TL;DR
This review discusses the anomalous Hall effect, its historical development, underlying mechanisms, and recent discoveries related to topological phenomena and materials over the past three decades.
Contribution
It synthesizes the evolution of understanding the anomalous Hall effect and highlights recent advances and new physics in the field.
Findings
The anomalous Hall effect results from magnetism, spin-orbit coupling, disorder, and electric fields.
It spans classical, quantum, and relativistic regimes.
Recent studies reveal new varieties and physics of the effect.
Abstract
This article reviews the main contributions to the anomalous Hall effect and its resurgence in the past three decades, which has been accompanied by the rise of topological phenomena and topological materials. I will show that the anomalous Hall effect stems from the interplay of magnetism, spin-orbit coupling, disorder scattering and driving electric fields, it spans the classical, quantum and relativistic worlds, and has generated controversy for nearly one and a half centuries. It has become the smoking gun for detecting magnetic order and, extraordinarily, it continues to reveal new physics, with several novel varieties reported in the past decade.
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