Phase separation and ferroelectric ordering in charge-frustrated

The transmission electron microscopy observations of the charge ordering (CO) which governs the electronic polarization in LuFe 2 O 4 − δ clearly show the presence of a remarkable phase separation at low temperatures. Two CO ground states are found to adopt the charge modulations of Q 1 = ( 1 / 3 , 1 / 3 , 0 ) and Q 2 = ( 1 / 3 + ε , 1 / 3 + ε , 3 / 2 ) , respectively. Our structural study demonstrates that the incommensurately Q 2 -modulated state is chiefly stable in samples with relatively lower oxygen contents. Data from theoretical simulations of the diffraction suggest that both Q 1 - and Q 2 -modulated phases have ferroelectric ordering. The effects of oxygen concentration on the phase separation and electric polarization in this layered system are discussed.