Theory of Ionic Ordering, Crystal Distortion, and Magnetic Exchange Due to Covalent Forces in Spinels

Elastic- and electrostatic-energy considerations are insufficient for an explanation of cation ordering between tetrahedral and octahedral sites in spinels. Tetrahedral, octahedral, and square covalent bonds are also important when cations are to be accommodated in these sites. The square bonds in octahedral sites can cause the tetragonal distortion observed in ${\mathrm{Mn}}_3$ ${\mathrm{O}}_4$ $\gamma$-${\mathrm{Mn}}_2$ ${\mathrm{O}}_3$, Zn${\mathrm{Mn}}_2$ ${\mathrm{O}}_4$, Cu${\mathrm{Fe}}_2$ ${\mathrm{O}}_4$, Cu${\mathrm{Cr}}_2$ ${\mathrm{O}}_4$, Ca${\mathrm{In}}_2$ ${\mathrm{O}}_4$, Cd${\mathrm{In}}_2$ ${\mathrm{O}}_4$, and metallic indium. A new magnetic exchange mechanism, "semicovalent exchange," which is consistent with the covalent model, is used to explain the magnetic properties of spinels.