  Recent work on layered structures of superconductors (S) or normal metals (N)
in contact with ferromagnetic insulators (FI) has shown how the properties of
the previous can be strongly affected by the magnetic proximity effect due to
the static FI magnetization. Here we show that such structures can also exhibit
a new electron thermalization mechanism due to the coupling of electrons with
the dynamic magnetization, i.e., magnons in FI. We here study the heat flow
between the two systems and find that in thin films the heat conductance due to
the interfacial electron-magnon collisions can dominate over the well-known
electron-phonon coupling below a certain characteristic temperature that can be
straightforwardly reached with present-day experiments. We also study the role
of the magnon band gap and the induced spin-splitting field induced in S on the
resulting heat conductance and show that heat balance experiments can reveal
information about such quantities in a way quite different from typical magnon
spectroscopy experiments.
