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

We recently showed that an electron wave packet undergoes an abrupt, sideways jump $\Delta y$ during scattering in the presence of spin-orbit interaction. This causes the Hall effect in ferromagnets around room temperature ($R_s\propto {\rho }^2$). The value of the side jump per collision ($\Delta y\approx {10}^{-10\mathrm{}}$ 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 $Q_s^{\mathrm{is}}\propto \rho T$, where $\rho$ is the resistivity. If spin-disorder scattering is also introduced, then the Hall conductivity ${\gamma }_{\mathrm{Hs}}$ is not affected, but the Nernst coefficient becomes $Q_s^{\mathrm{is}}=-T(\alpha +\beta \rho )$. 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 $\alpha$ is predicted to exist even in pure metals, in agreement with the above data but not with the Kondorskii theory.