Theory of the Spin Seebeck Effect at a Topological-Insulator/Ferromagnetic-Insulator Interface

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 the TI surface states scattering off the nonequilibrium 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 material parameters are consistent with recent experiments.