Ferroelectric control of layer-polarized anomalous Hall effects in bilayer and trilayer RuCl₂

Layer-polarized anomalous Hall effect (LP-AHE) attracts great interest in the fields of both condensed-matter physics and device applications. However, previous research on implementing the LP-AHE based on the paradigm of topological systems and persistent electric fields has hindered its further development. Here, we go beyond the paradigm and for the first time explore the LP-AHE in polar stacked trilayers, in addition to the bilayer. A general design principle for realizing the layer-locked valleys, spins, Berry curvatures and LP-AHE in bilayer and trilayers is mapped out based on comprehensive analysis of symmetry. Bilayers and trilayers, formed by polar stacking ferrovalley monolayers typically possessing ferromagnetism and hexagonal structure, exhibits valley polarization and out-of-plane electron polarization. Through interlayer sliding, the electric polarization and sign of valley polarization can be simultaneously reversed, yielding the sliding ferroelectricity and ferroelectricity-valley coupling. Owing to the Mˆ_zTˆ symmetry between AB and BA stacked bilayers, the interlayer sliding lead to the opposite sign of Berry curvatures and anomalous Hall velocity, implementing the LP-AHE. The interlayer sliding and Mˆ_z symmetry between ABC and CBA stacked trilayer lead to the layer controllable LP-AHE. We further demonstrate the feasibility of this design principle in the bilayer and trilayer constructed from ferrovalley H–RuCl₂ monolayers through first-principles calculations. Our work not only provides a new route to control the valley-dependent logic state without an external magnetic field, but also greatly enrich the research on LP-AHE.