Quasilinear spin-voltage profiles in spin thermoelectrics

Recent experiments show that spin thermoelectrics is a promising approach to generate spin voltages. While spin chemical potentials are often limited to a surface layer of the order of the spin-diffusion length, we show that thermoelectrically induced spin chemical potentials can extend much further in itinerant ferromagnets with paramagnetic impurities. In some cases, conservation laws, e.g., for a combination of spin and heat currents, give rise to a linear spin-voltage profile. More generally, we find quasilinear profiles involving a spin thermoelectric length scale which far exceeds the spin-diffusion length.

Figure 1

Inelastic spin-flip processes for electrons near the Fermi energy ${\mu }_0$. Arrows indicate electronic transitions while $\pm$ signs indicate the change of the local impurity spin $S_z$. Since $\uparrow$-spin electrons gain energy ${\epsilon }_i$ whereas $\downarrow$-spin electrons lose energy ${\epsilon }_i$, inelastic spin-flip scattering becomes asymmetric (finite ${\Gamma }_{-}$) for an energy-dependent density of states.