2009/04/26 by Naoto Nagaosa, Jairo Sinova, Shigeki Onoda +2 · 32 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Berry connection and curvature #Condensed matter physics #Electron #Ferromagnetism #Geometric phase #Hall effect #Magnetic field #Physics #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum anomalous Hall effect #Quantum mechanics #Semiclassical physics #Theoretical physics #Topological Materials and Phenomena #cond-mat.mes-hall
paper · pdf · doi:10.1103/revmodphys.82.1539
53 pages, 44 figures
arxiv created 2009/04/26 · openalex publication_date 2010/05/13 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The anomalous Hall effect (AHE) occurs in solids with broken time-reversal symmetry, typically in a ferromagnetic phase, as a consequence of spin-orbit coupling. Experimental and theoretical studies of the AHE are reviewed, focusing on recent developments that have provided a more complete framework for understanding this subtle phenomenon and have, in many instances, replaced controversy by clarity. Synergy between experimental and theoretical works, both playing a crucial role, has been at the heart of these advances. On the theoretical front, the adoption of the Berry-phase concepts has established a link between the AHE and the topological nature of the Hall currents. On the experimental front, new experimental studies of the AHE in transition metals, transition-metal oxides, spinels, pyrochlores, and metallic dilute magnetic semiconductors have established systematic trends. These two developments, in concert with first-principles electronic structure calculations, strongly favor the dominance of an intrinsic Berry-phase-related AHE mechanism in metallic ferromagnets with moderate conductivity. The intrinsic AHE can be expressed in terms of the Berry-phase curvatures and it is therefore an intrinsic quantum-mechanical property of a perfect crystal. An extrinsic mechanism, skew scattering from disorder, tends to dominate the AHE in highly conductive ferromagnets. The full modern semiclassical treatment of the AHE is reviewed which incorporates an anomalous contribution to wave-packet group velocity due to momentum-space Berry curvatures and correctly combines the roles of intrinsic and extrinsic (skew-scattering and side-jump) scattering-related mechanisms. In addition, more rigorous quantum-mechanical treatments based on the Kubo and Keldysh formalisms are reviewed, taking into account multiband effects, and demonstrate the equivalence of all three linear response theories in the metallic regime. Building on results from recent experiment and theory, a tentative global view of the AHE is proposed which summarizes the roles played by intrinsic and extrinsic contributions in the disorder strength versus temperature plane. Finally outstanding issues and avenues for future investigation are discussed.