Midinfrared absorption in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_6:$ Evidence for a failure of spin-wave theory for spin $\frac{1}{2}$ in two dimensions

The optical conductivity $\sigma \left(\omega \right)$ of undoped and very low doped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.0\delta }$ is studied in detail in the midinfrared range. We collect experimental evidence for a magnetic origin of the observed absorption. The main resonance peak is well described by a bimagnon-plus-phonon absorption spectrum calculated within spin-wave theory. But spin-wave theory fails to describe further resonances at higher frequencies with significant spectral weight, which grows with both temperature and doping. This underlines the importance of quantum fluctuations for the description of short-wavelength magnetic excitations in a two-dimensional spin-1/2 system.