  Nonlinear devices, such as transistors, enable contemporary computing
technologies. We theoretically investigate nonlinear effects, bearing a high
fundamental scientific and technical relevance, in magnonics with emphasis on
superconductor-ferromagnet hybrids. Accounting for finite magnon chemical
potential, we theoretically demonstrate magnonic spin-Joule heating, the spin
analogue of conventional electronic Joule heating. Besides suggesting a key
contribution to magnonic heat transport in a broad range of devices, it
provides insights into the thermal physics of non-conserved bosonic
excitations. Considering a spin-split superconductor self-consistently, we
demonstrate its interface with a ferromagnetic insulator to harbor large
tunability of spin and thermal conductances. We further demonstrate hysteretic
rectification I-V characteristics in this hybrid, where the hysteresis results
from the superconducting state bistability.
