Spin-Orbit Induced Spin-Flip Scattering by a Local Moment

Abstract

The spin‐orbit‐induced spin‐flip cross section presented to a conduction electron by a 3d impurity having a local moment is calculated. The Anderson model is treated in Hartree‐Fock (HF) approximation. The difference from the nonmagnetic case is that the total angular momentum j is not a good quantum number so that one cannot use its eigenstates to calculate the scattering phase shifts. Instead, the HF Hamiltonian has been diagonalized to first order in the spin‐orbit coupling H_so and the resulting eigenfunctions have been used to find the phase shifts. To maintain the spherical symmetry of the Hamiltonian when H_so is present it is found necessary to retain the matrix elements of the Coulomb interaction that connect four different orbitals m, m′ to $\text{m∓1,\hspace{0.17em}m′±1}$ . It is also necessary to abandon the simplification of assuming a single value for the exchange integral and to keep the actual dependence of the matrix elements on m and m′. The calculated cross section depends on an enhanced spin‐orbit coupling and on the local moment parameters.