  Condensed-matter analogs of the Higgs boson in particle physics allow
insights into its behavior in different symmetries and dimensionalities.
Evidence for the Higgs mode has been reported in a number of different
settings, including ultracold atomic gases, disordered superconductors, and
dimerized quantum magnets. However, decay processes of the Higgs mode (which
are eminently important in particle physics) have not yet been studied in
condensed matter due to the lack of a suitable material system coupled to a
direct experimental probe. A quantitative understanding of these processes is
particularly important for low-dimensional systems where the Higgs mode decays
rapidly and has remained elusive to most experimental probes. Here, we discover
and study the Higgs mode in a two-dimensional antiferromagnet using
spin-polarized inelastic neutron scattering. Our spin-wave spectra of
Ca$_2$RuO$_4$ directly reveal a well-defined, dispersive Higgs mode, which
quickly decays into transverse Goldstone modes at the antiferromagnetic
ordering wavevector. Through a complete mapping of the transverse modes in the
reciprocal space, we uniquely specify the minimal model Hamiltonian and
describe the decay process. We thus establish a novel condensed matter platform
for research on the dynamics of the Higgs mode.
