  We demonstrate the pumping of phonons by ferromagnetic resonance in a series
of [Co(0.8 nm)/Pd(1.5 nm)]$_n$ multilayers ($n =$ 6, 11, 15, and 20) with large
magnetostriction and perpendicular magnetic anisotropy. The effect is shown
using broadband ferromagnetic resonance over a range of temperatures (10 to 300
K), where a resonant damping enhancement is observed at frequencies
corresponding to standing wave phonons across the multilayer. The strength of
this effect is enhanced by approximately a factor of 4 at 10 K compared to room
temperature, which is anomalous in the sense that the temperature dependence of
the magnetostriction predicts an enhancement that is less than a factor of 2.
Lastly, we demonstrate that the damping enhancement is correlated with a shift
in the ferromagnetic resonance field as predicted quantitatively from linear
response theory.
