  Bulk glasses exhibit extra vibrational modes at low energies, known as the
boson peak. The microscopic dynamics in nanoscale alumina impact the
performance of qubits and other superconducting devices, however the existence
of the boson peak in these glasses has not been previously measured. Here we
report neutron spectroscopy on Al/Al$_2$O$_{3-x}$ nanoparticles consisting of
spherical metallic cores from 20 to 1000 nm surrounded by a 3.5 nm thick
alumina glass. An intense low-energy peak is observed at $\omega_{BP}$ = 2.8
$\pm$ 0.6 meV for highly oxidised particles, concurrent with an excess in the
density of states. The intensity of the peak scales inversely with particle
size and oxide fraction indicating a surface origin, and is red-shifted by 3
meV with respect to the van-Hove singularity of $\gamma$-phase Al$_2$O$_{3-x}$
nanocrystals. Molecular dynamics simulations of $\alpha$-Al$_2$O$_{3-x}$,
$\gamma$-Al$_2$O$_{3-x}$ and a-Al$_2$O$_{3-x}$ show that the observed boson
peak is a signature of the ultrathin glass surface, and the frequency is
softened compared to that of the hypothetical bulk glass.
