Superexchange Interactions and Magnetic Lattices of the Rhombohedral Sesquioxides of the Transition Elements and Their Solid Solutions

A semiempirical analysis of the superexchange interactions responsible for the formation of the magnetic lattices in ${\mathrm{Cr}}_2$ ${\mathrm{O}}_3$ and $\alpha$-${\mathrm{Fe}}_2$ ${\mathrm{O}}_3$ is given. The difference between the two magnetic lattices is attributed to the fact that ${\mathrm{Cr}}^{+3\mathrm{}}$ has a less-than-half-full $d$-shell and ${\mathrm{Fe}}^{+3\mathrm{}}$ a half-filled $d$-shell. We predict that the ${\mathrm{Cr}}_2$ ${\mathrm{O}}_3$-type magnetic lattice should be found in ${\mathrm{V}}_2$ ${\mathrm{O}}_3$, ${\mathrm{Ti}}_2$ ${\mathrm{O}}_3$, and TiFe${\mathrm{O}}_3$. One of the superchange interactions in the sesquioxides is compared with the $A-B$ interaction in magnetic spinels. The magnetic phase diagrams of the systems ${\mathrm{Fe}}_2$ ${\mathrm{O}}_3$—${\mathrm{Cr}}_2$ ${\mathrm{O}}_3$ and TiFe${\mathrm{O}}_3$—${\mathrm{Fe}}_2$ ${\mathrm{O}}_3$ are tentatively outlined from theoretical considerations. A ferrimagnetic structure is proposed for the crystals of the composition ${\mathrm{Ti}}_{\frac{2}{3}}{\mathrm{Fe}}_{\frac{4}{3}}{\mathrm{O}}_3$ which are found in nature and are conspicuously related to certain problems in rock-magnetism. The predictions derived from our semiempirical analysis should be tested by neutron diffraction experiments and magnetic measurements. The experiments of Forestier and of Pouillard on the ${\mathrm{Fe}}_2$ ${\mathrm{O}}_3$—${\mathrm{Cr}}_2$ ${\mathrm{O}}_3$ system are discussed.