Interband magnon drag in ferrimagnetic insulators

We propose a new drag phenomenon, an interband magnon drag, and report on interaction effects and multiband effects in magnon transport of ferrimagnetic insulators. We study a spin-Seebeck coefficient $S_{\textrm{m}}$, a magnon conductivity $\sigma_{\textrm{m}}$, and a magnon thermal conductivity $\kappa_{\textrm{m}}$ of interacting magnons for a minimal model of ferrimagnetic insulators using a $1/S$ expansion of the Holstein-Primakoff method, the linear-response theory, and a method of Green's functions. We show that the interband magnon drag enhances $\sigma_{\textrm{m}}$ and reduces $\kappa_{\textrm{m}}$, whereas its total effects on $S_{\textrm{m}}$ are small. This drag results from the interband momentum transfer induced by the magnon-magnon interactions. We also show that the higher-energy band magnons contribute to $S_{\textrm{m}}$, $\sigma_{\textrm{m}}$, and $\kappa_{\textrm{m}}$ even for temperatures smaller than the energy difference between the two bands.