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 Cr₂{O}₃$ and ${α}$-${Fe}₂O₃ is given. The difference between the two magnetic lattices is attributed to the fact that Cr⁺³ has a less-than-half-full d-shell and Fe⁺³ a half-filled d-shell. We predict that the Cr₂{O}₃$-type magnetic lattice should be found in ${V}₂O₃, Ti₂{O}₃$, and TiFe${O}₃$. 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 ${Fe}₂O₃---Cr₂{O}₃$ and TiFe${O}₃$---${Fe}₂O₃ are tentatively outlined from theoretical considerations. A ferrimagnetic structure is proposed for the crystals of the composition Ti2/3Fe4/3O₃ which are found in nature and are conspicuously related to certain problems in rock-magnetism. The predictions derived from our semiempirical analysis should be tested by neutron diffraction experiments and magnetic measurements. The experiments of Forestier and of Pouillard on the Fe₂{O}₃$---${Cr}₂O₃ system are discussed.