Revealing subsurface vibrational modes by atom-resolved damping force spectroscopy.

We propose to use the damping signal of an oscillating cantilever in dynamic atomic force microscopy as a noninvasive tool to study the vibrational structure of the substrate. We present atomically resolved maps of damping in carbon nanotube peapods, capable of identifying the location and packing of enclosed Dy@C_{82} molecules as well as local excitations of vibrational modes inside nanotubes of different diameter. We elucidate the physical origin of damping in a microscopic model and provide quantitative interpretation of the observations by calculating the vibrational spectrum and damping of Dy@C_{82} inside nanotubes with different diameters using ab initio total energy and molecular dynamics calculations.