Magnetic structure of V₂O₃ in the insulating phase

A phase diagram for all the possible collinear spin arrangements for V₂O₃ is derived within the atomic limit. Due to the fact that the a_1g electrons of the V atoms form a diamagnetic bond for the vertical pairs of V atoms, the magnetic structure of V₂O₃ can be considered to be essentially determined by the remaining one electron per V atom in a twofold degenerate e_g level. Depending on only two parameters: t_ij¹¹/t_ij²², the ratio of the hopping integrals within the two orbital states 1 and 2 and between a certain pair (i, j) of V atoms in the basal plane, and J/U, the ratio of the exchange constant to Hubbard's U, the regions of stability for a particular magnetic and orbital order are determined. The experimentally observed magnetic order falls into a region of values of these parameters which are expected for V₂O₃.