Direct observation of orbital ordering in the spinel oxide FeCr 2 O 4 through electrostatic potential using convergent-beam electron diffraction

A nanoscale structure analysis method using convergent-beam electron diffraction (CBED) has been applied to an orbital-ordered state of ${\text{Fe}}^{2+}3d$ electrons in a spinel oxide ${\text{FeCr}}_{2}{\text{O}}_{4}$. The atom positions, atomic displacement parameters, electrostatic potential, and electron density have been determined using CBED intensity data alone. A ferro-type ordered state of the $3{z}^{2}\ensuremath{-}{r}^{2}$ orbitals at the tetrahedrally coordinated Fe atoms has been successfully observed through the electrostatic potential obtained in the present analysis.