Do electron distributions with orbital degree of freedom exhibit anisotropy?

Orbital degrees of freedom appear in partially filled degenerate orbitals and are responsible for a variety of physical properties. Although many methods for directly observing orbital states in ordered states have been proposed, it is difficult to determine degenerate orbital states directly. We found that high-precision diffraction data obtained by synchrotron radiation X-rays can be used to observe only the valence electron density distribution with minimal analytical bias. The results obtained using this method clearly showed the anisotropy of the partially filled degenerate 3d orbital states in spinel vanadium oxide FeV2O4. The 3d orbital quantum state was successfully determined from this anisotropy.