Spin Seebeck coefficients of Fe, Co, Ni, and Ni80Fe20 3d-metallic thin films

It is challenge to quantitatively determine the spin Seebeck effect (SSE) of ferromagnetic metals (FM) due to many other thermoelectric signals including the anomalous Nernst effect (ANE), magnetic proximity-induced ANE, and inverse spin Hall effect (ISHE) in FM. By comparing the thermoelectric signals of single FM layer and FM/Pt bilayer and model-assisted analyses of ISHE contribution in FM, we are able to determine the pure SSE signals and the spin Seebeck coefficients of Fe, Co, Ni, and Ni₈₀Fe₂₀ over a temperature range from 90 to 300 K. The spin-dependent Seebeck coefficients $S_{\uparrow }$ and $S_{\downarrow }$, which is related to the density of states of FM, were also determined experimentally by combining the conventional Seebeck coefficient and the SSE coefficient. We further suggest the calculation of the SSE coefficient should include the spin-dependent conductivities via $S_s\equiv \frac{{\sigma }_{\uparrow }{S}_{\uparrow }-{\sigma }_{\downarrow }{S}_{\downarrow }}{{\sigma }_{\uparrow }+{\sigma }_{\downarrow }}$.