Temperature Dependence of the Anomalous Hall Effect from Electron Interactions

Abstract

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 $\sqrt{T}/\ln (T_0/T)$ in three dimensions and $\ln [\ln (T_0/T)]$ in two dimensions, where the scale of $T_0$ 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 HgCr${}_2$Se${}_4$.

arXiv comment5 pages, 3 figures

References in corpus (24)

• Berry Phase Effects on Electronic Properties
• Anomalous Hall effect
• Proper Scaling of the Anomalous Hall Effect
• Semiclassical theories of the anomalous Hall effect
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Berry phase, hyperorbits, and the Hofstadter spectrum
• Multivariable Scaling for the Anomalous Hall Effect
• Coordinate shift in the semiclassical Boltzmann equation and the anomalous Hall effect
• Anomalous Hall effect with massive Dirac fermions
• Localization corrections to the anomalous Hall effect in a ferromagnet
• Weak localization correction to the anomalous Hall effect in polycrystalline Fe films
• Anomalous Hall Effect in Chemically Disordered L10-Mn1.5Ga
• Unconventional Scaling of the Anomalous Hall Effect Accompanying Electron Localization Correction in the Dirty Regime
• Disorder and temperature dependence of the Anomalous Hall Effect in thin ferromagnetic films: Microscopic model
• Anomalous Hall effect in granular ferromagnetic metals and effects of weak localization
• Sensitivity of anomalous Hall effect to disorder correlations
• Kerr effect from diffractive skew scattering in chiral $p_x\pm i{p}_y$ superconductors
• Anomalous Hall effect in ferromagnetic disordered metals
• Unconventional temperature dependence of the anomalous Hall effect in HgCr2Se4
• Saturation of the Anomalous Hall Effect in Critically Disordered Ultra-thin CNi3 Films
• Localization and the Anomalous Hall Effect in a "Dirty" Metallic Ferromagnet
• Anomalous Hall Effect on the surface of topological Kondo insulators
• Two-particle collisional coordinate shifts and hydrodynamic anomalous Hall effect in systems without Lorentz invariance
• Transport theory of superconductors with singular interaction corrections

Cited by in corpus (5)

• X-ray Magnetic Circular Dichroism in Altermagnetic $\alpha$-MnTe
• Quantum kinetics of anomalous and nonlinear Hall effects in topological semimetals
• Does carrier localization affect the anomalous Hall effect?
• Semiconducting Electronic Structure of the Ferromagnetic Spinel $\mathbf{Hg}{\mathbf{Cr}}_2{\mathbf{Se}}_4$ Revealed by Soft-X-Ray Angle-Resolved Photoemission Spectroscopy
• Spin Hall conductivity of interacting two-dimensional electron systems