  Spin currents are generated within the bulk of magnetic materials due to heat
flow, an effect called intrinsic spin-Seebeck. This bulk bosonic spin current
consists of a diffusing thermal magnon cloud, parametrized by the magnon
chemical potential ($\mu_{m}$), with a diffusion length of several microns in
yttrium iron garnet (YIG). Transient opto-thermal measurements of the
spin-Seebeck effect (SSE) as a function of temperature reveal the time
evolution of $\mu_{m}$ due to intrinsic SSE in YIG. The interface SSE develops
at times < 2 ns while the intrinsic SSE signal continues to evolve at times >
500 $\mu$s, dominating the temperature dependence of SSE in bulk YIG.
Time-dependent SSE data are fit to a multi-temperature model of coupled
spin/heat transport using finite element method (FEM), where the magnon spin
lifetime ($\tau$) and magnon-phonon thermalization time ($\tau_{mp}$) are used
as fit parameters. From 300 K to 4 K, $\tau_{mp}$ varies from 1 to 10 ns,
whereas $\tau$ varies from 2 to 60 $\mu$s with the spin lifetime peaking at 90
K. At low temperature, a reduction in $\tau$ is observed consistent with
impurity relaxation reported in ferromagnetic resonance measurements. These
results demonstrate that the thermal magnon cloud in YIG contains extremely low
frequency magnons (~10 GHz) providing spectral insight to the microscopic
scattering processes involved in magnon spin/heat diffusion.
