Phonon Softening, Chaotic Motion, and Order-Disorder Transition inSn/Ge(111)

The phonon dynamics of the $\mathrm{S}\mathrm{n}/\mathrm{G}\mathrm{e}(111)$ interface is studied using high-resolution helium atom scattering and first-principles calculations. At room temperature we observe a phonon softening at the $\overline{K}$ point in the $(\sqrt{3}\times \sqrt{3})R30°$ phase, associated with the stabilization of a $(3\times 3)$ phase at low temperature. That phonon band is split into three branches in the $(3\times 3)$ phase. We analyze the character of these phonons and find out that the low- and room-temperature modes are connected via a chaotic motion of the Sn atoms. The system is shown to present an order-disorder transition.