Thermal spin current and magnetothermopower by Seebeck spin tunneling

The recently observed Seebeck spin tunneling, the thermoelectric analog of spin-polarized tunneling, is described. The fundamental origin is the spin dependence of the Seebeck coefficient of a tunnel junction with at least one ferromagnetic electrode. Seebeck spin tunneling creates a thermal flow of spin-angular momentum across a tunnel barrier without a charge tunnel current. In ferromagnet/insulator/semiconductor tunnel junctions this can be used to induce a spin accumulation (\Delta \mu) in the semiconductor in response to a temperature difference (\Delta T) between the electrodes. A phenomenological framework is presented to describe the thermal spin transport in terms of parameters that can be obtained from experiment or theory. Key ingredients are a spin-polarized thermoelectric tunnel conductance and a tunnel spin polarization with non-zero energy derivative, resulting in different Seebeck tunnel coefficients for majority and minority spin electrons. We evaluate the thermal spin current, the induced spin accumulation and \Delta\mu/\Delta T, discuss limiting regimes, and compare thermal and electrical flow of spin across a tunnel barrier. A salient feature is that the thermally-induced spin accumulation is maximal for smaller tunnel resistance, in contrast to the electrically-induced spin accumulation that suffers from the impedance mismatch between a ferromagnetic metal and a semiconductor. The thermally-induced spin accumulation produces an additional thermovoltage proportional to \Delta\mu, which can significantly enhance the conventional charge thermopower. Owing to the Hanle effect, the thermopower can also be manipulated with a magnetic field, producing a Hanle magnetothermopower.