  We combine $^{57}$Fe M\"ossbauer spectroscopy and $^{57}$Fe nuclear resonant
inelastic x-ray scattering (NRIXS) in nanoscale polycrystalline
[bcc-$^{57}$Fe/MgO] multilayers with various Fe layer thicknesses and
layer-resolved density-functional-theory (DFT) based first-principles
calculations of a (001)-oriented [Fe(8 ML)/MgO(8 ML)](001) heterostructure to
unravel the interface-related atomic vibrational properties of a multilayer
system. In theory and experiment, we observe consistently enhanced hyperfine
magnetic fields compared to bulk which are associated with the Fe/MgO interface
layers. NRIXS and DFT both reveal a strong reduction of the longitudinal
acoustic (LA) phonon peak in combination with an enhancement of the low-energy
vibrational density of states (VDOS) suggesting that the presence of interfaces
and the associated increase in the layer-resolved magnetic moments results in
drastic changes in the Fe-partial VDOS. From the experimental and calculated
VDOS, vibrational thermodynamic properties have been determined as a function
of Fe thickness and are found to be in excellent agreement.
