Spin Gap in the Hole-Doped Spin Ladder System(Sr2.5Ca11.5)Cu24O41: Neutron Inelastic Scattering Study

The spin liquid state in the hole-doped two-leg ladder system $\left({\mathrm{Sr}}_{2.5}{\mathrm{Ca}}_{11.5}\right){\mathrm{Cu}}_{24}\mathrm{O}{}_{41}$, which exhibits unique superconductivity under high pressure, has been studied by neutron inelastic scattering at ambient pressure. The spin gap energy for the ladder is found to be $32.1\pm 0.3\mathrm{meV}$, which is still almost the same as that of the parent material ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$. From the observed dispersion relation, the exchange coupling is roughly estimated at $J_{\parallel }\sim 90\pm 15\mathrm{meV}$ (along the ladders) and $J_{\perp }\sim 65\pm 10\mathrm{meV}$ (along the rungs). The coupling constant $J_{\parallel }$ is slightly decreased from that obtained for the parent compound.