Spin Dimer Analysis of the Magnetic Structures of Ba₃Cr₂O₈, Ba₃Mn₂O₈, Na₄FeO₄, and Ba₂CoO₄ with a Three-Dimensional Network of Isolated MO₄ (M = Cr, Mn, Fe, Co) Tetrahedra

The spin exchange interactions of the magnetic oxides Ba₃Cr₂O₈, Ba₃Mn₂O₈, Na₄FeO₄, and Ba₂CoO₄ with a three-dimensional network of isolated MO₄ (M = Cr, Mn, Fe, Co) tetrahedra were examined by performing spin dimer analysis on the basis of tight-binding electronic structure calculations. Although the shortest O···O distances between adjacent MO₄ tetrahedra are longer than the van der Waals distance, our analysis shows that the super-superexchange interactions between adjacent MO₄ tetrahedra are substantial and determine the magnetic structures of these oxides. In agreement with experiment, our analysis predicts a weakly interacting isolated AFM dimer model for both Ba₃Cr₂O₈ and Ba₃Mn₂O₈, the (0.0, 0.5, 0.0) magnetic superstructure for Na₄FeO₄, the (0.5, 0.0, 0.5) magnetic superstructure for Ba₂CoO₄, and the presence of magnetic frustration in Ba₂CoO₄. The comparison of the intra- and interdimer spin exchange interactions of Ba₃Cr₂O₈ and Ba₃Mn₂O₈ indicates that orbital ordering should be present in Ba₃Cr₂O₈.