We have investigated multiple losses and overtones of H vibrations at Ni(111) by using electron-energy-loss spectroscopy. We mapped the energies along the $\overline{\Gamma }\overline{M}$ direction of the surface Brillouin zone, and found two branches outside the two-phonon continua. This gives direct evidence of the existence of two-phonon bound states. Applying a one-dimensional model of coupled anharmonic oscillators, we derive the anharmonicity and discuss the localized property of the bound states.

• Received 6 October 2000

DOI:https://doi.org/10.1103/PhysRevB.63.233404