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 ${\mathrm{O}}^{\text{2−}}\to {\mathrm{S}}^{\text{2−}}\to {\mathrm{Se}}^{\text{2−}}$ . 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 ${\mathrm{O}}^{\text{2−}}\to {\mathrm{S}}^{\text{2−}}\to {\mathrm{Se}}^{\text{2−}}$ 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 ${\mathrm{O}}^{\text{2−}}\to {\mathrm{S}}^{\text{2−}}\to {\mathrm{Se}}^{\text{2−}}$ . 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 $\mathrm{d‐}\mathrm{function}$ energy, also reduces the third (antiferromagnetic) mechanism.