Spin-Wave Lifetimes Throughout the Brillouin Zone

We use a neutron spin-echo method with $\mu$eV resolution to determine the lifetimes of spin waves in the prototypical antiferromagnet MnF$_2$ over the entire Brillouin zone. A theory based on the interaction of magnons with longitudinal spin fluctuations provides an excellent, parameter-free description of the data, except at the lowest momenta and temperatures. This is surprising, given the prominence of alternative theories based on magnon-magnon interactions in the literature. The results and technique open up a new avenue for the investigation of fundamental concepts in magnetism. The technique also allows measurement of the lifetimes of other elementary excitations (such as lattice vibrations) throughout the Brillouin zone.