  Strong interactions between particles can lead to emergent collective
excitations. These phenomena have been extensively established in electronic
systems, but are also expected to occur for gases of neutral particles like
spin waves, also known as magnons, in a ferromagnet. In a hydrodynamic regime
where magnons are strongly interacting, they can form a slow collective density
mode -- in analogy to sound waves in water -- with characteristic low-frequency
signatures. While such a mode has been predicted in theory, its signatures have
yet to be observed experimentally. In this work, we isolate atomically-thin
sheets of ferromagnetic CrCl$_3$ where magnon interactions are strong, and
develop a technique to measure its collective magnon dynamics via the quantum
coherence of nearby Nitrogen-Vacancy (NV) centers in diamond. We find that the
thermal magnetic fluctuations generated by CrCl$_3$ exhibit an anomalous
temperature-dependence, whereby fluctuations increase upon decreasing
temperature. Our analysis reveals that this anomalous trend is a consequence of
the damping rate of a low-energy magnon sound mode which sharpens as magnon
interactions increase with increasing temperature, providing a first glimpse of
the magnon hydrodynamic regime.
