We report on a systematic study of nanomechanical dissipation in
high-frequency (approximatively 300 MHz) gallium arsenide optomechanical disk
resonators, in conditions where clamping and fluidic losses are negligible.
Phonon-phonon interactions are shown to contribute with a loss background
fading away at cryogenic temperatures (3 K). Atomic layer deposition of alumina
at the surface modifies the quality factor of resonators, pointing towards the
importance of surface dissipation. The temperature evolution is accurately
fitted by two-level systems models, showing that nanomechanical dissipation in
gallium arsenide resonators directly connects to their microscopic properties.
Two-level systems, notably at surfaces, appear to rule the damping and
fluctuations of such high-quality crystalline nanomechanical devices, at all
temperatures from 3 to 300K