Structural modulation, hole distribution, and hole-ordered structure of the incommensurate composite crystal (Sr₂Cu₂O₃)_0.70CuO₂

Modulated structure of incommensurate composite crystal (Sr₂Cu₂O₃)_0.70CuO₂, “Sr₁₄Cu₂₄O₄₁,” has been investigated by single-crystal x-ray-diffraction method using centrosymmetric (3 + 1)-dimensional superspace group. In (Sr₂Cu₂O₃)_0.70CuO₂, displacive modulation of O atom in the CuO₂ chain is fairly large. Considering the modulation of bond angles, it has been found that the Cu-O bond in the CuO₂ chain is tilting toward the Cu₂O₃ ladder in order that the O atom in the chain plays as apical oxygen for the CuO₄ square in the ladder. The bond-valence sum (BVS) method has been applied to investigate the hole distribution in the modulated structure of (Sr₂Cu₂O₃)_0.70CuO₂. It is indicated that the valence of Cu atom in the Cu₂O₃ ladder is +2.04, where about 0.03 holes are certainly transferred from the CuO₂ chain through the modulated O atom in the CuO₂. The BVS calculation has demonstrated that almost all of the holes are prepared in the CuO₂ chain by the large modulation of the Cu-O bond. Cu atoms in the modulated CuO₂ chain have been proved to form hole-ordered structure with next-nearest-neighbor Cu²⁺ ions separated by Cu³⁺ ion on the Zhang-Rice singlet site. The periodicity of the hole-ordered structure is five times of the average CuO₂ lattice along the crystallographic c axis, which is compatible with the spin-dimerized state at low temperature. The new model of the two-dimensional hole-ordered structure in the CuO₂ plane has been obtained by the BVS calculation. Furthermore, the two-dimensional configuration of the spin dimers has been successfully derived from the hole-ordered structure in the CuO₂ plane. It has been concluded that the valences of Cu atoms both in the Cu₂O₃ ladder and in the CuO₂ chain are well controlled by the modulated O atom in the CuO₂ chain.