Model for the spin-dependent Seebeck coefficient of InSb in a magnetic field

Abstract

We develop a simple theory for the spin-dependent Seebeck effect in $n$-doped InSb in an external magnetic field. We consider spin-$1/2$ electrons in the conduction band of InSb with a temperature gradient parallel to the applied magnetic field. In the absence of spin-orbit interactions, a Boltzmann equation approach leads to a spin current parallel to the field and proportional to the temperature gradient. The calculated spin-dependent Seebeck coefficient oscillates as a function of magnetic field $B$; the peak positions are approximately periodic in $1/B$. The oscillations arise when the Fermi energy crosses the bottom of a Landau band.