Two-phonon contributions to the inelastic x-ray scattering spectra of MgB 2

Two-phonon contributions to meV-resolved, inelastic x-ray scattering spectra of ${\mathrm{MgB}}_{2}$ at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ are identified, in good agreement, in both intensity and energy, with a harmonic calculation using the force constant matrix from ab initio calculations. This contribution impacts the determination of the linewidth of the ${E}_{2g}$ phonon mode that is so important for the high ${T}_{\mathrm{c}}$ of this material. To the best of our knowledge, this is the first observation of peaks in measurements of phonon dispersion $(qg0)$ due to two-phonon scattering in a non-rare-gas solid.