  We theoretically demonstrate that, in a ferromagnet/paramagnet bilayer, a
magnon instability accompanied by a gigahertz microwave emission can be driven
simply by means of a temperature bias. Employing many-body theory for
investigating the effects of a phonon heat current on the magnon lifetime, we
show that the magnon instability occurs upon the suppression of the Umklapp
scattering at low temperatures, leading to microwave emission. The present
finding provides crucial information about the interplay of spin current and
heat current.
