We develop a Boltzmann transport theory of coupled magnon-phonon transport in ferromagnetic insulators. The explicit treatment of the magnon-phonon coupling within the Boltzmann approach allows us to calculate the low-temperature magnetic-field dependence of the spin-Seebeck voltage. Within the Boltzmann theory we find that this magnetic field dependence shows similar features as found by Flebus et al. [Phys. Rev. B 95, 144420 (2017)] for a strongly coupled magnon phonon system that forms magnon-polarons, and consistent with experimental findings in yttrium iron garnet by Kikkawa et al. [Phys. Rev. Lett. 117, 207203 (2016)]. In addition to the anomalous magnetic-field dependence of the spin Seebeck effect, we also predict a dependence on the system size.
@article{arxiv.1806.10445,
title = {Boltzmann approach to the longitudinal spin Seebeck effect},
author = {Rico Schmidt and Francis Wilken and Tamara S. Nunner and Piet W. Brouwer},
journal= {arXiv preprint arXiv:1806.10445},
year = {2018}
}