Quasi-two-dimensional hole ordering and dimerized state in the CuO2-chain layers in Sr14Cu24O41

Neutron scattering experiments have been performed on Sr${}_{14}$Cu${}_{24}$O${}_{41}$ which consists of both chains and ladders of copper ions. We observed that the magnetic excitations from the CuO${}_2$ chain have two branches and that both branches are weakly dispersive along the $a$ and $c$ axes. The $\omega$-$Q$ dispersion relation as well as the intensities can be reasonably described by a random phase approximation with intradimer coupling between next-nearest-neighbor copper spins $J$=11 meV, interdimer coupling along the c axis $J_c$=0.75 meV, and interdimer coupling along the a axis $J_a$=0.75 meV. The dimer configuration indicates a quasi-two-dimensional hole ordering, resulting in an ordering of magnetic Cu${}^{2+}$ with spin-1/2 and nonmagnetic Cu, which forms the Zhang-Rice singlet. We have also studied the effect of Ca substitution for Sr on the dimer and the hole ordering.