Bulk Magnon Spin Current Theory for the Longitudinal Spin Seebeck Effect

The longitudinal spin Seebeck effect (LSSE) consists in the generation of a spin current parallel to a temperature gradient applied across the thickness of a bilayer made of a ferromagnetic insulator (FMI), such as yttrium iron garnet (YIG), and a metallic layer (ML) with strong spin orbit coupling, such as platinum. The LSSE is usually detected by a DC voltage generated along the ML due to the conversion of the spin current into a charge current perpendicular to the static magnetic field by means of the inverse spin Hall effect. Here we present a model for the LSSE that relies on the bulk magnon spin current created by the temperature gradient across the thickness of the FMI. We show that the spin current pumped into the metallic layer by the magnon accumulation in the FMI provides continuity of the spin current at the FMI/ML interface and is essential for the existence of the LSSE. The results of the theory are in good agreement with experimental LSSE data in YIG/Pt bilayers on the variation of the DC voltage with the sample temperature, with the FMI layer thickness and with the intensity of high magnetic fields.