  We propose a magnon-based thermal machine in two-dimensional (2D) magnetic
insulators. The thermodynamical cycles are engineered by exposing a magnon spin
system to thermal baths at different temperatures and tuning the
Dzyaloshinskii-Moriya (DM) interaction. We find for the Otto cycle that a
thermal gas of magnons converts a fraction of heat into energy in the form of
work, where the efficiency is maximized for specific values of DM, reaching the
corresponding Carnot efficiency. We witness a positive to negative net work
transition during the cycle that marks the onset of a refrigerator-like
behavior. The work produced by the magnonic heat engine enhances the magnon
chemical potential. The last enables a spin accumulation that might result in
the pumping of spin currents at the interfaces of metal-magnet
heterostructures. Our work opens new possibilities for the efficient leverage
of conventional two-dimensional magnets.
