Ferroelectricity from iron valence ordering in the charge-frustrated system LuFe2O4

Ferroelectric materials are widely used in modern electric devices such as memory elements, filtering devices and high-performance insulators. Ferroelectric crystals have a spontaneous electric polarization arising from the coherent arrangement of electric dipoles (specifically, a polar displacement of anions and cations). First-principles calculations and electron density analysis of ferroelectric materials have revealed that the covalent bond between the anions and cations, or the orbital hybridization of electrons on both ions, plays a key role in establishing the dipolar arrangement. However, an alternative model-electronic ferroelectricity-has been proposed in which the electric dipole depends on electron correlations, rather than the covalency. This would offer the attractive possibility of ferroelectric materials that could be controlled by the charge, spin and orbital degrees of freedom of the electron. Here we report experimental evidence for ferroelectricity arising from electron correlations in the triangular mixed valence oxide, LuFe(2)O(4). Using resonant X-ray scattering measurements, we determine the ordering of the Fe(2+) and Fe(3+) ions. They form a superstructure that supports an electric polarization consisting of distributed electrons of polar symmetry. The polar ordering arises from the repulsive property of electrons-electron correlations-acting on a frustrated geometry.