  We have theoretically investigated the spin Seebeck effect (SSE) in a normal
metal (NM)/paramagnetic insulator (PI) bilayer system. Through a linear
response approach, we calculated the thermal spin pumping from PI to NM and
backflow spin current from NM to PI, where the spin-flip scattering via the
interfacial exchange coupling between conduction-electron spin in NM and
localized spin in PI is taken into account. We found a finite spin current
appears at the interface under the difference in the effective temperatures
between spins in NM and PI, and its intensity increases by increasing the
density of the localized spin $S$. Our model well reproduces the
magnetic-field-induced reduction of the paramagnetic SSE in
Pt/Gd$_3$Ga$_5$O$_{12}$ experimentally observed when the Zeeman energy is
comparable to the thermal energy, which can be interpreted as the suppression
of the interfacial spin-flip scattering. The present finding provides an
insight into the mechanism of paramagnetic SSEs and the thermally induced
spin-current generation in magnetic materials.
