First discovered by Edwin Hall in 1881, the anomalous Hall effect describes the transverse flow of electric currents under a longitudinal electric field in a ferromagnetic metal with its magnetization perpendicular to the measurement plane. By flipping the magnetization direction of the ferromagnet the transverse current also changes sign. The behavior looks similar to electrons moving under the Lorentz force of a pair of orthogonal electric and magnetic fields, but the most interesting fact about the anomalous Hall effect is that it is definitely not due to the Lorentz force, since it exists even when the external magnetic field is zero, and the dipole field due to the magnetization is orders of magnitude too weak to explain it.
A century-long expedition in both experiment and theory has finally led us to a comprehensive microscopic understanding of the origin of the anomalous Hall effect. Basically it involves several contributions (intrinsic, skew scattering, and side jump), all having to do with time-reversal symmetry breaking (i.e. the material must be magnetic), and spin-orbit coupling (i.e. motion of an electron is correlated with its spin state). A quantized version of the anomalous Hall effect was predicted by the 2016 Nobel laureate F.D.M. Haldane and was experimentally verified in 2014. The geometric understanding of the quantum Hall effect (by another Nobel laureate of 2016, David Thouless) as well as the quantum anomalous Hall effect, basically paves the way to the booming topological phenomena in modern condensed matter physics.
However, just when people started to think that the anomalous Hall effect was almost fully understood, new surprises came. In 2014 together with Qian Niu and Allan MacDonald at UT Austin, we theoretically predicted that there can be large anomalous Hall effect in certain antiferromagnets, in which the total magnetization vanishes [1]. The reason why this was surprising is that it had been a conventional wisdom that the anomalous Hall effect is proportional to the net magnetization, and therefore should be zero in antiferromagnets. However, the understanding of the symmetry properties of the anomalous Hall effect gives a rather convincing argument that our prediction must be true, and the conventional wisdom is incorrect. In the original PRL we predicted the noncollinear antiferromagnets Mn3Ir, Mn3Pt, and Mn3Rh, which have cubic structures, to be such “anomalous Hall antiferromagnets”. In 2015 a beautiful experiment was done by the group of Satoru Nakatsuji at the University of Tokyo, where a large anomalous Hall effect at room temperature was measured in a closely related material, Mn3Sn, which has a hexagonal symmetry [2]. Subsequent experimental and theoretical works have demonstrated more interesting properties related to the anomalous Hall effect in the antiferromagnets family, including the magneto-optic Kerr effect, anomalous Nernst effect, Weyl fermions in the band structure, etc.
In a most recent paper published in Nature Electronics [3], a team formed by Prof. Zhi-Qi Liu at Beihang University and his colleagues on the experiment side, and Hua Chen (CSU) and Allan MacDonald (UT Austin) on the theory side, have successfully demonstrated the anomalous Hall effect in Mn3Pt, one of the first cubic anomalous Hall antiferromagnets predicted in our 2014 paper. The experimental team has successfully grown high-quality thin films of Mn3Pt epitaxially on a substrate of the ferroelectric material BaTiO3, and have measured its anomalous Hall effect. What is more intriguing is that Mn3Pt has a strange phase transition at about 360K, between a low-temperature noncollinear antiferromagnetic phase, and a high-temperature collinear antiferromagnetic phase, but only the former can have the anomalous Hall effect because of symmetry. The ferroelectric BaTiO3 substrate further makes it possible to slightly change the transition temperature through piezoelectric strain when an external electric field is applied. Thus by keeping the temperature constant, the Mn3Pt can be switched between the noncollinear and the collinear phases by electric fields, and the anomalous Hall effect is switched on and off accordingly. This is the first time that electric switching of the anomalous Hall effect is realized in an antiferromagnet and may lead to fancy device concepts in future electronics and spintronics.
[1] Hua Chen, Qian Niu, and Allan H. MacDonald, “Anomalous Hall effect arising from noncollinear antiferromagnetism”, Phys. Rev. Lett. 112, 017205 (2014).
[2] Satoru Nakatsuji, Naoki Kiyohara, and Tomoya Higo, “Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature”, Nature 527, 212 (2015).
[3] Z. Q. Liu, Hua Chen, J. M. Wang, J. H. Liu, K. Wang, Z. X. Feng, H. Yan, X. R. Wang, C. B. Jiang, J. M. D. Coey, and A. H. MacDonald, “Electrical switching of the topological anomalous Hall effect in a non-collinear antiferromagnet above room temperature”, Nature Electronics, 1, 172-177 (2018).
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