Spin and orbital occupation and phase transitions in ${\mathrm{V}}_2{\mathrm{O}}_3$

Polarization dependent x-ray-absorption measurements were performed on pure and Cr-doped ${\mathrm{V}}_2{\mathrm{O}}_3$ single crystals in the antiferromagnetic insulating, paramagnetic insulating, and metallic phases. The orbital occupation of the V ${3d}^2$ ion is found to depend appreciably on the phase, but always with the $S=1\mathrm{}$ character, requiring an explanation which is beyond the elegant simplicity of the pure one-band Hubbard model or of models in which the $a_{1g}$ orbital is projected out by means of a simple dimerization. The results reveal the critical role of the spin and orbital dependence of the on-site $3d-3d$ Coulomb energy, and a mechanism is proposed to explain the closing or opening of the band gaps which are of much higher energy scale than the transition temperatures.