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Anomalous Hall Effect

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Topology in Magnetism

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 192))

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Abstract

The anomalous Hall effect (AHE) is one of the most fundamental, practically important and for a long time most enigmatic phenomena exhibited by magnetic materials. Here, we briefly outline the relation of the anomalous Hall effect to the geometric properties of the electronic states as given by the Berry phase. The Berry phase origins of the AHE lead to its topological manifestations in insulators, which we review in detail based on key examples. In addition to the intrinsic AHE and its anisotropy in solids, we draw a deep correlation of this effect with orbital magnetism and magnetoelectric response, and discuss its emergence in non-collinear magnets.

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Acknowledgements

I would like to thank Frank Freimuth, Hongbin Zhang, Jürgen Weischenberg, Jan-Philipp Hanke, Patrick Buhl, Chengwang Niu, Gustav Bihlmayer, Klaus Seemann, Christopher Marrows, Martin Gradhand, Diemo Ködderitzsch, Hubert Ebert, Jairo Sinova, Stefan Blügel, Jakub Železný, Bernd Zimmermann and Ivo Souza for numerous discussions on the anomalous Hall effect.

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Authors and Affiliations

  1. Institute for Advanced Simulation, Forschungszentrum Jülich GmbH, Jülich, Germany

    Yuriy Mokrousov

  2. Institute of Physics, Johannes Gutenberg-University Mainz, Mainz, Germany

    Yuriy Mokrousov

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  1. Yuriy Mokrousov
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Correspondence to Yuriy Mokrousov .

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Editors and Affiliations

  1. University of New Hampshire, Durham, NH, USA

    Jiadong Zang

  2. Unité Mixte de Physique CNRS/Thales, Palaiseau, France

    Vincent Cros

  3. Materials Science Division, Argonne National Laboratory, Lemont, IL, USA

    Axel Hoffmann

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Mokrousov, Y. (2018). Anomalous Hall Effect. In: Zang, J., Cros, V., Hoffmann, A. (eds) Topology in Magnetism. Springer Series in Solid-State Sciences, vol 192. Springer, Cham. https://doi.org/10.1007/978-3-319-97334-0_6

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