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Magnon breakdown in a two dimensional triangular lattice Heisenberg antiferromagnet of multiferroic LuMnO$_3$

The breakdown of magnons, the quasiparticles of magnetic systems, has rarely been seen. By using an inelastic neutron scattering technique we report the observation of spontaneous magnon decay in multiferroic LuMnO$_3$, a simple two-dimensional Heisenberg triangular lattice antiferromagnet, with large spin, S = 2. The origin of this rare phenomenon lies in the non-vanishing cubic interaction between magnons in the spin Hamiltonian arising from the noncollinear 120$^o$ spin structure. We observed all three key features of the nonlinear effects as theoretically predicted: a roton-like minimum, a flat mode, and a linewidth broadening, in our inelastic neutron scattering measurements of single crystal LuMnO$_3$. Our results show that quasiparticles in a system hitherto thought of as "classical" can indeed break down.