Layer Hall Detection of the Néel Vector in Centrosymmetric Magnetoelectric Antiferromagnets

The efficient detection of the N\'eel vector in antiferromagnets is one of the prerequisites toward antiferromagnetic spintronic devices and remains a challenging problem. Here, we propose that the layer Hall effect can be used to efficiently detect the N\'eel vector in centrosymmetric magnetoelectric antiferromagnets. Thanks to the robust surface magnetization of magnetoelectric antiferromagnets, the combination of sizable exchange field and an applied electric field results in the layer-locked spin-polarized band edges. Moreover, the Berry curvature can be engineered efficiently by an electric field, which consequently gives rise to the layer-locked Berry curvature responsible for the layer Hall effect. Importantly, it is demonstrated that the layer Hall conductivity strongly depends on the N\'eel vector orientation and exhibits rich electromagnetic responses, which can be used to detect the N\'eel vector reversal. Based on density functional theory calculations, we exemplify those phenomena in the prototypical ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$ compound. A complete list of the magnetic point groups sustaining the layer Hall effect is presented, aiding the search for realistic materials. Our work proposes a novel approach to detect the N\'eel vector and holds great promise for antiferromagnetic spintronic applications.