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.
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