  When magnons and phonons, the fundamental quasiparticles of the solid, are
coupled to one another, they form a new hybrid quasi-particle, leading to novel
phenomena and interesting applications. Despite its wide-ranging importance,
however, detailed experimental studies on the underlying Hamiltonian is rare
for actual materials. Moreover, the anharmonicity of such magnetoelastic
excitations remains largely unexplored although it is essential for a proper
understanding of their diverse thermodynamic behaviour as well as intrinsic
zero-temperature decay. Here we show that in noncollinear antiferromagnets, a
strong magnon-phonon coupling can significantly enhance the anharmonicity,
resulting in the creation of magnetoelastic excitations and their spontaneous
decay. By measuring the spin waves over the full Brillouin zone and carrying
out anharmonic spin wave calculations using a Hamiltonian with an explicit
magnon-phonon coupling, we have identified a hybrid magnetoelastic mode in
(Y,Lu)MnO3 and quantified its decay rate and the exchange-striction coupling
term required to produce it. Our work has wide implications for understanding
of the spin-phonon coupling and the resulting excitations of the broad classes
of noncollinear magnets.
