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 Δμ in the semiconductor in response to a temperature difference ΔT 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 nonzero energy derivative, resulting in different Seebeck tunnel coefficients Sst ↑ and Sst ↓ for majority and minority spin electrons. We evaluate the thermal spin current, the induced spin accumulation and Δμ/ΔT, 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 Δμ, 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.