  We consider alignment-dependent spin and heat transport across a magnon spin
valve in the tunneling regime, i.e., a junction consisting of two weakly
coupled ferromagnetic insulators. We determine the difference in spin and heat
conductance between the parallel and antiparallel configuration of the
magnetization direction. The dependence of these conductances on both the
Gilbert damping and ellipticity is studied. We find that both magnon
ellipticity and dissipation open channels for magnons to tunnel through in the
antiparallel configuration. Our results highlight an important difference
between electronic and magnon spin transport in spin-valve structures and may
be important for the development of devices based on magnetic insulators.
