  The spin Seebeck effect (SSE) in ferrimagnetic insulators (FMI) provides a
simple method of using heat to manipulate magnons, which could be used as
carriers of information and energy conversion. However, a theory that can
quantitively interpret experimental results is still lacking. In this paper, we
develop a transport theory of magnons in FMI at low temperatures by combining
the macroscopic Boltzmann equation with microscopic quantum scattering theory.
It is found that the scattering of magnons is dominated by phonons rather than
magnons, and the relaxation time of magnon is inversely proportional to the
cube of temperature. At extremely low temperature region, the magnon enters the
ballistic transport process. In addition, we also derive the linear spatial
distribution of the transverse SSE signal with sample position. All the
theoretical results are in excellent agreement with the experimental data.
