  We theoretically investigate spin transfer between a system of
quasiequilibrated Bose-Einstein condensed magnons in an insulator in direct
contact with a conductor. While charge transfer is prohibited across the
interface, spin transport arises from the exchange coupling between insulator
and conductor spins. In normal insulator phase, spin transport is governed
solely by the presence of thermal and spin-diffusive gradients; the presence of
Bose-Einstein condensation (BEC), meanwhile, gives rise to a
temperature-independent condensate spin current. Depending on the thermodynamic
bias of the system, spin may flow in either direction across the interface,
engendering the possibility of a dynamical phase transition of magnons. We
discuss experimental feasibility of observing a BEC steady state (fomented by a
spin Seebeck effect), which is contrasted to the more familiar spin-transfer
induced classical instabilities.
