Contributions from two-particle scattering to the extraordinary Hall effect in Kondo systems.

Abstract

The contributions of skew scattering to the extraordinary Hall effect (EHE) in Kondo-type systems have been evaluated by using current-current correlation functions. By using this formalism we take account of two-electron scattering processes that are neglected in the conventional one-electron scattering theory of the EHE. We evaluate the correlation functions for dilute Kondo systems by considering only independent single-site scattering. We find there are two types of contributions to the EHE. Type-I terms come from diagrams in which the energies of the propagators are held fixed. We find that these type-I contributions reproduce the EHE found by the one-electron formalism, i.e., the elastic impurity- or potential-scattering contribution; in addition, there is a spin-scattering contribution which was not previously incorporated in the one-electron scattering formalism. The type-II contributions come from diagrams in which energy is exchanged between resonant and nonresonant scattering channels. These contributions to the EHE are new, i.e., they require two-electron scattering processes, and therefore perforce cannot be accounted for in a one-electron formalism. We find the type-II contributions to the EHE are as large as those of type I at low temperatures T${T}_{0}$, where ${T}_{0}$ is the characteristic energy scale of the single-ion Kondo problem; at high temperatures T\ensuremath{\gg}${T}_{0}$, they are negligible compared with type-I contributions. To obtain the Hall effect we must have scattering in two partial-wave channels whose orbital angular momenta differ by 1\ensuremath{\Elzxh}. To account for the dominant resonant Kondo scattering, we use the Anderson mixing interaction and consider the local electron is in a spin-orbit-coupled j state. In the nonresonant channel we consider two-electron charge- and spin-scattering terms whose origins could be, interalia, the direct and exchange parts of the Coulomb interaction between local and conduction electrons.