Thermal spin transport and electron-magnon interactions in easy-plane ferromagnets

Abstract

We investigate the dynamics of magnons in easy-plane ferromagnetic materials. We use the Boltzmann and the Gross-Pitaevskii equation to derive the transport coefficients and the hydrodynamic equations for both thermal and condensed magnon currents in ferromagnetic insulators. Assuming a linear thermal gradient, we calculate both these magnon currents for the normal state, in which all magnons are thermal, and for the superfluid state, in which our system obeys the two-fluid model. We also consider ferromagnetic conductors. We study electron-magnon interactions in order to construct the transport coefficients and the hydrodynamic equations for magnon currents and electric currents. To find these currents explicitly, we apply these general results to the particular situation in which the temperature gradient is linear. Finally, we calculate the Seebeck coefficient for the normal and the superfluid state.