  We investigate the spontaneous disintegration of magnons in two-dimensional
ferromagnets and antiferromagnets dominated by long-range dipolar interactions.
Analyzing kinematic constraints, we show that the unusual dispersion of dipolar
ferromagnets in a uniform magnetic field precludes magnon-decay at all fields,
in sharp contrast to short-range exchange-driven magnets. However, in a
staggered magnetic field, used for state preparation in recent Rydberg array
experiments, magnons can decay in both dipolar ferromagnets and
antiferromagnets. Remarkably, such decays do not require a minimum threshold
field, and happen over a nearly fixed fraction of the Brillouin Zone in the XY
limit, highlighting the significant role played by dipolar interactions. In
addition, topological transitions in the decay surfaces lead to singularities
in the magnon spectrum. Regularizing such singular behavior via a
self-consistent approach, we make predictions for dynamical spin correlations
accessible to near-term quantum simulators and sensors.
