  We develop a simple theory for the longitudinal spin 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 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.
