Quasi-two-dimensional hole ordering and dimerized state in the ${\mathrm{CuO}}_2$-chain layers in ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$

Neutron-scattering experiments have been performed on ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ that consists of both chains and ladders of copper ions. We observed that the magnetic excitations from the ${\mathrm{CuO}}_2$ 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 $J=11\mathrm{}\hspace{0.5em}\mathrm{meV},$ interdimer coupling along the c axis $J_c=0.75\mathrm{}\hspace{0.5em}\mathrm{meV},$ and interdimer coupling along the a axis $J_a=0.75\mathrm{}\hspace{0.5em}\mathrm{meV}.$ The dimer configuration indicates a quasi-two-dimensional hole ordering, resulting in an ordering of magnetic ${\mathrm{Cu}}^{2+}$ with spin-$\frac{1}{2}$ 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.