One- and Two-Triplon Spectra of a Cuprate Ladder

We have performed inelastic neutron scattering on the near ideal spin-ladder compound ${\mathrm{La}}_4{\mathrm{Sr}}_{10}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ as a starting point for investigating doped ladders and their tendency toward superconductivity. A key feature was the separation of one-triplon and two-triplon scattering. Two-triplon scattering is observed quantitatively for the first time and so access is realized to the important strong magnetic quantum fluctuations. The spin gap is found to be $26.4\pm 0.3\mathrm{meV}$. The data are successfully modeled using the continuous unitary transformation method, and the exchange constants are determined by fitting to be $J_{\mathrm{leg}}=186\mathrm{meV}$ and $J_{\mathrm{rung}}=124\mathrm{meV}$ along the leg and rung, respectively; a substantial cyclic exchange of $J_{\mathrm{cyc}}=31\mathrm{meV}$ is confirmed.