Magnon theory data

In this work, we treat magnon dispersion in ferrimagnetic insulator and magnon scattering heuristically to drive the thermal-driven magnon current via semi-classical Boltzmann approach. We find that the temperature-dependent longitudinal SSE is dominated by magnon-phonon scattering at low temperature region, rather than magnon-magnon scattering. The relaxation time of magnon-phonon scattering follows T -3.3 dependence. At very low temperature region, the magnon enters the ballistic transport process, the temperature dependence of the relaxation time is T -1/2 . This model fits well with the experiment data. In addition, we have also derived equations that explains the position dependence of SSE with in-plan temperature gradient. The transverse distribution of the magnon temperature corresponding to the number of magnons is consistent with the experimental measurement, and the linear spatial distribution of the transverse SSE signal with position is given.