Hole Doping in the Two-Leg Ladder Plane of Sr2.5Ca11.5Cu24O41 by Accurate Determination of Modulated Composite Crystal Structure Using the Information Criterion

Atomic modulation of incommensurate composite crystal structure of Sr2.5Ca11.5Cu24O41 has been investigated by single-crystal x-ray-diffraction method using the Information Criterion (IC). The minimizing IC method has successfully selected the most likely modulated model of Sr2.5Ca11.5Cu24O41 with first- and second-order displacive modulations constrained by the centrosymmetric (3 + 1)-dimensional [(3 + 1)D] superspace groups, Fmmm(11 gamma) : Fmmmo(11 gamma). The present modulated model obtained by using a common internal coordinate, t, in the (3 + 1)D superspace has revealed some remarkable properties involving pyramidal CuO5 polyhedrons on the two-leg Cu2O3 ladder plane. In the pyramidal CuO5 polyhedron with the closest-apical O (Oc-apical) atom from the one-dimensional (1D) CuO2 chain, the minimum length interladder Cu-O bond by the large modulation between the two-leg ladders is stronger than the Cu-O bond in the rung, which leads to new structural mechanism of hole doping, that is, the self-doping of holes between the two-leg ladders. The bond-valence sum (BVS) analysis shows that the number of holes by the self-doping is considerably larger than that of holes by the well-known transfer from the CuO2 chain. The BVS calculations have revealed that the pyramidal CuO5 polyhedrons with the Oc- apical atoms form the Cu2.25+ -O -Cu2.25+ hole-pair in the rung of the two-leg ladder. The Cu2+ -Cu2+ dimer-like behavior in the 1D CuO2 chain shows that Cu-ladder(2.25+) -Oc- apical-(Cu2+ -Cu2+) chain coupling, as well as a small number of hole transfer (0.05 hole per Cu in the ladder), is possible between the Cu2O3 ladder and the CuO2 chain. The coupled Cu2.25+ -O -Cu2.25+ hole-pairs formed across the two adjacent rungs suggest that the trellis lattice as a two-dimensional (2D) coupled ladder is an important candidate of Cu network together with the square lattice within the two-leg ladder for the emergence of superconductivity. The charge distribution in the Cu2O3 ladder plane along the rung direction gives a possible explanation for the anisotropic transport properties of Sr2.5Ca11.5Cu24O41.