  There has been a recent upsurge of interest in the quantum properties of
magnons for quantum information processing. An important issue is to examine
the stability of quantum states of magnons against various relaxation and
dephasing channels. Since the interaction of magnons in magnetic systems may
fall in the ultra-strong and even deep-strong coupling regimes, the relaxation
process of magnon states is quite different from the more common quantum
optical systems. Here we study the relaxation and dephasing of magnons based on
the Lindblad formalism and derive a generalized master equation that describes
the quantum dynamics of magnons. Employing this master equation, we identify
two distinct dissipation channels for squeezed magnons, i.e., the local
dissipation and collective dissipation, which play a role for both ferromagnets
and antiferromagnets. The local dissipation is caused by the independent
exchange of angular momentum between the magnonic system and the environment,
while the collective dissipation is dressed by the parametric interactions of
magnons and it enhances the quantumness and thermal stability of squeezed
magnons. Further, we show how this formalism can be applied to study the pure
dephasing of magnons caused by four-magnon scattering and magnon-phonon
interactions. Our results provide the theoretical tools to study the
decoherence of magnons within a full quantum-mechanical framework and further
benefit the use of quantum states of magnons for information processing.
