The influence of magnon renormalization and interband coupling on the spin Seebeck effect in YIG

With exceptionally low magnetic damping, YIG has been extensively applied in the realm of magnetism, encompassing the researches into the spin Seebeck effect. YIG has 20 magnon bands, including 8 higher-energy bands denoted as $\alpha_{1\sim8}$, and 12 lower-energy bands denoted as $\beta_{1\sim12}$. Here, we study the impact of the complex intraband and interband magnon couplings on the transport coefficients of YIG. Four-magnon processes in YIG are considered, and a self-consistent mean-field approximation is made for these interaction terms. We find that the $\beta$ bands exhibit minimal variation with increasing temperature, whereas the $\alpha$ bands undergo a noticeable decline as the temperature rises. These counterintuitive results agree well with the observation of earlier inelastic neutron scattering experiments and the results of the theoretical calculations in recent years. We also find it sufficient to include only the contribution of magnons on the acoustic band $\beta_1$ when studying the spin conductivity ($\sigma_m$). However, when calculating the spin Seebeck coefficient ($S_m$) and the magnon thermal conductivity ($\kappa_m$), the results calculated using only $\beta_{1}$ show noticeable deviations over a large temperature range compared to the full band calculations. These deviations are well mitigated when the $\beta_{2}$ and $\beta_{3}$ bands are considered. Finally, we find our results satisfy the Wiedemann-Franz law for magnon transport.