  Collinear antiferromagnets (AFs) support two degenerate magnon excitations
carrying opposite spin polarizations, by which magnons can function as
electrons in various spin-related phenomena. In an insulating
ferromagnet(F)/AF/F trilayer, we explore the magnon-mediated interlayer
coupling by calculating the magnon thermal energy in the AF as a function of
the orientations of the Fs. The effect manifests as an interlayer exchange
interaction and a perpendicular magnetic anisotropy; they both depend on
temperature and the AF thickness. In particular, the exchange interaction turns
out to be antiferromagnetic at low temperatures and ferromagnetic at high
temperatures, whose magnitude can be $10-100$ $\mu$eV for nanoscale
separations, allowing experimental verification.
