Boltzmann approach to the longitudinal spin Seebeck effect

TL;DR

This paper develops a Boltzmann transport theory for coupled magnon-phonon systems in ferromagnetic insulators, explaining the magnetic field and size dependence of the spin Seebeck effect and aligning with experimental observations.

Contribution

It introduces a Boltzmann approach explicitly including magnon-phonon coupling to analyze the spin Seebeck effect in ferromagnetic insulators.

Findings

Magnetic field dependence of the spin Seebeck voltage matches experimental data.

Predicted size dependence of the spin Seebeck effect.

Similar features to magnon-polaron behavior observed in the theory.

Abstract

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.