Systematics of the Right-Angle Nearest-Neighbor Exchange Interaction for d3 Ions

In the chromium chalcogenide spinels the strength of the ferromagnetic nearest-neighbor exchange interaction increases as the anion is changed from O2−→S2−→Se2−. This tendancy was first revealed by the experiments of Baltzer et al. In order to explain this behavior, various mechanisms contributing to the right-angle exchange coupling are examined. Both the superexchange and the direct exchange interactions between the magnetic ions are taken into account. For the four-electron, three-center model in which a ligand orbital forms a π-bond with one magnetic ion, but is orthogonal to the other, it is demonstrated that: (1) An increase in the Cr3+ ligand covalency along the series O2−→S2−→Se2− leads to an enhancement of the ferromagnetic interaction. (2) There is a reduction in the antiferromagnetic direct cation-cation interactions, because the Cr3+ ions are further apart. (3) For those ligand orbitals which form π-bonds with both magnetic ions, the antiferromagnetic interaction tends to become stronger in going from O2−→S2−→Se2−. The last effect is shown to be overcome by a corresponding increase in the first (ferromagnetic term) described above. Larger covalency, leading to a reduction in the magnitude of the electron d-function energy, also reduces the third (antiferromagnetic) mechanism.