Anomalous Hall Coefficient in Heavy Electron Systems

Abstract

The anomalous Hall effects at low temperatures in the heavy electron system are discussed on the basis of the periodic Anderson Hamiltonian with degenerate orbitals. We take into account the skew scattering through the spin-orbit coupling of the f-orbitals. Following the Fermi liquid theory, we derive the general expression for the anomalous Hall coefficient in the coherent regime. The expression shows that the anomalous Hall coefficient, which is added to the ordinary Hall coefficient, is proportional to the product of the susceptibility and the square of the resistivity at low temperatures. This behavior is confirmed to be in good agreement with the experimental results. The extension of this theory to the cuprate high temperature superconductor is also discussed shortly.