<i>Colloquium</i>: Spontaneous magnon decays

A theoretical overview of the phenomenon of spontaneous magnon decays in quantum antiferromagnets is presented. The intrinsic zero-temperature damping of magnons in quantum spin systems is a fascinating many-body effect, which has recently attracted significant attention in view of its possible observation in neutron-scattering experiments. An introduction to the theory of magnon interactions and a discussion of necessary symmetry and kinematic conditions for spontaneous decays are provided. Various parallels with the decays of anharmonic phonons and excitations in superfluid $^{4}\mathrm{He}$ are extensively used. Three principal cases of spontaneous magnon decays are considered: field-induced decays in Heisenberg antiferromagnets, zero-field decays in spiral antiferromagnets, and triplon decays in quantum-disordered magnets. Analytical results are compared with available numerical data and prospective materials for experimental observation of the decay-related effects are briefly discussed.