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

Abstract

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.

Magnetic excitations of the gapped quantum spin dimer antiferromagnetSr3Cr2O8

“…Stone et al 7 found that the magnetic excitations are gapped, dispersive magnons modes typical of a dimerized magnet. Magnetic exchange constants have been extracted by fitting the single mode approximation to the data 7 , and by spin dimer analysis based on a extended Hückel tight binding calculation 8 . The magnetization shows two magnetic plateaux.…”

Infrared phonons and specific heat in the gapped quantum magnet Ba3Cr2O8

“…5 The detailed magnetic structure has been studied theoretically based on extended Hückel tight binding calculations. 15 The authors of Ref. 15 have examined all the possible exchange paths between the nearest-neighboring Cr ions.…”

“…15 The authors of Ref. 15 have examined all the possible exchange paths between the nearest-neighboring Cr ions. They found that the exchange interaction between adjacent Cr 5+ ions in the hexagonal c h direction is most important, while the other exchange interactions are much smaller.…”

Determination of Strongly Interacting Spin Exchange Paths in Cu2(O3PCH2PO3) on the Basis of Spin Dimer Analysis

“…4 It has been well established that the spin lattice of a magnetic solid does not necessarily have the same geometrical feature as does the arrangement of its magnetic ions or spin-carrying molecules, because magnetic orbitals are generally anisotropic in shape and because the strength of a spin exchange interaction between adjacent spin sites is determined by the overlap between their magnetic orbitals (i.e., singly occupied molecular orbitals). 5,6,11 In the present work, we examine the spin exchange interactions of Cu 2 -(O 3 PCH 2 PO 3 ) on the basis of EHTB calculations to evaluate its spin exchange interactions and hence identify the spin lattice responsible for its magnetic properties.…”