  We develop a theory of the spin battery effect in
superconductor/ferromagnetic insulator (SC/FI) systems taking into account the
magnetic proximity effect. We demonstrate that the spin-energy mixing enabled
by the superconductivity leads to the enhancement of spin accumulation by
several orders of magnitude relative to the normal state. This finding can
explain the recently observed giant inverse spin Hall effect generated by
thermal magnons in the SC/FI system. We suggest a non-local electrical
detection scheme which can directly probe the spin accumulation driven by the
magnetization dynamics. We predict a giant Seebeck effect converting the magnon
temperature bias into the non-local voltage signal. We also show how this can
be used to enhance the sensitivity of magnon detection even up to the
single-magnon level.
