Whereas ferromagnets have been known and used for millennia, antiferromagnets were only discovered in the 1930s¹. At large scale, because of the absence of global magnetization, antiferromagnets may seem to behave like any non-magnetic material. At the microscopic level, however, the opposite alignment of spins forms a rich internal structure. In topological antiferromagnets, this internal structure leads to the possibility that the property known as the Berry phase can acquire distinct spatial textures^2,3. Here we study this possibility in an antiferromagnetic axion insulator—even-layered, two-dimensional MnBi₂Te₄—in which spatial degrees of freedom correspond to different layers. We observe a type of Hall effect—the layer Hall effect—in which electrons from the top and bottom layers spontaneously deflect in opposite directions. Specifically, under zero electric field, even-layered MnBi₂Te₄ shows no anomalous Hall effect. However, applying an electric field leads to the emergence of a large, layer-polarized anomalous Hall effect of about 0.5e²/h (where e is the electron charge and h is Planck’s constant). This layer Hall effect uncovers an unusual layer-locked Berry curvature, which serves to characterize the axion insulator state. Moreover, we find that the layer-locked Berry curvature can be manipulated by the axion field formed from the dot product of the electric and magnetic field vectors. Our results offer new pathways to detect and manipulate the internal spatial structure of fully compensated topological antiferromagnets^4,5,6,7,8,9. The layer-locked Berry curvature represents a first step towards spatial engineering of the Berry phase through effects such as layer-specific moiré potential.

尽管铁磁体已为人所知并使用了数千年，但反铁磁体仅在 1930 年代¹才被发现。在大尺度上，由于没有全局磁化，反铁磁体的行为可能看起来像任何非磁性材料。然而，在微观层面上，自旋的相反排列形成了丰富的内部结构。在拓扑反铁磁体中，这种内部结构导致被称为贝里相的特性可能获得不同的空间纹理^2,3。在这里，我们研究了反铁磁轴子绝缘体中的这种可能性——偶数层二维 MnBi ₂ Te ₄——其中空间自由度对应于不同的层。我们观察到一种霍尔效应——层霍尔效应——其中来自顶层和底层的电子自发地向相反方向偏转。具体而言，在零电场下，偶层MnBi ₂ Te ₄没有表现出异常霍尔效应。然而，施加电场会导致出现大约 0.5 e ² / h的大的层极化反常霍尔效应（其中e是电子电荷，h是普朗克常数）。这种层霍尔效应揭示了一个不寻常的层锁定贝里曲率，它用于表征轴子绝缘体状态。此外，我们发现层锁贝里曲率可以通过由电场和磁场矢量的点积形成的轴子场来操纵。我们的结果提供了新的途径来检测和操纵完全补偿拓扑反铁磁体的内部空间结构^4,5,6,7,8,9。层锁定贝里曲率代表了通过层特定莫尔电位等效应对贝里相进行空间工程的第一步。