Incommensurate Charge Ordering in Charge-Frustrated LuFe₂O₄ System

The charge ordering process of a mixed valence LuFe₂O₄ system has been studied, focusing attention on the frustration effect associated with the charge configuration, ft is revealed that the system undergoes successive phase transitions following the sequence of disorder→2D CDW→3D CDW. In the 2D-CDW state, the charge density wave defined by the wave vector (1/3,1/3), is formed in the hexagonal layer. On the nodal lines of the CDW, the charge order is still undetermined due to the charge frustration. From a dielectric viewpoint, this phase is viewed as random stacking of 2D ferroelectric layers. In the 3D-CDW state, antiphase stacking of the 2D ordered layer develops. At the same time, the in-plane charge order exhibits a doubly modulated long-period structure. From a dielectric viewpoint, this phase is characterized by an incommensurate antiferroelectric phase. Relevance of the charge ordering mechanism to the observed anomalously large dielectric constant in LuFe₂O₄ is discussed.