Occupation switching of $d$ orbitals probed via hyperfine interactions in vanadium dioxide

Metal-insulator transition was microscopically investigated by orbital-resolved nuclear magnetic resonance (OR-NMR) spectroscopy in a single crystal of vanadium dioxide VO${}_2$. Observations of the anisotropic ${}^{51}$V Knight shift and the nuclear quadrupole frequency allow us to evaluate orbital-dependent spin susceptibility and $d$ orbital occupations. The result is consistent with the degenerated $t_{2g}$ orbitals in a correlated metallic phase and the $d$ orbital ordering in a nonmagnetic insulating phase. The predominant orbital pointing along the chain facilitates a spin-singlet formation triggering metal-insulator transition. The asymmetry of magnetic and electric hyperfine tensors suggests the $d$ orbital reformation favored by a low-symmetry crystal field, forming a localized molecular orbital. The result highlights the cooperative electron correlation and electron-phonon coupling in Mott transition with orbital degrees of freedom.