Much of modern condensed matter physics is understood in terms of elementary excitations, or quasiparticles—fundamental quanta of energy and momentum^{1, 2}. 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: in some systems the very existence of quasiparticles cannot be taken for granted. 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. Such quasiparticle breakdown was first predicted for an exotic state of matter—super-fluid ⁴He at temperatures close to absolute zero, a quantum Bose liquid where zero-point atomic motion precludes crystallization^{1, 2, 3, 4}. Here we show, using neutron scattering, that quasiparticle breakdown 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 quantum magnet, piperazinium hexachlorodicuprate (PHCC)⁵, in which spin-1/2 copper ions form a non-magnetic quantum spin liquid, and find remarkable similarities with excitations in superfluid ⁴He. We observe 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 excited states are no longer quasiparticles but occupy a wide band of energy. Our findings have important ramifications for understanding excitations with gapped spectra in many condensed matter systems, ranging from band insulators to high-transition-temperature superconductors⁶.

1. Condensed Matter Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
   
2. Condensed Matter Physics and Material Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
   
3. Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
   
4. National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA

Correspondence to: Igor A. Zaliznyak² Correspondence and requests for materials should be addressed to I.A.Z. (Email: zaliznyak@bnl.gov).