Layer Hall effect in a 2D topological axion antiferromagnet.

Whereas ferromagnets have been known and used for millennia, antiferromagnets were only discovered in the 1930s. 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. Here we study this possibility in an antiferromagnetic axion insulator-even-layered, two-dimensional MnBiTe-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 MnBiTe shows no anomalous Hall effect. However, applying an electric field leads to the emergence of a large, layer-polarized anomalous Hall effect of about 0.5e/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. The layer-locked Berry curvature represents a first step towards spatial engineering of the Berry phase through effects such as layer-specific moiré potential.