Side-Jump Mechanism for the Hall Effect of Ferromagnets

The center of mass of a wave packet undergoes a discontinuous and finite sideways displacement on scattering by a central potential, in the presence of spin-orbit interaction. This is the main Hall-effect mechanism (${\rho }_H\propto {\rho }^2$) for Fe, Ni, and their alloys above 100 K, while asymmetric scattering dominates below 100 K. Displacement $\Delta y$ per actual collision is calculated by partial waves. In the case of Born expansion, the leading term of $\Delta y or \frac{{\rho }_H}{{\rho }^2}$ is of zero order in the scattering potential. The magnitude is predicted correctly ($\Delta y\approx {10}^{-10\mathrm{}}-{10}^{-11\mathrm{}}$ m) when using the effective spin-orbit Hamiltonian derived by Fivaz from spin-orbit interband mixing. The calculation of ${\rho }_H$ is extended to arbitrary ${\omega }_c\tau$ for compensated and un-compensated metals. Other nonclassical physical mechanisms proposed by Karplus and Luttinger and by Doniach and by Fivaz are spurious for the dc Hall effect.