  Much of modern condensed matter physics is understood in terms of elementary
excitations, or quasiparticles - fundamental quanta of energy and momentum.
Various strongly-interacting atomic systems are successfully treated as a
collection of quasiparticles with weak or no interactions. However, there are
interesting limitations to this description: the very existence of
quasiparticles cannot be taken for granted in some systems. Like unstable
elementary particles, quasiparticles cannot survive beyond a threshold where
certain decay channels become allowed by conservation laws - their spectrum
terminates at this threshold. This regime of quasiparticle failure was first
predicted for an exotic state of matter, super-fluid helium-4 at temperatures
close to absolute zero - a quantum Bose-liquid where zero-point atomic motion
precludes crystallization. Using neutron scattering, here we show that it can
also occur in a quantum magnet and, by implication, in other systems with
Bose-quasiparticles. We have measured spin excitations in a two dimensional
(2D) quantum-magnet, piperazinium hexachlorodicuprate (PHCC) in which spin-1/2
copper ions form a non-magnetic quantum spin liquid (QSL), and find remarkable
similarities with excitations measured in superfluid 4He. There is a threshold
momentum beyond which the quasiparticle peak merges with the two-quasiparticle
continuum. It then acquires a finite energy width and becomes indistinguishable
from a leading-edge singularity, so that lowest excited states occupy a wide
band of energy. Our findings have important ramifications for understanding
phenomena involving excitations with gapped spectra in many condensed matter
systems, including high-transition-temperature superconductors.
