  The longitudinal spin Seebeck effect (LSSE) in Pt/Y$_3$Fe$_5$O$_{12}$ (YIG)
junction systems has been investigated at various magnetic fields and
temperatures. We found that the LSSE voltage in a Pt/YIG-slab system is
suppressed by applying high magnetic fields and this suppression is critically
enhanced at low temperatures. The field-induced suppression of the LSSE in the
Pt/YIG-slab system is too large at around room temperature to be explained
simply by considering the effect of the Zeeman gap in magnon excitation. This
result requires us to introduce magnon-frequency-dependent mechanism into the
scenario of LSSE; low-frequency magnons dominantly contribute to the LSSE. The
magnetic field dependence of the LSSE voltage was observed to change by
changing the thickness of YIG, suggesting that the thermo-spin conversion by
the low-frequency magnons is suppressed in thin YIG films due to the long
characteristic lengths of such magnons.
