Ab initio calculation of thermoelectric properties in 3d ferromagnets based on spin-dependent electron-phonon coupling

Crossed magneto-thermo-electric coefficients are central to novel sensors and spin(calori)tronic devices. Within the framework of Boltzmann’s transport theory, we calculate the resistivity and Seebeck coefficients of the most common 3d ferromagnetic metals: Fe, Co, and Ni. We use a fully first-principles variational approach, explicitly taking electron-phonon scattering into account. The electronic band structures, phonon dispersion curves, phonon linewidths, and transport spectral functions are reported, comparing with experimental data. Successive levels of approximation are discussed: constant relaxation time approximation, scattering for a non-magnetic configuration, then spin polarized calculations with and without spin-orbit coupling (enabling spin-flips). Spin polarization and explicit electron-phonon coupling are found to be necessary to reach a correct qualitative picture: the effect of spin flipping is substantial for resistivity and very delicate for the Seebeck coefficient. The spin-dependent Seebeck effect is also predicted.