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 threedimensional 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 (OO)-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.