Application of the Side-Jump Model to the Hall Effect and Nernst Effect in Ferromagnets

Abstract

We recently showed that an electron wave packet undergoes an abrupt, sideways jump $\ensuremath{\Delta}y$ during scattering in the presence of spin-orbit interaction. This causes the Hall effect in ferromagnets around room temperature (${R}_{s}\ensuremath{\propto}{\ensuremath{\rho}}^{2}$). The value of the side jump per collision ($\ensuremath{\Delta}y\ensuremath{\approx}{10}^{\ensuremath{-}10}$ m) seems the same for impurity and phonon scattering. A more complete justification of the side-jump model is given here. This model is used to derive the isothermal Nernst coefficient ${Q}_{s}^{\mathrm{is}}$, giving ${Q}_{s}^{\mathrm{is}}\ensuremath{\propto}\ensuremath{\rho}T$, where $\ensuremath{\rho}$ is the resistivity. If spin-disorder scattering is also introduced, then the Hall conductivity ${\ensuremath{\gamma}}_{\mathrm{Hs}}$ is not affected, but the Nernst coefficient becomes ${Q}_{s}^{\mathrm{is}}=\ensuremath{-}T(\ensuremath{\alpha}+\ensuremath{\beta}\ensuremath{\rho})$. This formula agrees with the data of Kondorskii and Vasileva on Fe, Ni, Co, Gd, and Fe-Ni. The side jump is assumed to have the same value for spin disorder as for impurity or phonon scattering. The constant $\ensuremath{\alpha}$ is predicted to exist even in pure metals, in agreement with the above data but not with the Kondorskii theory.