Model of the Longitudinal Spin Seebeck Coefficient of InSb in a Magnetic Field

We develop a simple theory for the longitudinal spin Seebeck effect in n-doped InSb in an external magnetic field. We consider spin-$1\mathrm{/}2$ 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 longitudinal spin Seebeck coefficients 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.