  Spin-waves e.g. magnons are the conventional elementary excitations of
ordered magnets. However, other possibilities exist. For instance, magnon
bound-states can arise due to attractive magnon-magnon interactions and
drastically impact the static and dynamic properties of materials. Here, we
demonstrate a zoo of distinct multi-magnon quasiparticles in the frustrated
spin-1 triangular antiferromagnet FeI$_2$ using time-domain terahertz
spectroscopy. The energy-magnetic field excitation spectrum contains signatures
of one-, two-, four- and six-magnon bound-states, which we analyze using an
exact diagonalization approach for a dilute gas of interacting magnons. The
two-magnon single-ion bound states occur due to strong anisotropy and the
preponderance of even higher order excitations arises from the tendency of the
single-ion bound states to themselves form bound states due to their very flat
dispersion. This menagerie of tunable interacting quasiparticles provides a
unique platform in a condensed matter setting that is reminiscent of the
few-body quantum phenomena central to cold-atom, nuclear, and particle physics
experiments.
