The hole distribution in Sr${}_{14}$Cu${}_{24}$O${}_{41}$ is studied by low-temperature polarization-dependent O $K$ near-edge x-ray absorption fine-structure measurements and state-of-the-art electronic structure calculations that include core-hole and correlation effects in a mean-field approach. Contrary to all previous analysis, based on semiempirical models, we show that correlations and antiferromagnetic ordering favor the strong chain-hole attraction. For the remaining small number of holes accommodated on ladders, leg sites are preferred to rung sites. The small hole affinity of rung sites explains naturally the one-dimensional to two-dimensional crossover in the phase diagram of (La,Y,Sr,Ca)${}_{14}$Cu${}_{24}$O${}_{41}$.

• Received 9 November 2011

DOI:https://doi.org/10.1103/PhysRevB.85.075108