Magnetic structure ofV2O3in the insulating phase

Abstract

A phase diagram for all the possible collinear spin arrangements for ${\mathrm{V}}_2$ ${\mathrm{O}}_3$ 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 ${\mathrm{V}}_2$ ${\mathrm{O}}_3$ 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: $\frac{t_{\mathrm{ij}}^{11}}{t_{\mathrm{ij}}^{22}}$, 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 $\frac{J}{U}$, 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 ${\mathrm{V}}_2$ ${\mathrm{O}}_3$.