High-frequency spin waves in Y${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.15}$

Pulsed neutron spectroscopy is used to absolute measurements of the dynamic magnetic susceptibility of insulating Y${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.15}$. Acoustic and optical modes, derived from in- and out-of-phase oscillation of spins in adjacent Cu${\mathrm{O}}_2$ planes, dominate the spectra and are observed up to 250 meV. The optical modes appear first at 74±5 meV. Linear-spin-wave theory gives an excellent description of the data and yields intralayer and interlayer exchange constants of $J_{\parallel }=125\mathrm{}\pm 5$ meV and $J_{\perp }=11\mathrm{}\pm 2$ meV, respectively, and a spin-wave intensity renormalization $Z_{\chi }=0.4\mathrm{}\pm 0.1$.