In the anomalous Hall effect (AHE), the magnetization, electric field, and Hall current are presumed to be mutually vertical to each other. In this paper, we propose an unconventional AHE where the magnetization, electric field, and Hall current stay inside the same plane. Such an AHE is odd under time reversal and exists even when the magnetization is parallel to the electric field or Hall current, different from the planar Hall effect which is even under time reversal. Here, we term it parallel anomalous Hall effect (PAHE). We reveal that the PAHE exists when all the point group rotational and reflection symmetries are broken where the Berry curvature field is not necessarily parallel to the magnetization axis. We further demonstrate the PAHE in a ferrimagnetic Weyl semimetal ${\mathrm{FeCr}}_2{\mathrm{Te}}_4$.

中文翻译：

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来自平行于电场的磁化的非常规异常霍尔效应

在反常霍尔效应 (AHE) 中，假设磁化强度、电场和霍尔电流相互垂直。在本文中，我们提出了一种非常规 AHE，其中磁化强度、电场和霍尔电流保持在同一平面内。这种AHE在时间反转下是奇数，即使在磁化平行于电场或霍尔电流时也存在，不同于平面霍尔效应，即使在时间反转下。在这里，我们将其称为平行异常霍尔效应 (PAHE)。我们揭示了当所有点组旋转和反射对称性被破坏时 PAHE 存在，其中 Berry 曲率场不一定平行于磁化轴。我们进一步证明了亚铁磁性外尔半金属中的 PAHE${\mathrm{铬铁}}_2{特}_4$.