  Transient response of the spin Peltier effect (SPE) in a Pt/yttrium iron
garnet junction system has been investigated by means of a lock-in
thermoreflectance method. We applied an alternating charge current to the Pt
layer to drive SPE through the spin Hall effect, and measured the AC response
of the resultant SPE-induced temperature modulation at frequencies ranging from
10 Hz to 1 MHz. We found that the SPE-induced temperature modulation decreases
with increasing the frequency when the frequency is >1 kHz. This is a
characteristic feature of SPE revealed by the high frequency measurements based
on the lock-in thermoreflectance, while previous low frequency measurements
showed that the SPE signal is independent of the frequency. We attribute the
decrease of the temperature modulation to the length scale of the SPE-induced
heat current; by comparing the experimental results with one-dimensional heat
conduction calculations, the length scale of SPE is estimated to be 0.94
{\mu}m.
