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Anomalous Hall effect (AHE) and spin Hall effect (SHE) are fundamentalphenomena, and their potential for application is great. However, we understandthe interaction effects unsatisfactorily, and should have clarified issuesabout the roles of the Fermi sea term and Fermi surface term of theconductivity of the intrinsic AHE or SHE of an interacting multiorbital metaland about the effects of spin-Coulomb drag on the intrinsic SHE. Here weresolve the first issue and provide the first step about the second issue bydeveloping a general formalism in the linear response theory with appropriateapproximations and using analytic arguments. The most striking result is thateven without impurities the Fermi surface term, a non-Berry-curvature term,plays dominant roles at high or slightly low temperatures. In particular, thisFermi surface term causes the temperature dependence of the dc anomalous Hallor spin Hall conductivity due to the interaction-induced quasiparticle dampingand the correction of the dc spin Hall conductivity due to the spin-Coulombdrag. Those results revise our understanding of the intrinsic AHE and SHE. Wealso find that the differences between the dc anomalous Hall and longitudinalconductivities arise from the difference in the dominant multiband excitations.This not only explains why the Fermi sea term such as the Berry-curvature termbecomes important in clean and low-temperature case only for interbandtransports but also provides the useful principles on treating theelectron-electron interaction in an interacting multiorbital metal for generalformalism of transport coefficients. Several correspondences between ourresults and experiments are finally discussed.

physical review. b./physical review. b

Fermi surface versus Fermi sea contributions to intrinsic anomalous and  spin Hall effects of multiorbital metals in the presence of Coulomb  interaction and spin-Coulomb drag