu2Te2O5X2 (X = Cl,Br) and Ca3.1Cu0.9RuO6 on the basis of electronic structure considerations: cases for strong super-superexchange interactions involving Cu2+ ions

For super-superexchange interactions between Cu(2+) ions, a qualitative rule was formulated to assess their strengths based on the geometrical parameters of the exchange paths. Spin dimer analysis was carried out for Cu(2)Te(2)O(5)X(2) (X = Cl, Br) and Ca(3.1)Cu(0.9)RuO(6) to evaluate the relative strengths of their superexchange and super-superexchange interactions. The strongest antiferromagnetic interactions in Cu(2)Te(2)O(5)X(2) (X = Cl, Br) are given by the super-superexchange interactions involving the most linear Cu-X.X-Cu paths between tetrahedral clusters Cu(4)O(8)X(4) along the (a +/- b)-directions. The adjacent CuRuO(6) chains of Ca(3.1)Cu(0.9)RuO(6) are antiferromagnetically coupled through the most linear Cu-O.O-Cu paths along the direction perpendicular to the plane of the CuRu zigzag chain. The spin lattices of Cu(2)Te(2)O(5)X(2) and Ca(3.1)Cu(0.9)RuO(6) deduced from our spin dimer analysis are consistent with the available magnetic data. The spin lattice of a magnetic solid should be determined on the basis of appropriate electronic structure considerations.