Temperature Dependence of the Anomalous Hall Effect from Electron Interactions

We consider the impact of electron-electron interactions on the temperature dependence of the anomalous Hall effect in disordered conductors. The microscopic analysis is carried out within the diagrammatic approach of the
linear response Kubo-Streda formula with an account of both extrinsic skew-scattering and side-jump mechanisms of the anomalous Hall effect arising in the presence of spin-orbit coupling. We demonstrate the importance of
electron interactions in the Cooper channel even for nominally non-superconducting materials and find that the corresponding low-temperature dependence of the anomalous Hall conductivity is asymptotically of the form
T^1/2/ln(T₀/T) in three dimensions and ln[ln(T₀/T)] in two dimensions, where the scale of T₀ is parametrically of the order of Fermi energy. These results, in particular, may provide an explanation for the recently observed unconventional temperature dependence of the anomalous Hall effect in HgCr₂Se₄.