Topological layer Hall effect in two-dimensional type-I multiferroic heterostructure.

Magnetic skyrmion and layer physics have attracted considerable interest for their significance in fundamental research and practical device applications. Here, through symmetry and model analysis, we propose a mechanism for coupling magnetic skyrmion and layer physics in two-dimensional type-I multiferroic heterostructure, which generates the concept of topological layer Hall effect. Distinct from the existing layer Hall effects that are all driven by momentum-space Berry phase relied on fine-tuned bands, topological layer Hall effect correlates to the layer-polarized real-space Berry physics from noncoplanar spin textures of layer-locked magnetic skyrmion with nontrivial topology. Such layer-polarized real-space Berry physics acts as equivalent electromagnetic field and forces conduction electrons to transversely deflect to specific boundary of one given layer, yielding the anomalous Hall conductivity and thus topological layer Hall effect. Moreover, magnetoelectric coupling can enforce topological layer Hall effect being effectively controllable through ferroelectricity and magnetism. Using first-principles calculations and atomic spin model simulations, we also demonstrate this mechanism in two-dimensional multiferroic heterostructure of CrInSe