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Anomalous Hall effect

Naoto Nagaosa, Jairo Sinova, Shigeki Onoda, A. H. MacDonald, and N. P. Ong

Naoto Nagaosa

  • Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan and Cross-Correlated Materials Research Group (CMRG), and Correlated Electron Research Group (CERG), ASI, RIKEN, Wako, 351-0198 Saitama, Japan

Jairo Sinova

  • Department of Physics, Texas A&M University, College Station, Texas 77843-4242, USA and Institute of Physics ASCR, Cukrovarnická 10, 162 53 Praha 6, Czech Republic

Shigeki Onoda

  • Condensed Matter Theory Laboratory, ASI, RIKEN, Wako, 351-0198 Saitama, Japan

A. H. MacDonald

  • Department of Physics, University of Texas at Austin, Austin, Texas 78712-1081, USA

N. P. Ong

  • Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

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Rev. Mod. Phys. 82, 1539 – Published 13 May, 2010

DOI: https://doi.org/10.1103/RevModPhys.82.1539

Abstract

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.

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Rev. Mod. Phys. 82, 1539– Published 13 May, 2010

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