  Using a functional renormalization group approach we show that at low
temperatures and in a certain range of magnetic fields the longitudinal dynamic
structure factor of quantum Heisenberg ferromagnets in dimensions $D\leq 2$
exhibits a well-defined quasi-particle peak with linear dispersion that we
identify as zero-magnon sound. In $D>2$ the larger phase space available for
the decay into transverse spin waves leads only to a broad hump centered at
zero frequency whose width scales linearly in momentum.
