Phonon Dispersion and Lifetimes inMgB2

We measure phonon dispersion and linewidth in a single crystal of ${\mathrm{M}\mathrm{g}\mathrm{B}}_2$ along the $\Gamma \mathrm{\text{−}}A$, $\Gamma \mathrm{\text{−}}M$, and $A\mathrm{\text{−}}L$ directions using inelastic x-ray scattering. We use density functional theory to compute the effect of both electron-phonon coupling and anharmonicity on the linewidth, obtaining excellent agreement with experiment. Anomalous broadening of the $E_{2g}$ phonon mode is found all along $\Gamma \mathrm{\text{−}}A$. The dominant contribution to the linewidth is always the electron-phonon coupling.