Theory of the Topological Spin-Seebeck Effect

The spin-Seebeck effect refers to voltage signals induced in metals by thermally driven spin-currents in adjacent magnetic systems. We present a theory of the spin-Seebeck signal in the case where the conductor that supports the voltage signal is the topologically-protected two-dimensional surface-state system at the interface between a ferromagnetic insulator (FI) and a topological insulator (TI). Our theory uses a Dirac model for the TI surface-states and assumes Heisenberg exchange coupling between the TI quasiparticles and the FI magnetization. The spin-Seebeck voltage is induced by TI surface-state scattering off the non-equilibrium magnon population at the surface of the semi-infinite thermally driven FI. Our theory is readily generalized to spin-Seebeck voltages in any two-dimensional conductor that is exchange coupled to the surface of a FI. Surface state carrier-density dependent signal strengths calculated using Bi$_2$Te$_3$ and yttrium iron garnet (YIG) materials parameters are consistent with recent experiments.